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The concept of rainbow connection number of a graph was introduced by Chartrand et al. in 2008. Inspired by this concept, other concepts on colored version of connectivity in graphs were introduced, such as the monochromatic connection number by Caro and Yuster in 2011, the proper connection number by Borozan et al. in 2012, and the conflict-free connection number by Czap et al. in 2018, as well as some other variants of connection numbers later on. Chakraborty et al. proved that to compute the rainbow connection number of a graph is NP-hard. For a long time, it has been tried to fix the computational complexity for the monochromatic connection number, the proper connection number and the conflict-free connection number of a graph. However, it has not been solved yet. Only the complexity results for the strong version, i.e., the strong proper connection number and the strong conflict-free connection number, of these connection numbers were determined to be NP-hard. In this paper, we prove that to compute each of the monochromatic connection number, the proper connection number and the conflict free connection number for a graph is NP-hard. This solves a long standing problem in this field, asked in many talks of workshops and papers. [ABSTRACT FROM AUTHOR]

Let G = (V , E) be a graph. A double Roman dominating function (DRDF) of G is a function f : V → { 0 , 1 , 2 , 3 } such that (i) each vertex v with f (v) = 0 is adjacent to either a vertex u with f (u) = 3 or two vertices u 1 and u 2 with f (u 1) = f (u 2) = 2 , and (ii) each vertex v with f (v) = 1 is adjacent to a vertex u with f (u) > 1. The double Roman domination number of G is the minimum weight of a DRDF along all DRDFs on G , where the weight of a DRDF f on G is f (V) = ∑ v ∈ V f (v). In this paper, we first propose an algorithm to compute the double Roman domination number of an interval graph G = (V , E) in O (| V | + | E |) time, answering a problem posed in Banerjee et al. (2020) [2]. Next, we show that the decision problem associated with the double Roman domination is NP-complete for split graphs. Finally, we show that the computational complexities of the Roman domination problem and the double Roman domination problem are different. [ABSTRACT FROM AUTHOR]

The Minimum Maximum Outdegree Problem (MMO) is to assign a direction to every edge in an input undirected, edge-weighted graph so that the maximum weighted outdegree taken over all vertices becomes as small as possible. In this paper, we introduce a new variant of MMO called the p-Split Minimum Maximum Outdegree Problem (p -Split-MMO) in which one is allowed to perform a sequence of p split operations on the vertices before orienting the edges, for some specified non-negative integer p , and study its computational complexity. [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]

The concept of rainbow connection was introduced by Chartrand et al. [] in 2008. It is interesting and recently quite a lot papers have been published about it. In this survey we attempt to bring together most of the results and papers that dealt with it. We begin with an introduction, and then try to organize the work into five categories, including (strong) rainbow connection number, rainbow k-connectivity, k-rainbow index, rainbow vertex-connection number, algorithms and computational complexity. This survey also contains some conjectures, open problems and questions. [ABSTRACT FROM AUTHOR]

In order to run a dataflow with as low cost as possible, it is often faced with deciding which data-sets in a data-set sequence should be stored, with the rest regenerated. The Intermediate Data-set Storage problem arises from this situation. The current best algorithm for this problem takes O ( n 4 ) time. In this paper, we present two improved algorithms for this problem, the first of which can achieve a time complexity O ( n 2 ) , the second of which O ( r n ) , where n is the number of data-sets in a dataflow, r is a numerical number which indicates how large it is for the maximum storage cost to be divided by the minimum computation cost in the dataflow. [ABSTRACT FROM AUTHOR]

In this paper, we show an algorithmic procedure to compute abelian subalgebras and ideals of a given finite-dimensional Leibniz algebra, starting from the non-zero brackets in its law. In order to implement this method, the symbolic computation package MAPLE 12 is used. Moreover, we also show a brief computational study considering both the computing time and the memory used in the two main routines of the implementation. Finally, we determine the maximal dimension of abelian subalgebras and ideals for 3-dimensional Leibniz algebras and 4-dimensional solvable ones over. [ABSTRACT FROM PUBLISHER]

In this paper we prove that the Minimum Latency Aggregation Scheduling (MLAS) problem in the Signal-to-Interference-Noise-Ratio (SINR) model is APX-hard in the uniform power model. [ABSTRACT FROM AUTHOR]

Abstract: For a fixed positive integer , a -tuple total dominating set of a graph is a set such that every vertex of is adjacent to at least vertices in . The -tuple total domination problem is to determine a minimum -tuple total dominating set of . This paper studies -tuple total domination from an algorithmic point of view. In particular, we present a linear-time algorithm for the -tuple total domination problem for graphs in which each block is a clique, a cycle or a complete bipartite graph, which include trees, block graphs, cacti and block-cactus graphs. We also establish NP-hardness of the -tuple total domination problem in undirected path graphs. [Copyright &y& Elsevier]

Abstract: Privacy-preserving data publishing (PPDP) deals with data publishing while preserving individual's privacy in the data. Recent researches show that knowledge of mechanism of anonymization provides a loophole for attacks [1,2], we call this kind of attack a mechanism-based attack. In this paper, we first give a comprehensive study of mechanism-based attack and point out that the range of mechanism-based disclosure is much broader than ever said. Then, we analyze the rationale of mechanism-based attack and give the definition of mechanism-based attack formally. To counteract mechanism-based attack, we introduce a model called e-secrecy and corresponding solution algorithm MAIA. We conduct a comprehensive set of experiments to show mechanism-based attacks are practical concern in the real-world data sets and that our method introduces better data utility and very minor computation than the existing algorithms. [Copyright &y& Elsevier]

The error linear complexity spectrum of a periodic sequence is defined to be the ordered list of $$k$$ k -error linear complexities of the sequence. In this paper, we present an algorithm which computes the error linear complexity spectrum for binary sequences with period $$p^{n}$$ p n , where $$p$$ p is an odd prime and $$2$$ 2 is a primitive root modulo $$p^{2}$$ p 2 . [ABSTRACT FROM AUTHOR]

The m-machine no-wait flowshop scheduling problem, with the objective of minimizing total completion time subject to the constraint that makespan has to be less than or equal to a certain value, is addressed in this paper. First, an algorithm is proposed to find an upper bound on the makespan in case the upper bound is not given or unknown. Given the upper bound on makespan, a proposed algorithm ( PAL) with five versions L (1, 5, 10, 15, and 20) and a genetic algorithm ( GA) are utilized for solving the problem. Furthermore, a dominance relation is established for the case of four machines. The five versions of PAL and GA are evaluated on randomly generated problems with different number of jobs and number of machines. Computational experiments show that the errors of PA10, PA15, and PA20 are much smaller than that of GA while the CPU times of PA10, PA15, and PA20 are significantly smaller than that of GA. Therefore, the algorithms PA10, PA15, and PA20 are superior to the GA algorithm. [ABSTRACT FROM AUTHOR]

This paper describes a generic branch-and-cut algorithm applicable to the solution of multiobjective optimization problems for which a lower bound can be defined as a polynomially solvable multiobjective problem. The algorithm closely follows standard branch and cut except for the definition of the lower and upper bounds and some optional speed-up mechanisms. It is applied to a routing problem called the multilabel traveling salesman problem, a variant of the traveling salesman problem in which labels are attributed to the edges. The goal is to find a Hamiltonian cycle that minimizes the tour length and the number of labels in the tour. Implementations of the generic multiobjective branch-and-cut algorithm and speed-up mechanisms are described. Computational experiments are conducted, and the method is compared to the classical ∈-constraint method. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we study planar polynomial differential systems of this form: where and , , and. A lot of properties of planar polynomial differential systems are related to irreducible Darboux polynomials of the corresponding derivation: . Darboux polynomials are usually computed with the method of undetermined coefficients. With this method we have to solve a polynomial system. We show that this approach can give rise to the computation of an exponential number of reducible Darboux polynomials. Here we show that the Lagutinskii–Pereira algorithm computes irreducible Darboux polynomials with degree smaller than , with a polynomial number, relatively to , and , binary operations. We also give a polynomial-time method to compute, if it exists, a rational first integral with bounded degree. [Copyright &y& Elsevier]

Although data prefetching algorithms have been extensively studied for years, there is no counterpart research done for metadata access performance. Existing data prefetching algorithms, either lack of emphasis on group prefetching, or bearing a high level of computational complexity, do not work well with metadata prefetching cases. Therefore, an efficient, accurate, and distributed metadata-oriented prefetching scheme is critical to leverage the overall performance in large distributed storage systems. In this paper, we present a novel weighted-graph-based prefetching technique, built on both direct and indirect successor relationship, to reap performance benefit from prefetching specifically for clustered metadata servers, an arrangement envisioned necessary for petabyte-scale distributed storage systems. Extensive trace-driven simulations show that by adopting our new metadata prefetching algorithm, the miss rate for metadata accesses on the client site can be effectively reduced, while the average response time of metadata operations can be dramatically cut by up to 67 percent, compared with legacy LRU caching algorithm and existing state-of-the-art prefetching algorithms. [ABSTRACT FROM AUTHOR]

In this paper we describe a singly exponential algorithm for computing the first Betti number of a given semi-algebraic set. Singly exponential algorithms for computing the zeroth Betti number, and the Euler–Poincaré characteristic, were known before. No singly exponential algorithm was known for computing any of the individual Betti numbers other than the zeroth one. As a consequence we also obtain algorithms for computing semi-algebraic descriptions of the semi-algebraically connected components of any given real algebraic or semi-algebraic set in singly exponential time, which improves on the complexity of the previously published algorithms for this problem. [ABSTRACT FROM AUTHOR]

To construct a phylogenetic tree or phylogenetic network for describing the evolutionary history of a set of species is a well-studied problem in computational biology. One previously proposed method to infer a phylogenetic tree/network for a large set of species is by merging a collection of known smaller phylogenetic trees on overlapping sets of species so that no (or as little as possible) branching information is lost. However, little work has been done so far on inferring a phylogenetic tree/network from a specified set of trees when in addition, certain evolutionary relationships among the species are known to be highly unlikely. In this paper, we consider the problem of constructing a phylogenetic tree/network which is consistent with all of the rooted triplets in a given set $\mathcal{C}$ and none of the rooted triplets in another given set $\mathcal{F}$. Although NP-hard in the general case, we provide some efficient exact and approximation algorithms for a number of biologically meaningful variants of the problem. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we investigate various properties and problems associated with the maximum weight triangulation of a point set in the plane. We prove that the weight of a maximum weight triangulation of any planar point set with diameter D is bounded above by , where ɛ is any constant and n is the number of points in the set. If we use the so-called spoke-scan algorithm to find a triangulation of the point set, we obtain an approximation ratio of 4.238. Furthermore, if the point set forms a semi-circled convex polygon, then its maximum weight triangulation can be found in time. [Copyright &y& Elsevier]

In this paper, a fast low power scheduling algorithm is presented for high-level synthesis with multiple voltages. The resources are assumed to operate at different voltages and their power consumption and delay for each voltage level is known in advance. The proposed methodology achieves maximal power reduction of functional units by identifying the maximal available parallelism of power hungry operators in an initial schedule. The proposed methodology is developed in the framework of a modified stochastic evolution mechanism in order to tame the computational complexity. The proposed scheduling technique is extremely fast and it runs in quadratic complexity in the number of the nodes in the data flow graph of the design. This is the fastest reported time of scheduling algorithms for resource-and-latency constrained scheduling with resources operating at multiple voltages. The algorithm produces results within accuracy of 3%–5% of the linear programming method. [ABSTRACT FROM AUTHOR]

In this paper, at first we describe a digraph representing all the weak-order extensions of a partially ordered set and algorithms for generating them. Then we present a digraph representing all of the minimal weak-order extensions of a partially ordered set. This digraph also implies generation algorithms. Finally, we prove that the number of weak-order extensions of a partially ordered set is a comparability invariant, whereas the number of minimal weak-order extensions of a partially ordered set is not a comparability invariant. [Copyright &y& Elsevier]

A signed graph H =( V , E , σ) consists of a graph G =( V , E ) together with a sign function σ : E → {-, +}. A fundamental concept in both, the theory and applications of signed graphs is that of balance . We present a new dynamic programming algorithm to detect balance in signed graphs which traverses each line of the signed graph at most once. Furthermore the computer implementation of the proposed algorithm requires three linear arrays of length | V | only, and the graph need not be stored in computer's memory. Thus the proposed algorithm is optimal with respect to both time and space complexities: The line index for balance of an unbalanced signed graph is the minimum number of lines needed to be removed to make the signed graph balanced. Barahona has proved that finding the line index for balance of a signed graph is an NP- complete problem. In this paper, we prove a stronger result, namely that the problem remains NP- complete even when restricted to signed graphs having negative signs only. [ABSTRACT FROM AUTHOR]