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A fast dynamics model that captures the deployment dynamics of self-actuated, origami-inspired, folded planar spacecraft structures is desired for design and verification applications. In this paper, a general simulation framework for numerically generating the equations of motion of any structure that complies with a set of pattern assumptions is presented. The framework is built through application of the articulated body forward dynamics algorithm and the tree-augmented approach for closed-chain forward dynamics. These are multi-body dynamics approaches developed in the literature for complex robotic manipulator systems. Unique adaptations are required to address the highly constrained nature of a folding structure. This solution is desirable due to the computational efficiency of the base algorithms and the ability to analyze multiple systems without reformulation of the core dynamics algorithm. Baumgarte stabilization techniques are applied to address constraint violations, but are found to be a continuing challenge for folding structures with several closed-chains. • Graph theory analysis of benchmark origami fold patterns is presented. • Dynamics algorithms are adapted for origami-folded spacecraft structures. • The approach is demonstrated with multiple numerical cases and constraint challenges are discussed. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we empirically profile three algorithms for the Shortest Negative Cost Cycle (SNCC) problem. In this problem, we are given a directed, weighted graph G = 〈 V , E , c 〉 , and the goal is to identify a negative cost cycle with the fewest number of edges. The SNCC problem finds applications in a number of domains ranging from program verification to certifying algorithm design. The first polynomial time algorithm for this problem was proposed in Subramani (2009). Since then, several additional techniques, including a randomized approach, have been proposed for the SNCC problem. Our goal in this paper is to analyze three algorithmic paradigms for this problem from the empirical perspective. Towards this end, we profile these algorithmic approaches over a wide range of inputs. Our results indicated that the randomized algorithm is the algorithm of choice over a number of graph classes. [ABSTRACT FROM AUTHOR]

Abstract The paper is devoted to a Gram classification of an important class of signed graphs with loops playing an important role in many branches of mathematics, physics and computer science including game theory, crystallography, Diophantine geometry, Lie theory, spectral graph theory, a graph coloring technique, algebraic methods in graph theory. They have many deep applications in spectral machine learning methods, electrical networks, to link sign prediction in signed unipartite and bipartite networks, and community partition in social networks. We continue the study of finite connected edge-bipartite graphs Δ (bigraphs, for short), with m ≥ 2 vertices (a class of signed graphs), started in Simson (2013) and developed in Simson (2016) by means of the non-symmetric Gram matrix G ˇ Δ ∈ M m (Z) defining Δ , its symmetric Gram matrix G Δ : = 1 2 [ G ˇ Δ + G ˇ Δ t r ] ∈ M m (1 2 Z) , and the Gram quadratic form q Δ : Z m → Z. In the present paper, given n ≥ 1 , we mainly study connected principal Cox-regular edge-bipartite graphs Δ with loops and n + 1 ≥ 2 vertices, in the sense that the symmetric Gram matrix G Δ ∈ M n + 1 (Z) of Δ is positive semi-definite of rank n ≥ 1. Our aim is to classify such edge-bipartite graphs by means of an inflation algorithm, up to the weak Gram Z -congruence Δ ∼ Z Δ ′ , where Δ ∼ Z Δ ′ means that G Δ ′ = B t r ⋅ G Δ ⋅ B , for some B ∈ M n + 1 (Z) with det B = ± 1. Our main result of the paper asserts that, given a principal Cox-regular connected edge-bipartite graph Δ with n + 1 ≥ 2 vertices, there exists an edge-bipartite Euclidean graph D n + 1 of Tables A and B, and a suitably chosen sequence t • − of the inflation operators, each of one of the forms Δ ′ ↦ t a − Δ ′ or Δ ′ ↦ t a b − Δ ′ , such that the composite operator Δ ↦ t • − Δ reduces Δ to the bigraph D n + 1 such that: (i) Δ ∼ Z D n + 1 and (ii) the bigraphs Δ , and D n + 1 have the same number of loops. The algorithm does not change loops and computes a matrix B ∈ M n + 1 (Z) , with det B = ± 1 , defining the weak Gram Z -congruence Δ ∼ Z D n + 1 , that is, satisfying the equation G D n + 1 = B t r ⋅ G Δ ⋅ B. [ABSTRACT FROM AUTHOR]

In this paper, we study the most basic domination invariants in graphs, in which number 2 is intrinsic part of their definitions. We classify them upon three criteria, two of which give the following previously studied invariants: the weak 2 -domination number, γ w 2 ( G ) , the 2 -domination number, γ 2 ( G ) , the { 2 } -domination number, γ { 2 } ( G ) , the double domination number, γ × 2 ( G ) , the total { 2 } -domination number, γ t { 2 } ( G ) , and the total double domination number, γ t × 2 ( G ) , where G is a graph in which the corresponding invariant is well defined. The third criterion yields rainbow versions of the mentioned six parameters, one of which has already been well studied, and three other give new interesting parameters. Together with a special, extensively studied Roman domination, γ R ( G ) , and two classical parameters, the domination number, γ ( G ) , and the total domination number, γ t ( G ) , we consider 13 domination invariants in graphs. In the main result of the paper we present sharp upper and lower bounds of each of the invariants in terms of every other invariant, a large majority of which are new results proven in this paper. As a consequence of the main theorem we obtain new complexity results regarding the existence of approximation algorithms for the studied invariants, matched with tight or almost tight inapproximability bounds, which hold even in the class of split graphs. [ABSTRACT FROM AUTHOR]

Calculating and analyzing the number of spanning trees of graphs (network models) is an important and interesting research project in wide variety of fields, such as mathematics, physics, theoretical computer science, chemistry and so on. The number of spanning trees of graphs (models) displays amounts of information on its structural features and also on some relevant dynamical properties, in particular network security, random walks and percolation. In this paper, firstly, due to lots of graphs (models) are built on the basis of various simple and small elements (components), we provide primarily some helpful network-operation, such as link-operation and merge-operation, to generate more realistic and complicated graphs (models). Secondly, considering reliability of fault-tolerance to random faults and of intrusion-tolerance to selectively remove attacks, synchronization capability and diffusion properties of networks, we present an iterative method (algorithm) for computing the total number of spanning trees. As a pellucid example, we apply our method to tree space and cycle space, notice that it is proved to be indeed a better tool. In order to reflect more widely practical meanings, we study its applications in graph theory, including ladder-graph with zero clustering coefficient, wheel-graph having nonzero clustering coefficient as constituent ingredients of maximal planar graphs. In the rest of this paper, we make a brief summary that the method described by us can be designed a program (algorithm) for obtaining easily the exact number of spanning trees of some models. [ABSTRACT FROM AUTHOR]

A circulant graph C n ( a 1 , … , a k ) is a graph with n vertices { v 0 , … , v n − 1 } such that each vertex v i is adjacent to vertices v ( i + a j ) m o d n , for j = 1 , … , k . In this paper we investigate the vertex colouring problem on circulant graphs. We approach the problem in a purely combinatorial way based on an array representation and propose an exact O ( k 3 log 2 n + n ) algorithm for a subclass of 3-chromatic C n ( a 1 , … , a k ) ’s with k ≥ 2 , which are characterized in the paper. [ABSTRACT FROM AUTHOR]

Many hard graph problems, such as Hamiltonian Cycle, become FPT when parameterized by treewidth, a parameter that is bounded only on sparse graphs. When parameterized by the more general parameter clique-width, Hamiltonian Cycle becomes W[1]-hard, as shown by Fomin et al. (2010). Sæther and Telle address this problem in their paper (Sæther and Telle, 2016) by introducing a new parameter, split-matching-width, which lies between treewidth and clique-width in terms of generality. They show that even though graphs of restricted split-matching-width might be dense, solving problems such as Hamiltonian Cycle can be done in FPT time. Recently, it was shown that Hamiltonian Cycle parameterized by treewidth is in EPT (Bodlaender et al., 2013; Fomin et al., 2014), meaning it can be solved in n O ( 1 ) 2 O ( k ) -time. In this paper, using tools from Fomin et al. (2014), we show that also parameterized by split-matching-width Hamiltonian Cycle is EPT. To the best of our knowledge, this is the first EPT algorithm for any “globally constrained” graph problem parameterized by a non-trivial and non-sparse structural parameter. To accomplish this, we also give an algorithm constructing a branch decomposition approximating the minimum split-matching-width to within a constant factor. Combined, these results show that the algorithms in Sæther and Telle (2016) for Edge Dominating Set, Chromatic Number and Max Cut all can be improved. In fact, using our new approximation algorithm, under the Exponential Time Hypothesis, the Hamiltonian Cycle algorithm of this paper, and the three algorithms for MaxCut, Edge Dominating Set, and Chromatic Number, are asymptotically optimal. [ABSTRACT FROM AUTHOR]

This paper presents a new algorithmic framework for some basic problems on binary images. Algorithms for binary images such as one of extracting a connected component containing a query pixel and that of connected components labeling play basic roles in image processing. Those algorithms usually use linear work space for efficient implementation. In this paper we propose algorithms for several basic problems on binary images which are efficient in time and space, using space-efficient algorithms for grid graphs. More exactly, some of them run in O ( n log n ) time using O ( 1 ) work space and the others run in O ( n ) or O ( n log n ) time using O ( n ) work space for a binary image of n pixels stored in a read-only array. [ABSTRACT FROM AUTHOR]

Abstract We study the parameterized complexity of domination problems on sparse graphs and beyond. The nowhere dense classes of graphs have been proposed as the main model for sparseness that can be utilized algorithmically. The class of d -degenerate graphs is not nowhere dense, yet domination remains fixed-parameter tractable. Both nowhere dense classes of graphs and d -degenerate graph classes are biclique-free classes, meaning there is an integer t such that no graph in the class contains K t , t as a subgraph. In this paper we show that various domination problems are fixed-parameter tractable on biclique-free classes of graphs. Our algorithms are simple and rely on results from extremal graph theory that bound the number of edges in a t -biclique free graph. In particular, the problems k -Dominating Set , Connected k -Dominating Set , Independent k -Dominating Set and Minimum Weight k -Dominating Set are shown to be FPT, when parameterized by t + k , on graphs not containing K t , t as a subgraph. With the exception of Connected k -Dominating Set all described algorithms are linear in the size of the input graph. [ABSTRACT FROM AUTHOR]

Abstract An edge metric generator of a connected graph G is a vertex subset S for which every two distinct edges of G have distinct distance to some vertex of S , where the distance between a vertex v and an edge e is defined as the minimum of distances between v and the two endpoints of e in G. The smallest cardinality of an edge metric generator of G is the edge metric dimension, denoted by dim e (G). It follows that 1 ≤ dim e (G) ≤ n − 1 for any n -vertex graph G. A graph whose edge metric dimension achieves the upper bound is topful. In this paper, the structure of topful graphs is characterized, and many necessary and sufficient conditions for a graph to be topful are obtained. Using these results we design an O (n 3) time algorithm which determines whether a graph of order n is topful or not. Moreover, we describe and address an interesting class of topful graphs whose super graphs obtained by adding one edge are not topful. [ABSTRACT FROM AUTHOR]

Abstract Several graph theoretic watermark methods have been proposed to encode numbers as graph structures in software watermarking environments. In this paper we propose an efficient and easily implementable codec system for encoding watermark numbers as reducible permutation flow-graphs and, thus, we extend the class of graphs used in such a watermarking environment. More precisely, we present an algorithm for encoding a watermark number w as a self-inverting permutation π ∗ , an algorithm for encoding the self-inverting permutation π ∗ into a reducible permutation graph F [ π ∗ ] whose structure resembles the structure of real program graphs, as well as decoding algorithms which extract the permutation π ∗ from the reducible permutation graph F [ π ∗ ] and the number w from π ∗. Both the encoding and the decoding process take, in the worst-case, time and space linear in the length of the binary representation of w. The two main components of our proposed codec system, i.e., the self-inverting permutation π ∗ and the reducible permutation graph F [ π ∗ ] , incorporate the binary representation of the watermark w in their structure and possess important structural properties, which make our system resilient to attacks; to this end, we experimentally evaluated our system under edge modification attacks on the graph F [ π ∗ ] and the results suggest that we can detect such attacks with high probability. [ABSTRACT FROM AUTHOR]

Abstract Airline network, including airports as network nodes and flight routes as directed network edges, has a lot of special features such as departure and arrival times, air ticket budget, flight capacity, transportation cost, etc. Thus, analyzing network behavior and service performance for such a network is much more difficult than that for many other networks. In this paper, taking China domestic airline network as a representative, we try to discuss the reachability issue for each airport respectively, which could reflect its regional connectivity level and service quality of civil aviation. More specifically, we evaluate reachability through many features including node degree, betweenness, closeness, etc. To get the values of some features, we design a fast Dijkstra-based all-pair shortest path algorithm with both time and budget requirements, then use Fenwick Tree to further improve the time efficiency. Actually, it is a shortest path problem with time windows and other constraints. Furthermore, we propose a faster solution by reducing the edges in the duplicated graph as a simplification and then provide the time complexity proof. Finally, we implement Analytic Hierarchy Process (AHP) to convert the reachability feature into numerical values for all airports to measure their service qualities precisely. Our results for China domestic airline network with 210 airports and 69,160 flight routes will definitely become a guide to airline companies and civil aviation administration for their further development and management. [ABSTRACT FROM AUTHOR]

Abstract Containing many classic optimization problems, the family of vertex deletion problems has an important position in algorithm and complexity study. The celebrated result of Lewis and Yannakakis gives a complete dichotomy of their complexity. It however has nothing to say about the case when the input graph is also special. This paper initiates a systematic study of vertex deletion problems from one subclass of chordal graphs to another. We give polynomial-time algorithms or proofs of NP-completeness for most of the problems. In particular, we show that the vertex deletion problem from chordal graphs to interval graphs is NP-complete. [ABSTRACT FROM AUTHOR]

Abstract Given a graph G and a pair of vertices u , v the interval I G [ u , v ] is the set of all vertices that are in some shortest path between u and v. Given a subset X of vertices of G , the interval I G [ X ] of X , is the union of the intervals for all pairs of vertices in X and we say that X is geodetic if its interval do coincide with the set of vertices in the graph. A minimum geodetic set is a minimum cardinality geodetic set of G. The problem of computing a minimum geodetic set is known to be NP-Hard for general graphs but is known to be polynomially solvable for maximal outerplanar graphs. In this paper we show a polynomial time algorithm for finding a minimum geodetic set in general outerplanar graphs. [ABSTRACT FROM AUTHOR]

A graph is equimatchable if all of its maximal matchings have the same size. A graph is claw-free if it does not have a claw as an induced subgraph. In this paper, we provide the first characterization of claw-free equimatchable graphs by identifying the equimatchable claw-free graph families. This characterization implies an efficient recognition algorithm. [ABSTRACT FROM AUTHOR]

Given a graph G = ( V , E ) of order n and maximum degree Δ , the NP -complete S - labeling problem consists in finding a labeling of G , i.e. a bijective mapping ϕ : V → { 1 , 2 … n } , such that SL ϕ ( G ) = ∑ u v ∈ E min { ϕ ( u ) , ϕ ( v ) } is minimized. In this paper, we study the S - labeling problem, with a particular focus on algorithmic issues. We first give intrinsic properties of optimal labelings, which will prove useful for our algorithmic study. We then provide lower bounds on SL ϕ ( G ) , together with a generic greedy algorithm, which collectively allow us to approximate the problem in several classes of graphs—in particular, we obtain constant approximation ratios for regular graphs and bounded degree graphs. We also show that deciding whether there exists a labeling ϕ of G such that SL ϕ ( G ) ≤ | E | + k is solvable in O ∗ ( 2 2 k ( 2 k ) ! ) time, thus fixed-parameterized tractable in k . We finally show that the S - Labeling problem is polynomial-time solvable for two classes of graphs, namely split graphs and (sets of) caterpillars. [ABSTRACT FROM AUTHOR]

Maximum Edge Biclique and related problems have wide applications in management science, bioinformatics, etc. In this paper, we study parameterized algorithms for Parameterized Edge Biclique problem, Parameterized Edge Biclique Packing problem, Parameterized Biclique Edge Deletion problem, and Parameterized Bipartite Biclique Clustering problem. For the Parameterized Edge Biclique problem, the current best result is of running time O ⁎ ( 2 k ) , and we give a parameterized algorithm of running time O ( n k 2.5 k ⌈ k ⌉ ) , where k is the parameter and n is the number of vertices in the given graph. For the Parameterized Edge Biclique Packing problem, based on randomized divide-and-conquer technique, a parameterized algorithm of running time O ⁎ ( k ⌈ k ⌉ l o g k 4 ( 2 k − 1 ) t ) ) is given, where k is the parameter and t is the number of bicliques in the solution. We study the Parameterized Biclique Edge Deletion problem on bipartite graphs and general graphs, and give parameterized algorithms of running time O ⁎ ( 2 k ) and O ⁎ ( 3 k ) , respectively. For the Parameterized Bipartite Biclique Clustering problem, based on modular decomposition method, a kernel of size O ( k 2 ) and a parameterized algorithm of running time O ( 2.42 k ( n + m ) ) are presented, where k is the parameter, n is the number of vertices, and m is the number of edges in the given graph. [ABSTRACT FROM AUTHOR]

In the field of parameterized counting complexity, the problems that are #W[1]-hard and admit fixed-parameter tractable randomized approximation scheme (FPTRAS) have attracted much attention in recent years. In this paper, we focus on the problems on parameterized counting matching and packing. These problems include counting set packing , counting matching , and counting subgraph packing (including both vertex-disjoint and edge-disjoint versions). We study the parameterized complexity on these problems. On the basis of some results for counting graph matchings, we show that a series of problems are #W[1]-hard. Furthermore, by extending the previous algorithm for counting 3- d matching , we obtain FPTRAS for each considered problem, respectively. Our results indicate that the problems on parameterized counting matching and packing form a large family of problems that are #W[1]-hard and admit FPTRAS. [ABSTRACT FROM AUTHOR]

The Grundy number of a graph is the maximum number of colors used by the greedy coloring algorithm over all vertex orderings. In this paper, we study the computational complexity of Grundy Coloring , the problem of determining whether a given graph has Grundy number at least k . We also study the variants Weak Grundy Coloring (where the coloring is not necessarily proper) and Connected Grundy Coloring (where at each step of the greedy coloring algorithm, the subgraph induced by the colored vertices must be connected). We show that Grundy Coloring can be solved in time O ∗ ( 2 . 44 3 n ) and Weak Grundy Coloring in time O ∗ ( 2 . 71 6 n ) on graphs of order n . While Grundy Coloring and Weak Grundy Coloring are known to be solvable in time O ∗ ( 2 O ( w k ) ) for graphs of treewidth w (where k is the number of colors), we prove that under the Exponential Time Hypothesis (ETH), they cannot be solved in time O ∗ ( 2 o ( w log w ) ) . We also describe an O ∗ ( 2 2 O ( k ) ) algorithm for Weak Grundy Coloring , which is therefore FPT for the parameter k . Moreover, under the ETH, we prove that such a running time is essentially optimal (this lower bound also holds for Grundy Coloring ). Although we do not know whether Grundy Coloring is in FPT , we show that this is the case for graphs belonging to a number of standard graph classes including chordal graphs, claw-free graphs, and graphs excluding a fixed minor. We also describe a quasi-polynomial time algorithm for Grundy Coloring and Weak Grundy Coloring on apex-minor graphs. In stark contrast with the two other problems, we show that Connected Grundy Coloring is NP -complete already for k = 7 colors. [ABSTRACT FROM AUTHOR]

A graph G = ( V , E ) is a word-representable graph if there exists a word W over the alphabet V such that letters x and y alternate in W if and only if ( x , y ) ∈ E for each x ≠ y . In this paper we give an effective characterization of word-representable graphs in terms of orientations. Namely, we show that a graph is word-representable if and only if it admits a semi-transitive orientation defined in the paper. This allows us to prove a number of results about word-representable graphs, in particular showing that the recognition problem is in NP, and that word-representable graphs include all 3-colorable graphs. We also explore bounds on the size of the word representing the graph. The representation number of G is the minimum k such that G is a representable by a word, where each letter occurs k times; such a k exists for any word-representable graph. We show that the representation number of a word-representable graph on n vertices is at most 2 n , while there exist graphs for which it is n / 2 . [ABSTRACT FROM AUTHOR]

This paper introduces the notion of involution module, the first generalization of the modular decomposition of 2-structures which has a unique linear-sized decomposition tree. We derive an O ( n 2 ) decomposition algorithm and we take advantage of the involution modular decomposition tree to obtain several algorithmic results. It is well-known that cographs (or equivalently P 4 -free graphs) are the graphs that are totally decomposable w.r.t modular decomposition. In a similar way, we introduce the class of switch cographs, as the class of graphs that are totally decomposable w.r.t involution modular decomposition. This class generalizes the class of cographs and appears to be exactly the class of (Bull, Gem, Co-Gem, C 5 )-free graphs. We use our new decomposition tool to design three practical algorithms for the maximum cut, vertex cover and vertex separator problems. The complexity of these problems was still unknown for this class of graphs. This paper also improves the complexity of the maximum clique, the maximum independent set, the chromatic number and the maximum clique cover problems by giving efficient algorithms, thanks to the decomposition tree. Eventually, we show that this class of graphs has clique-width at most 4 and that a clique-width expression can be computed in linear time. [ABSTRACT FROM AUTHOR]

Intelligence analysis is a domain characterized by a torrent of streaming data within which a very small portion contains useful knowledge or actionable intelligence. Intelligence analysts have to sift through the compiled data and weave through a complex web of convoluted connections in an attempt to illuminate information requirements (IR) and maintain situational awareness. Automated methodologies have eased the manual burden of this process to some extent. Data are naturally modeled in a graphical form representing the known people, places, events and the relationships between them. Graph matching algorithms in which an information requirement is formulated as a template graph or situation of interest to be found in the observed data graph have been successfully employed in intelligence analysis processes. Absent from these past contributions is the recognition that partial information requirements, such as indicators and warnings, are not mutually exclusive to a specific IR, and an understanding of the characteristics of the underlying data can lead to significant performance benefits. The knowledge of overlapping template sections forms the motivation for precedence tree guided search and AND/OR templates. Through the recognition of the overlapping sections, a single AND/OR template can be created to answer many information requirements. This paper presents a novel algorithm for the intelligent traversal of an AND/OR template, providing increased algorithmic efficiency over the execution of multiple sequential graph matching instances. This paper focuses on development of an algorithm for intelligent AND/OR template traversal with computational results illustrating the effectiveness of the developed methods. The results indicate a significant improvement in runtime (with a speedup over 5 in some cases) while maintaining a good solution quality (within 2% of multiple AND path graph matching executions) in AND/OR and precedence tree guided graph matching. [ABSTRACT FROM AUTHOR]

We study the problem of finding in a graph an inclusionwise maximal independent set of minimum cardinality, known as minimum maximal independent set or independent dominating set problem. This is one of the hardest problems in algorithmic graph theory. In particular, restricted to the class of so called SAT-graphs, this problem coincides with satisfiability , the central problem of theoretical computer science. The class of SAT-graphs, and many other important graph classes, such as graphs of bounded vertex degree or line graphs, can be characterized by finitely many forbidden induced subgraphs. We call such classes finitely defined. The paper [R. Boliac and V. Lozin, Independent domination in finitely defined classes of graphs, Theoretical Computer Science, 301 (2003) 271–284] reveals various conditions under which the independent dominating set problem remains NP-hard in a finitely defined class. In the present paper, we identify a number of finitely defined classes where the problem admits polynomial-time solutions. In particular, we prove that the problem is solvable in polynomial time in the class of P 2 + P 3 -free graphs by correcting a mistake of the first two authors of the paper in their earlier solution. This result is in a sharp contrast with the fact that in the class of P 3 + P 3 -free graphs the problem is known to be NP-hard, since this class contains all SAT-graphs. [ABSTRACT FROM AUTHOR]

In this paper, using the properties of graph convergence of H(.,.)-accretive operators, we construct a perturbed algorithm for solving systems of ill-posed variational inclusions involving H(.,.)-accretive operators. Under some suitable conditions, we prove that the sequence generated by the proposed method is strongly convergent to the unique solution of the problem. The main results presented in this paper generalize and improve some recent results in the literature. [ABSTRACT FROM AUTHOR]

High-utility itemset mining (HUIM) is an extension of frequent-itemset mining (FIM) but considers the unit profit and quantity of items to discover the set of high-utility itemsets (HUIs). Traditionally, the utility of an itemset is the summation of the utilities of the itemset in all the transactions regardless of its length. This approach is, however, inappropriate in real-world applications since the utility of the itemset increases along with the number of items within it. High average-utility itemset mining (HAUIM) was designed to provide more reasonable utility measure by taking the size of the itemset into account. Existing algorithms can only handle, however, the static database and unsuitable for the dynamic environment since the size of data is frequently changed in real-life situations. In this paper, an incremental high-average utility pattern mining (IHAUPM) algorithm is presented to handle the incremental database with transaction insertion. The well-known fast updated (FUP) concept in the FIM is modified to adopt the designed algorithm, thus efficiently updating the discovered HAUIs. Based on the designed model for HAUIM with transaction insertion, the proposed IHAUPM algorithm can easily only handle the inserted transactions. Experiments are carried on six datasets and the results showed that the designed algorithm has better performance than the state-of-the-art algorithms performing in the batch manner. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new convexity on graphs similar to the well known P 3 -convexity, which we will call P 3 ∗ -convexity. We show that several P 3 ∗ -convexity parameters (hull number, convexity number, Carathéodory number, Radon number, interval number and percolation time) are NP-hard even on bipartite graphs. We prove a strong relationship between this convexity and the well known geodesic convexity, which implies several NP-hardness results for the latter. In order to show that, we prove that the hull number for the P 3 -convexity is NP-hard even for subgraphs of grids and that the convexity number for the P 3 -convexity is NP-hard even for bipartite graphs with diameter 3. We also obtain linear time algorithms to determine those parameters for the above mentioned convexities for cographs and P 4 -sparse graphs. [ABSTRACT FROM AUTHOR]

For a finite, simple, undirected graph G with a vertex weight function, the Maximum Weight Independent Set (MWIS) problem asks for an independent vertex set of G with maximum weight. MWIS is a well-known NP-hard problem of fundamental importance. For claw-free graphs, MWIS can be solved in polynomial time—in 1980, the first two such algorithms were independently found by Minty for MWIS and by Sbihi for the unweighted case. For a constant ℓ ≥ 2 , let ℓ G denote the disjoint union of ℓ copies of G . In this paper, using a dynamic programming approach (inspired by Farber’s result about MWIS for 2 K 2 -free graphs), we show that for any fixed ℓ , MWIS can be solved in polynomial time for ℓ claw-free graphs. This solves the open cases for MWIS on ( P 3 + claw)-free graphs and on ( 2 K 2 + claw)-free graphs and extends known results for claw-free graphs, ℓ K 2 -free graphs, ( K 2 + claw)-free graphs, and ℓ P 3 -free graphs. [ABSTRACT FROM AUTHOR]

The signless Laplacian Estrada index of a graph is defined as S L E E ( G ) = ∑ i = 1 n e q i , where q 1 , q 2 , … , q n are the eigenvalues of the signless Laplacian matrix of G . In this paper, we determine the unique bicyclic graph with maximum S L E E and the unique bipartite bicyclic graph with maximum S L E E , respectively. [ABSTRACT FROM AUTHOR]

Given a family F of graphs, let Free ( F ) be the class of graphs that do not contain any member of F as an induced subgraph. When F is a set of four-vertex graphs the complexity of the vertex coloring problem in Free ( F ) is known, with three exceptions: F = { claw , 4 K 1 } , F = { claw , 4 K 1 , co-diamond } , and F = { C 4 , 4 K 1 } . In this paper, we study the coloring problem for Free (claw, 4 K 1 ). We solve the vertex coloring problem for a subclass of Free (claw, 4 K 1 ) which contains the class of 4 K 1 -free line graphs. [ABSTRACT FROM AUTHOR]

Feature selection, both for supervised as well as for unsupervised classification is a relevant problem pursued by researchers for decades. There are multiple benchmark algorithms based on filter, wrapper and hybrid methods. These algorithms adopt different techniques which vary from traditional search-based techniques to more advanced nature inspired algorithm based techniques. In this paper, a hybrid feature selection algorithm using graph-based technique has been proposed. The proposed algorithm has used the concept of Feature Association Map (FAM) as an underlying foundation. It has used graph-theoretic principles of minimal vertex cover and maximal independent set to derive feature subset. This algorithm applies to both supervised and unsupervised classification. The performance of the proposed algorithm has been compared with several benchmark supervised and unsupervised feature selection algorithms and found to be better than them. Also, the proposed algorithm is less computationally expensive and hence has taken less execution time for the publicly available datasets used in the experiments, which include high-dimensional datasets. [ABSTRACT FROM AUTHOR]

The Event-B formalism allows program specifications to be modelled at an abstract level and refined towards a concrete model. However, Event-B lacks explicit control flow structure and ordering is implicitly encoded in event guards. This makes it difficult to identify and apply rules for transformation of Event-B models to sequential code. This paper introduces a scheduling language to support the incremental derivation of algorithmic control structure for events as part of the Event-B refinement process. We provide intermediate control structures for non-deterministic iteration and choice that ease the transition from abstract specifications to sequential implementations. We present rules for transforming algorithmic structures to more concrete refinements. We illustrate our approach by applying our method to the Schorr–Waite graph marking algorithm. [ABSTRACT FROM AUTHOR]

Data collection is an important operation in a wireless sensor network (WSN). During data collection, the interference among nodes cannot be ignored. In a multi-hop WSN, one conventional way of defining interference neighbors is to prohibit a node from using the same time slot as those of its 1-hop and 2-hop neighbors. Recently, it is proved that for data collection in a WSN, since the set of communication nodes is limited and the transmission directions are toward the sink, a less strict set of interference neighbors can be defined [16] . The interference problem in a duty-cycle WSN (DC-WSN) with a corona structure is studied in [7] . In this paper, we solve the same problem by using the relaxed interference set defined in [16] . In particular, we give a complete classification of non-interference sets in 2-hop neighbors. We also propose a distributed 6-coloring algorithm. We prove a lower bound of six colors that every tree-based data collection algorithm requires in a dense DC-WSN, which proves our algorithm to be optimal. [ABSTRACT FROM AUTHOR]

The Hamiltonian path problem for general grid graphs is NP-complete. In this paper, we give the necessary conditions for the existence of a Hamiltonian path between two given vertices in a rectangular grid graph with a rectangular hole; where the size of graph is even. In addition, we show that the Hamiltonian path in these graphs can be computed in linear-time. [ABSTRACT FROM AUTHOR]

This paper deals with open shops subject to the constraint that some conflicting jobs cannot be processed simultaneously on different machines. In the context of our study, these conflicts are given by an undirected graph, called the conflict graph. We seek a schedule that minimizes the maximum completion time (makespan). We first prove the NP-hardness of different versions of this problem. Then, we present polynomial-time solvable cases, for which we devise simple and efficient algorithms. On the other hand, we present heuristics and lower bounds for the general case. The heuristics are based on the construction of matchings in bipartite graphs as well as on a specific insertion technique combined with beam search. Finally, we test the efficiency of the heuristics and report our computational experiments that display satisfying results. [ABSTRACT FROM AUTHOR]

Large graphs are scale free and ubiquitous having irregular relationships. Clustering is used to find existent similar patterns in graphs and thus help in getting useful insights. In real-world, nodes may belong to more than one cluster thus, it is essential to analyze fuzzy cluster membership of nodes. Traditional centralized fuzzy clustering algorithms incur high communication cost and produce poor quality of clusters when used for large graphs. Thus, scalable solutions are obligatory to handle huge amount of data in less computational time with minimum disk access. In this paper, we proposed a parallel fuzzy clustering algorithm named ‘PGFC’ for handling scalable graph data. It will be advantageous from the viewpoint of expert systems to develop a clustering algorithm that can assure scalability along with better quality of clusters for handling large graphs.The algorithm is parallelized using bulk synchronous parallel (BSP) based Pregel model. The cluster centers are initialized using degree centrality measure, resulting in lesser number of iterations. The performance of PGFC is compared with other state of art clustering algorithms using synthetic graphs and real world networks. The experimental results reveal that the proposed PGFC scales up linearly to handle large graphs and produces better quality of clusters when compared to other graph clustering counterparts. [ABSTRACT FROM AUTHOR]

Abstract: In this paper 1 [1] The extended abstract of this paper appeared on PPAM 2009, LNCS 6067 (2010) 11–20. we study the problem of interval incidence coloring of bipartite graphs. We show the upper bound for interval incidence coloring number ( ) for bipartite graphs , and we prove that holds for regular bipartite graphs. We solve this problem for subcubic bipartite graphs, i.e. we fully characterize the subcubic graphs that admit 4, 5 or 6 coloring, and we construct a linear time exact algorithm for subcubic bipartite graphs. We also study the problem for bipartite graphs with and we show that 5-coloring is easy and 6-coloring is hard ( -complete). Moreover, we construct an time optimal algorithm for trees. [Copyright &y& Elsevier]

Abstract: Case-Based reasoning (CBR) applications are increasingly used for problems involving structured data, especially in process-oriented domains. Available CBR frameworks rely primarily on flat case representations, leaving developers of process-oriented CBR systems without general-purpose tools aimed at their needs. This paper discusses needs to support structure-based retrieval for CBR and how they have been addressed in the development of the Structure Access Interface (SAI), a toolkit for representation and retrieval of structured cases which is now available for general use. Integrating SAI into a CBR project eliminates the need for developing a storage scheme for graph data structures and facilitates the development of retrieval algorithms by (1) providing useful code for common retrieval tasks and (2) delineating the tasks which may require domain-specific implementations. SAI maintains flexibility through its customizability yet carries solutions for many common tasks for CBR developers, as well as illuminating some general principles for addressing common representation and retrieval needs for process-oriented CBR tasks and the relationship between CBR needs for structured retrieval and needs and methods in graph oriented database research. The paper closes with an evaluation of SAI's scalability and demonstration of the value of enabling developers to select retrieval methods suited to their tasks. It closes with a discussion of SAI's relationship to the growing body of work on graph databases. [Copyright &y& Elsevier]

Abstract: This paper studies a variation of domination in graphs called rainbow domination. For a positive integer , a -rainbow dominating function of a graph is a function such that for any vertex with . The -rainbow domination number of is the minimum value of , where runs over all -rainbow dominating functions of . A related concept is as follows. A weak -dominating function of is a function such that for any vertex with . The weak -domination number of is the minimum value of , where runs over all weak -dominating functions of . In this paper, we prove that for any strongly chordal graph . Our approach is a more general setting called the -function, which leads to interesting results on other variations of domination. We also give a linear-time algorithm for finding the weak -domination numbers of block graphs. [Copyright &y& Elsevier]

In this paper we present improved results on the problem of counting triangles in edge streamed graphs. For graphs with m edges and at least T triangles, we show that an extra look over the stream yields a two-pass streaming algorithm that uses O ( m ε 2.5 T polylog ( m ) ) space and outputs a ( 1 + ε ) approximation of the number of triangles in the graph. This improves upon the two-pass streaming tester of Braverman, Ostrovsky and Vilenchik, ICALP 2013, which distinguishes between triangle-free graphs and graphs with at least T triangle using O ( m T 1 / 3 ) space. Also, in terms of dependence on T , we show that more passes would not lead to a better space bound. In other words, we prove there is no constant pass streaming algorithm that distinguishes between triangle-free graphs from graphs with at least T triangles using O ( m T 1 / 2 + ρ ) space for any constant ρ ≥ 0 . [ABSTRACT FROM AUTHOR]

Graph editing problems offer an interesting perspective on sub- and supergraph identification problems for a large variety of target properties. They have also attracted significant attention in recent years, particularly in the area of parameterized complexity as the problems have rich parameter ecologies. In this paper we examine generalisations of the notion of editing a graph to obtain a regular subgraph. In particular we extend the notion of regularity to include two variants of edge-regularity along with the unifying constraint of strong regularity. We present a number of results, with the central observation that these problems retain the general complexity profile of their regularity-based inspiration: when the number of edits k and the maximum degree r are taken together as a combined parameter, the problems are tractable (i.e. in FPT ), but are otherwise intractable. We also examine variants of the basic editing to obtain a regular subgraph problem from the perspective of parameterizing by the treewidth of the input graph. In this case the treewidth of the input graph essentially becomes a limiting parameter on the natural k + r parameterization. [ABSTRACT FROM AUTHOR]

Just as ordinary hypergraphs are a generalization of graphs, directed hypergraphs (DH) are a natural generalization of digraphs. A DH consists of a set of vertices V and a set of hyperarcs H , where a hyperarc is a pair < S , v > , S non empty subset of V and v ∈ V . DHs have a variety of applications: they have been used to represent functional dependency in databases, Horn formulae in propositional logic, and–or graphs, context free grammars etc. In the paper, after providing a brief historical introduction on the notion of DH and some relevant applications, various problems regarding DHs are surveyed and analyzed. In particular we consider the complexity of the reachability problem (together with its application in the related satisfiability problem for Horn CNF formulae) and the computation of transitive closure and transitive reduction of directed hypergraphs (together with its application to the computation of minimum coverings for a set of functional dependencies). Finally a short introduction to the problem of computing shortest hyperpaths in directed hypergraphs is provided. [ABSTRACT FROM AUTHOR]

Abstract: Let and be fixed positive integers. Assume that the vertices of a planar graph are partitioned into blocks (or empires) each containing exactly vertices. The -colouring problem (- COL r ) asks for a colouring of the vertices of the graph that uses at most colours, never assigns the same colour to adjacent vertices in different empires and, conversely, assigns the same colour to all vertices in the same empire, disregarding adjacencies. For the problem coincides with the classical vertex colouring problem on planar graphs. The generalization for was defined by Percy Heawood in 1890 in the same paper in which he refuted a previous “proof” of the famous Four Colour Theorem. In a recent paper we have shown that if , - COL r is NP-hard for linear forests if . Furthermore, the hardness extends to (resp. ) when (resp. for ) for arbitrary planar graphs. For trees, our argument entails a nice dichotomy: - COL r is NP-hard for and solvable in polynomial time for any other positive value of . In this paper we argue that linear forests do not make the problem any easier, even for small values of . We prove that the - COL r problem is NP-hard for linear forests even if and , or and . [Copyright &y& Elsevier]

Abstract: In this paper, we study the geodetic convexity of graphs, focusing on the problem of the complexity of computing a minimum hull set of a graph in several graph classes. For any two vertices of a connected graph , the closed interval of and is the set of vertices that belong to some shortest -path. For any , let . A subset is geodesically convex or convex if . In other words, a subset is convex if, for any and for any shortest -path , . Given a subset , the convex hull of is the smallest convex set that contains . We say that is a hull set of if . The size of a minimum hull set of is the hull number of , denoted by . The Hull Number problem is to decide whether , for a given graph and an integer . Dourado et al. showed that this problem is NP-complete in general graphs. In this paper, we answer an open question of Dourado et al. (2009) [1] by showing that the Hull Number problem is NP-hard even when restricted to the class of bipartite graphs. Then, we design polynomial-time algorithms to solve the Hull Number problem in several graph classes. First, we deal with the class of complements of bipartite graphs. Then, we generalize some results in Araujo et al. (2011) [2] to the class of -graphs and to cacti. Finally, we prove tight upper bounds on the hull numbers. In particular, we show that the hull number of an -node graph without simplicial vertices is at most in general, at most if is regular or has no triangle, and at most if has girth at least . [Copyright &y& Elsevier]

Abstract: Building the behaviour for non-player characters in a game is a complex collaborative task among AI designers and programmers. In this paper we present a visual authoring tool for game designers that supports behaviour reuse. We describe a visual editor, capable of storing, indexing, retrieving and reusing behaviours previously designed by AI programmers. One of the most notable features of our editor is its capability for sketch-based retrieval: searching in a repository for behaviours that are similar to the one the user is drawing, and making suggestions about how to complete it. As this process relies on graph behaviour comparison, in this paper, we describe different algorithms for graph comparison, and demonstrate, through empirical evaluation in a particular test domain, that we can provide structure-based similarity for graphs that preserves behaviour similarity and can be computed at reasonable cost. [Copyright &y& Elsevier]

The method of augmenting graphs is a general approach to solve the Maximum Independent Set problem. Our objective is to employ this approach to develop polynomial-time algorithms for some so-called Maximum Set problems, i.e. problems which can be stated as follows. Given a (simple) graph G , find a maximum vertex subset S of G such that the subgraph induced by S satisfies a given property Π . Such problems were shown to be NP-hard in general if the properties considered are non-trivial and hereditary Lewis and Yannakakis (1980) and Yannakakis (1978). In this paper, using the augmenting graph technique, we describe a graph class, in which some problems can be solved in polynomial time. We also prove the NP-hardness of some Maximum Set problems where the considered properties are not hereditary. [ABSTRACT FROM AUTHOR]

This paper deals with optimization problems on rotagraphs and fasciagraphs. These graphs are repetitive structures that generalize grids and toroidal grids, respectively. We develop a theoretical framework and get linear-time and constant-time generic algorithms for wide classes of combinatorial problems which are defined in a purely combinatorial way. These classes of problems include in particular many classical optimization problems that are NP-complete in general. Our results unify in a single framework many results of the literature, in particular on the topic of domination–and its variants–in grids. [ABSTRACT FROM AUTHOR]

Abstract: In recent years, the use of extensible processors has been increased. Extensible processors extend the base instruction set of a general-purpose processor with a set of custom instructions. Custom instructions that can be implemented in special hardware units make it possible to improve performance and decrease power consumption in extensible processors. The key issue involved is to generate and select automatically the custom instructions from a high-level application code. In this paper, we propose a new efficient algorithm for the automatic generation of all candidate instructions (or patterns). Our pattern generation algorithm identify all feasible connected and disjoint patterns under different constraints. Compared to a previously proposed well-known algorithm, our algorithm solves the problem more efficiently by taking advantage of the topological property of data flow graph (DFG) as well as overcoming the drawbacks of the previously proposed algorithm. An extension of the proposed algorithm is also presented in this paper. The extended algorithm further radically reduce the search space by considering the input resolving nodes. Experimental results show that our algorithms can achieve orders of magnitude speedup over the well-know algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, a novel image registration method is proposed to achieve accurate registration between images having large shape differences with the help of a set of appropriate intermediate templates. We first demonstrate that directionality is a key factor in both pairwise image registration and groupwise registration, which is defined in this paper to describe the influence of the registration direction and paths on the registration performance. In our solution, the intermediate template selection and intermediate template guided registration are two coherent steps with directionality being considered. To take advantage of the directionality, a directed graph is built based on the asymmetric distance defined on all ordered image pairs in the image population, which is fundamentally different from the undirected graph with symmetric distance metrics in all previous methods, and the shortest distance between template and subject on the directed graph is calculated. The allocated directed path can be thus utilized to better guide the registration by successively registering the subject through the intermediate templates one by one on the path towards the template. The proposed directed graph based solution can also be used in groupwise registration. Specifically, by building a minimum spanning arborescence (MSA) on the directed graph, the population center, i.e., a selected template, as well as the directed registration paths from all the rest of images to the population center, is determined simultaneously. The performance of directed graph based registration algorithm is demonstrated by the spatial normalization on both synthetic dataset and real brain MR images. It is shown that our method can achieve more accurate registration results than both the undirected graph based solution and the direct pairwise registration. [Copyright &y& Elsevier]

Abstract: In this paper we consider the problem of connected edge searching of weighted trees. Barrière et al. claim in [L. Barrière, P. Flocchini, P. Fraigniaud, N. Santoro, Capture of an intruder by mobile agents, in: SPAA’02: Proceedings of the Fourteenth Annual ACM Symposium on Parallel Algorithms and Architectures, ACM, New York, NY, USA, 2002, pp. 200–209] that there exists a polynomial-time algorithm for finding an optimal search strategy, that is, a strategy that minimizes the number of used searchers. However, due to some flaws in their algorithm, the problem turns out to be open. It is proven in this paper that the considered problem is strongly NP-complete even for node-weighted trees (the weight of each edge is 1) with one vertex of degree greater than 2. It is also shown that there exists a polynomial-time algorithm for finding an optimal connected search strategy for a given bounded degree tree with arbitrary weights on the edges and on the vertices. This is an FPT algorithm with respect to the maximum degree of a tree. [Copyright &y& Elsevier]

Abstract: A project is an enterprise consisting of several activities which are to be carried out in some specific order. The activities and the order in which they need to be carried out can be represented by a PERT network. The PERT technique is a traditional, well-known approach to the expert of project management. When networks are used, it often becomes necessary to draw dummy activities. Since the computation of project completion time is proportional to the number of arcs, including dummy arcs, it is desirable to draw a network with as few dummy activities as possible. In this paper, we propose a new method for constructing, for a given project scheduling problem, a PERT network having as small as possible the number of dummy arcs by using some results on line graphs. This algorithm deals with the existence of transitive arcs. The paper contains illustrative examples, proofs of some theoretical results as well as a comparative study with a similar algorithm known in the literature. Computational results showed the superiority of our algorithm. [Copyright &y& Elsevier]