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An edge-bicolored graph G = ( V , R ∪ B ) is called Red/Blue-split graph if there exists a partition I B and I R of V such that I B and I R are independent sets in ( V , B ) and ( V , R ) , respectively. Red/Blue-split graphs generalize several well studied graph classes including split graphs, bipartite graphs and König–Egerváry graphs. In this paper we consider the algorithmic complexity of various optimization problems like minimum edge (or vertex) deletion and maximum edge (or vertex) induced subgraph related to Red/Blue split graphs. All these problems are NP -hard and thus we look at them from algorithmic paradigms that are meant for coping with NP -hardness. We obtain various hardness as well as algorithmic results for these problems in the realm of approximation algorithms and parameterized complexity. The main tool we use to obtain all our results is polynomial time transformations between appropriate problems. On the way, we also resolve some problems related to inapproximability about certain optimization problems mentioned by Korach et al. (2006) [17] . [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]

The Lyndon factorization of a string w is a unique factorization ℓ 1 p 1 , … , ℓ m p m of w such that ℓ 1 , … , ℓ m is a sequence of Lyndon words that is monotonically decreasing in lexicographic order. In this paper, we consider the reverse-engineering problem on Lyndon factorization : Given a sequence S = ( ( s 1 , p 1 ) , … , ( s m , p m ) ) of ordered pairs of positive integers, find a string w whose Lyndon factorization corresponds to the input sequence S , i.e., the Lyndon factorization of w is in a form of ℓ 1 p 1 , … , ℓ m p m with | ℓ i | = s i for all 1 ≤ i ≤ m . Firstly, we show that there exists a simple O ( n ) -time algorithm if the size of the alphabet is unbounded, where n is the length of the output string. Secondly, we present an O ( n ) -time algorithm to compute a string over an alphabet of the smallest size. Thirdly, we show how to compute only the size of the smallest alphabet in O ( m ) time. Fourthly, we give an O ( m ) -time algorithm to compute an O ( m ) -size representation of a string over an alphabet of the smallest size. Finally, we propose an efficient algorithm to enumerate all strings whose Lyndon factorizations correspond to S . [ABSTRACT FROM AUTHOR]

Two space efficient algorithms to solve the L C S k problem and L C S ≥ k problem are presented in this paper. The algorithms improve the time and space complexities of the algorithms of Benson et al. [4] . The space cost of the first algorithm to solve the L C S k problem is reduced from O ( n 2 ) to O ( k n ) , if the size of the two input sequences are both n . The time and space costs of the second algorithm to solve the L C S ≥ k problem are both improved. The time cost is reduced from O ( k n 2 ) to O ( n 2 ) , and the space cost is reduced from O ( n 2 ) to O ( k n ) . In the case of k = O ( 1 ) , the two algorithms are both linear space algorithms. [ABSTRACT FROM AUTHOR]

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]

The algorithms of Pan (1995) [20] and Pan (2002) [22] approximate the roots of a complex univariate polynomial in nearly optimal arithmetic and Boolean time but require a precision of computing that exceeds the degree of the polynomial. This causes numerical stability problems when the degree is large. We observe, however, that such a difficulty disappears at the initial stage of the algorithms, and in our present paper we extend this stage to root-finding within a nearly optimal arithmetic and Boolean complexity bounds provided that some mild initial isolation of the roots of the input polynomial has been ensured. Furthermore our algorithm is nearly optimal for the approximation of the roots isolated in a fixed disc, square or another region on the complex plane rather than all complex roots of a polynomial. Moreover the algorithm can be applied to a polynomial given by a black box for its evaluation (even if its coefficients are not known); it promises to be of practical value for polynomial root-finding and factorization, the latter task being of interest on its own right. We conclude with summarizing our algorithms and their extension to the approximation of isolated multiple roots and root clusters. [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]

In this paper we study a cooperative card game called Hanabi from the viewpoint of algorithmic combinatorial game theory. In Hanabi, each card has one among c colors and a number between 1 and n . The aim is to make, for each color, a pile of cards of that color with all increasing numbers from 1 to n . At each time during the game, each player holds h cards in hand. Cards are drawn sequentially from a deck and the players should decide whether to play, discard or store them for future use. One of the features of the game is that the players can see their partners' cards but not their own and information must be shared through hints. We introduce a single-player, perfect-information model and show that the game is intractable even for this simplified version where we forego both the hidden information and the multiplayer aspect of the game, even when the player can only hold two cards in her hand. On the positive side, we show that the decision version of the problem—to decide whether or not numbers from 1 through n can be played for every color—can be solved in (almost) linear time for some restricted cases. [ABSTRACT FROM AUTHOR]

In this paper, we present a linear algorithm to find a perfect matching in a polyomino graph or show that there are none. [ABSTRACT FROM AUTHOR]

In this paper, we consider the online buffer management problem, which formulates the problem of managing network switches supporting Quality of Service guarantee. We improve competitive ratios of the 2-value multi-queue switch model, where the value of a packet is restricted to 1 or α ( ≥ 1 ) . We use a similar approach as Azar and Richter (STOC 2003 and Algorithmica 43(1-2), 2005) did for the multi-value multi-queue switch model. Namely, we show that the competitive ratio of “the relaxed model” of the 2-value multi-queue switch model is at most x = min ⁡ { c + 2 − c α ( 2 − c ) + c − 1 , c α } , if the competitive ratio of an online algorithm for the unit-value multi-queue switch model is at most c . Azar and Richter's technique implies that if the competitive ratio of the 2-value single-queue switch model is x ′ , then the competitive ratio of the 2-value multi-queue switch model is at most x x ′ . We obtain several results using known c and x ′ . [ABSTRACT FROM AUTHOR]

The Small Exponent Test (SET) for exponentiation is an essential batch-verification technique that is widely applied. In this paper, we propose a simplified SET that can securely batch-verify n instances with only n − 1 randomizing exponents. We show that the structure of the proposed batch test is compact in the sense that it works with a minimal number of randomizing exponents for the SET. Thus, our test offers various advantages. Overall, compared to the original SET, the proposed simplified SET is more efficient for any sized batch instance. In particular, unlike the SET, our proposal performs well even when the size of a batch instance is small, e.g., n = 1 , 2 , 3 , and 4. This feature can be also used to significantly reduce pairing computations in a signature scheme where several pairing equations are verified. In addition, our test can be combined easily and generically with existing batch techniques such as the use of sparse exponents, the bucket test for large batch sizes, or an automated tool to generate a batch algorithm. Finally, with our simplified test, an efficient identification algorithm can be constructed to discover incorrect instances in a batch. [ABSTRACT FROM AUTHOR]

This article explores the computational power of bi-dimensional cellular automata acting on periodical configurations. It extends in some sense the results of a similar paper dedicated to the one-dimensional case. More precisely, we present an algorithm that computes a “minimal pattern network”, i.e. a minimal pattern and the two translation vectors it can use to tile the entire configuration. This problem is equivalent to the computation of a leader, which is one equivalence class of the cells of the periodical configuration. [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]

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, an algorithm is proposed that detects the existence of common ancestor gene sequences for non-overlapping inversion (reversed complement) metric given two input DNA sequences. Theoretical worst case running time complexity of the algorithm is proven to be O ( n 4 ) , where n is the length of each input sequence. However, by experiment, the running time complexity is found to be O ( n 3 ) for the worst case and O ( n 2 ) for average case. Moreover, the worst case occurs when both input sequences have the similarity of around 90% which is very rare. This work is motivated by the purpose of diagnosing an unknown genetic disease that shows allelic heterogeneity , a case where a normal gene mutates in different orders resulting in two different gene sequences causing two different genetic diseases. Our algorithm can potentially save huge energy and cost of the existing diagnostic approaches. The algorithm can be useful as well in the study of breed-related hereditary conditions to determine the genetic spread of a defective gene in the population. [ABSTRACT FROM AUTHOR]

The Range Minimum Query problem consists in answering efficiently the simple question: “what is the minimal element between two specified indices of a given array?”. In this paper we present a novel structure that offers a trade-off between time and space. Moreover we show how the structure can be easily maintained whenever an insertion, modification or deletion modifies the input sequence. [ABSTRACT FROM AUTHOR]

Given two strings X ( | X | = m ) and Y ( | Y | = n ) over an alphabet Σ, the edit distance between X and Y can be computed in O ( m n / t ) time with the help of the Four-Russians' lookup table whose block size is t . The Four-Russians' lookup table can be constructed in O ( ( 3 | Σ | ) 2 t t 2 ) time using O ( ( 3 | Σ | ) 2 t t ) space. However, the construction time and space requirement of the lookup table grow very fast as the alphabet size increases and thus it has been used only when | Σ | is very small. For example, when a string is a protein sequence, | Σ | = 20 and thus it is almost impossible to use the Four-Russians' lookup table on typical workstations. In this paper, we present an efficient alphabet-independent Four-Russians' lookup table. It requires O ( 3 2 t ( 2 t ) ! t ) space and can be constructed in O ( 3 2 t ( 2 t ) ! t 2 ) time. Thus, the Four-Russians' lookup table can be constructed and used irrespective of the alphabet size. The time and space complexity were achieved by compacting the lookup table using a clever encoding of the preprocessed strings. Experimental results show that the space requirement of the lookup table is reduced to about 1/5,172,030 of its original size when | Σ | = 26 and t = 4 . Furthermore, we present efficient multithreaded parallel algorithms for edit distance computation using the Four-Russians' lookup table. The parallel algorithm for lookup table construction runs in O ( t ) time and the parallel algorithm for edit distance computation between X and Y runs in O ( m + n ) time. Experiments performed on CUDA-supported GPU show that our algorithm runs about 942 times faster than the sequential version of the original Four-Russians' algorithm for 100 pairs of random strings of length approximately 1,000 when | Σ | = 4 and t = 4 . [ABSTRACT FROM AUTHOR]

In this paper we investigate jumbled (Abelian) versions of three classical strings problems. In all these problems we assume the input string S [ 1 . . n ] is given in its run-length format S ′ [ 1 . . r ] . The Jumbled Indexing problem is the problem of indexing a string S ′ [ 1 . . r ] over | Σ | for histogram queries, i.e. given a pattern P , we want to find all substrings of S that are permutations of P . We provide an algorithm that constructs an index of size O ( r 2 | Σ | ) in time O ( r 2 ( log ⁡ r + | Σ | log ⁡ | Σ | ) ) , which allows answering histogram queries in O ( | Σ | 3 log ⁡ r ) -time. The Jumbled Border problem is the problem of finding for every location j in S , the longest proper prefix of S [ 1 . . j ] that is also a permutation of a proper suffix of S [ 1 . . j ] , if such exists. We provide an algorithm that solves this problem in O ( | Σ | ( r 2 + n ) ) time, and O ( | Σ | n ) space. A Jumbled Square is a string of the form x x ¯ , where x ¯ is a permutation of x . The Jumbled Square problem is the problem of finding for every location j in S , the longest jumbled square that ends in j , if such exists. We provide an algorithm that solves this problem in O ( | Σ | ( r 2 + n ) ) time, and O ( | Σ | n ) space. [ABSTRACT FROM AUTHOR]

The suffix array is frequently augmented with the longest-common-prefix (LCP) array that stores the lengths of the longest common prefixes between lexicographically adjacent suffixes of a text. While the sum of the values in the LCP array can be Ω ( n 2 ) for a text of length n , the sum of so-called irreducible LCP values was shown to be O ( n lg ⁡ n ) a few years ago. In this paper, we improve the bound to O ( n lg ⁡ r ) , where r ≤ n is the number of runs in the Burrows–Wheeler transform of the text. We also show that our bound is tight up to lower order terms (unlike the previous bound). Our results and the techniques used in proving them provide new insights into the combinatorics of text indexing and compression, and have immediate applications to LCP array construction algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a semi-online scheduling problem on two uniform machines with the speed ratio s . It is assumed that all jobs have their processing times between p and tp ( p > 0 , t ≥ 1 ). The objective is to minimize the makespan. We give the competitive ratio of LS algorithm which is a piecewise function on t ≥ 1 and s ≥ 1 . It shows that LS is an optimal algorithm for most regions on s and t . We further present two optimal algorithms. The algorithm H 1 with competitive ratio of s is optimal for 1.325 ≤ s ≤ 1 + 5 2 and s < t ≤ s 2 − 1 1 + s − s 2 . The algorithm H 2 with competitive ratio of s is optimal for 1.206 ≤ s ≤ 1.5 and s ≤ t ≤ min ⁡ { 2 s − 1 , 2 ( s 2 − 1 ) 1 + s − s 2 } , and it is also optimal for 1 ≤ s ≤ 1 + 17 4 and max ⁡ { 2 s − 1 , − s + 9 s 2 + 8 s 2 s } ≤ t ≤ 2 s with competitive ratio of 1 + t 2 . [ABSTRACT FROM AUTHOR]

In this paper, we consider rainbow connection number of maximal outerplanar graphs (MOPs) on algorithmic aspect. For the (MOP) G , we give sufficient conditions to guarantee that r c ( G ) = d i a m ( G ) . Moreover, we produce the graph with given diameter D and give their rainbow coloring in linear time. X. Deng et al. [4] give a polynomial time algorithm to compute the rainbow connection number of MOPs by the Maximal fan partition method, but only obtain a compact upper bound. J. Lauri [11] proved that, for chordal outerplanar graphs given an edge-coloring, to verify whether it is rainbow connected is NP-complete under the coloring, it is so for MOPs. Therefore we construct Central-cut-spine of MOP G , by which we design an algorithm to give a rainbow edge coloring with at most 2 r a d ( G ) + 2 + c , 0 ≤ c ≤ r a d ( G ) − 2 colors in polynomial time. [ABSTRACT FROM AUTHOR]

Suppose that we are given two dominating sets D s and D t of a graph G whose cardinalities are at most a given threshold k . Then, we are asked whether there exists a sequence of dominating sets of G between D s and D t such that each dominating set in the sequence is of cardinality at most k and can be obtained from the previous one by either adding or deleting exactly one vertex. This decision problem is known to be PSPACE-complete in general. In this paper, we study the complexity of this problem from the viewpoint of graph classes. We first prove that the problem remains PSPACE-complete even for planar graphs, bounded bandwidth graphs, split graphs, and bipartite graphs. We then give a general scheme to construct linear-time algorithms and show that the problem can be solved in linear time for cographs, forests, and interval graphs. Furthermore, for these tractable cases, we can obtain a desired sequence if it exists such that the number of additions and deletions is bounded by O ( n ) , where n is the number of vertices in the input graph. [ABSTRACT FROM AUTHOR]

We consider the problem of proper learning of a boolean halfspace with integer weights { 0 , 1 , … , t } , from membership queries only. The best known algorithm for this problem is an adaptive algorithm that asks n O ( t 5 ) membership queries, while the best lower bound for the number of membership queries is n Ω ( t ) [1] . In this paper we close this gap and give an adaptive proper learning algorithm with two rounds, and asking n O ( t ) membership queries. We also give a non-adaptive proper learning algorithm that asks n O ( t 3 ) membership queries. [ABSTRACT FROM AUTHOR]

In this paper we investigate the parameterized complexity of the Maximum-Duo Preservation String Mapping Problem, the complementary of the Minimum Common String Partition Problem. We show that this problem is fixed-parameter tractable when parameterized by the number k of conserved duos, by first giving a parameterized algorithm based on the color-coding technique and then presenting a reduction to a kernel of size O ( k 6 ) . [ABSTRACT FROM AUTHOR]

This paper provides efficient algorithms that decide membership for classes of several Boolean hierarchies for which efficiency (or even decidability) were previously not known. We develop new forbidden-chain characterizations for the single levels of these hierarchies and obtain the following results: • The classes of the Boolean hierarchy over level Σ 1 of the dot-depth hierarchy are decidable in NL (previously only the decidability was known). The same remains true if predicates mod d for fixed d are allowed. • If modular predicates for arbitrary d are allowed, then the classes of the Boolean hierarchy over level Σ 1 are decidable. • For the restricted case of a two-letter alphabet, the classes of the Boolean hierarchy over level Σ 2 of the Straubing–Thérien hierarchy are decidable in NL. This is the first decidability result for this hierarchy. • The membership problems for all mentioned Boolean-hierarchy classes are logspace many-one hard for NL. • The membership problems for quasi-aperiodic languages and for d -quasi-aperiodic languages are logspace many-one complete for PSPACE. [ABSTRACT FROM AUTHOR]

This paper presents a new Electromagnetism-like Mechanism (EM) algorithm with Split, Probe and Compare feature (SPC-EM). The proposed algorithm replaces the local search segment of a standard EM with a new search scheme named Split, Probe, and Compare (SPC). A nonlinear equation is designed to systematically and dynamically adjust the length of the probes based on the outcome of the Compare segment in each iteration. Extensive computational simulations and comparisons on 10 different benchmark problems from the literature were carried out. Results show that the new modified mechanism outperformed all other algorithms involved in the benchmarking. We thus conclude that the proposed SPC-EM works well with the designed probe-length tuning equation in solving numerical optimization problems. [ABSTRACT FROM AUTHOR]

Scaled matching and permutation matching are two well known paradigms in the domain of pattern matching. Scaled matching refers to finding an occurrence of a pattern which is enlarged proportionally by some scale k within a larger text. Permutation matching is the problem of finding all substrings within a text where the character statistics of the substring and the pattern are the same. Permutation matching is easy, while scaled matching requires innovative solutions. One interesting setting of applications is the merge of the two. The problem of scaled permuted matching (i.e. first permuting and then scaling) has been addressed and solved optimally. However, it was left as an open problem whether there are efficient algorithms for permuted scaled matching. In this paper we solve the problem efficiently in a deterministic setting and optimally in a randomized setting. [ABSTRACT FROM AUTHOR]

In this paper we describe a fast algorithm that creates a wavelet tree for a sequence of symbols. We show that a wavelet tree can be constructed in O ( n ⌈ log ⁡ σ / log ⁡ n ⌉ ) time where n is the number of symbols and σ is the alphabet size. [ABSTRACT FROM AUTHOR]

In the Property Indexing Problem the goal is to preprocess a text T of size n over a constant sized alphabet Σ and a set of intervals π over the text positions, such that given a query pattern P of size m we can report all of the occurrences of P in T which are completely contained within some interval from π . This type of matching is extremely helpful for scenarios in molecular biology where it has long been a practice to consider special areas in the genome by their structure. It is also helpful for solving pattern matching problems over weighted sequences. So far the focus has been on the static version of this problem where the intervals are given a priori and never changed. This paper focuses on several dynamic settings of π including an incremental version where new intervals are inserted into π , a decremental version where intervals are deleted from π , a fully dynamic version where intervals may be inserted into or deleted from π , and a batched insertions version where sets of intervals are inserted into π . In particular, the batched version provides a new (optimal) algorithm for the static case. [ABSTRACT FROM AUTHOR]

Several papers in the available literature tackled problems concerning convex polyominoes in discrete tomography. An interesting subclass consists of L-convex polyominoes, since the related reconstruction problem can have only a unique solution. On the other hand, recent studies have modeled an approach to reconstruct objects even in the case that some of the projections are unavailable, due to a particularly dense part of the scanned object, that we refer to as a blocking component. In this work we merge the two problems in order to obtain efficient reconstruction algorithms for convex and L-convex polyominoes, in case a blocking component is included. [ABSTRACT FROM AUTHOR]

Various papers have analyzed the noisy optimization of convex functions. This analysis has been made according to several criteria used to evaluate the performance of algorithms: uniform rate, simple regret and cumulative regret. We propose an iterative optimization framework, a particular instance of which, using Hessian approximations, provably (i) reaches the same rate as Kiefer–Wolfowitz algorithm when the noise has constant variance, (ii) reaches the same rate as Evolution Strategies when the noise variance decreases quadratically as a function of the simple regret, (iii) reaches the same rate as Bernstein-races optimization algorithms when the noise variance decreases linearly as a function of the simple regret. [ABSTRACT FROM AUTHOR]

In the Possible winner problem in computational social choice theory, we are given a set of partial preferences and the question is whether a distinguished candidate could be made winner by extending the partial preferences to linear preferences. Previous work has provided, for many common voting rules, fixed parameter tractable algorithms for the Possible winner problem, with number of candidates as the parameter. However, the corresponding kernelization question is still open and in fact, has been mentioned as a key research challenge [10] . In this paper, we settle this open question for many common voting rules. We show that the Possible winner problem for maximin, Copeland, Bucklin, ranked pairs, and a class of scoring rules that includes the Borda voting rule does not admit a polynomial kernel with the number of candidates as the parameter. We show however that the Coalitional manipulation problem which is an important special case of the Possible winner problem does admit a polynomial kernel for maximin, Copeland, ranked pairs, and a class of scoring rules that includes the Borda voting rule, when the number of manipulators is polynomial in the number of candidates. A significant conclusion of our work is that the Possible winner problem is harder than the Coalitional manipulation problem since the Coalitional manipulation problem admits a polynomial kernel whereas the Possible winner problem does not admit a polynomial kernel. [ABSTRACT FROM AUTHOR]

Hoare logic for the set of while-programs with the first-order logical language L and the first-order theory T ⊂ L is denoted by HL ( T ) . Bergstra and Tucker have pointed out that the complete number theory Th ( N ) is the only extension T of Peano arithmetic PA for which HL ( T ) is logically complete. The completeness result is not satisfying, since it allows inputs to range over nonstandard models. The aim of this paper is to investigate under what circumstances HL ( T ) is logically complete when inputs range over the standard model N . PA + is defined by adding to PA all the unprovable Π 1 -sentences that describe the nonterminating computations. It is shown that each computable function in N is uniformly Σ 1 -definable in all models of PA + , and that PA + is arithmetical. Finally, it is established, based on the reduction from HL ( T ) to T , that PA + is the minimal extension T of PA for which HL ( T ) is logically complete when inputs range over N . This completeness result has an advantage over Bergstra's and Tucker's one, in that PA + is arithmetical while Th ( N ) is not. [ABSTRACT FROM AUTHOR]

An inconsistent database is a database instance violating integrity constraints. A repair of an inconsistent database is a maximal consistent subset. Sampling from the repair space is an alternative approach meeting the needs of many applications. In this paper, we introduce a new class of repair, query feedback restricted repair, based on the feedback on user's witness query. We first map out a picture of both data and combined complexities of repair existence problems under different cases to identify the intractable cases. Especially, we show that if the query is a projection or a union query, then the decision problem is NP- complete ; even worse, if the query is a conjunctive query, the decision problem becomes Σ 2 P - complete . However, we prove that the combined complexity of the repair existence problem is in LOGSPACE when the witness query is a selection-join query, and this conclusion also implies that the combined complexity of side-effect free deletion propagation problem under group-deletion is in LOGSPACE which is not considered in previous works. Additionally, we provide a polynomial random repair sampling algorithm under combined complexity. At last, we revisit the key preserving condition [1] and show that it will simplify the problem, i.e., some cases become tractable for certain key preserving views, as opposed to their counterparts that are not key preserving. [ABSTRACT FROM AUTHOR]

Being the unbalanced version of the famous Min s – t Cut problem, the Min k -Size s – t Cut problem asks to find a k -size s – t cut with the minimum capacity, where a k -size s – t cut means an s – t cut with its s -side having size at most k . This problem is fundamental and has extensive applications, especially in community identification in social and information networks. It is known that the Min k -Size s – t Cut problem is NP-hard and can be approximated within O ( log ⁡ n ) , where n is the number of vertices in the input graph. In this paper, we give a new approximation algorithm for the Min k -Size s – t Cut problem based on the parametric flow technique. The algorithm is very simple and has only three lines to state. Its approximation ratio is k + 1 k + 1 − k ⁎ , where k ⁎ is the size of the s -side of an optimal solution. [ABSTRACT FROM AUTHOR]

For two positive integers m , k and a connected graph G = ( V , E ) with a nonnegative vertex weight function w , the balanced m -connected k -partition problem, denoted as BC m P k , is to find a partition of V into k disjoint nonempty vertex subsets ( V 1 , V 2 , … , V k ) such that each G [ V i ] (the subgraph of G induced by V i ) is m -connected, and min 1 ≤ i ≤ k ⁡ { w ( V i ) } is maximized. The optimal value of BC m P k on graph G is denoted as β m ⁎ ( G , k ) , that is, β m ⁎ ( G , k ) = max ⁡ min 1 ≤ i ≤ k ⁡ { w ( V i ) } , where the maximum is taken over all m -connected k -partition of G . In this paper, we study the BC 2 P k problem on interval graphs, and obtain the following results. (1) For k = 2 , a 4/3-approximation algorithm is given for BC 2 P 2 on 4-connected interval graphs. (2) In the case that there exists a vertex v with weight at least W / k , where W is the total weight of the graph, we prove that the BC 2 P k problem on a 2 k -connected interval graph G can be reduced to the BC 2 P k − 1 problem on the ( 2 k − 1 ) -connected interval graph G − v . In the case that every vertex has weight at most W / k , we prove a lower bound β 2 ⁎ ( G , k ) ≥ W / ( 2 k − 1 ) for 2 k -connected interval graph G . (3) Assuming that weight w is integral, a pseudo-polynomial time algorithm is obtained. Combining this pseudo-polynomial time algorithm with the above lower bound, a fully polynomial time approximation scheme (FPTAS) is obtained for the BC 2 P k problem on 2 k -connected interval graphs. [ABSTRACT FROM AUTHOR]

The main result of this paper is a simulation algorithm which, under quite general constraints, transforms algorithms running in the Congested Clique model into algorithms running in the MapReduce model. As a case study of applying this simulation algorithm, we first present a distributed O ( Δ ) -coloring algorithm running on the Congested Clique in O ( 1 ) rounds, if Δ ≥ log 2 ⁡ n , and O ( log ⁡ log ⁡ log ⁡ n ) rounds otherwise. Applying the simulation theorem to this Congested Clique O ( Δ ) -coloring algorithm yields an O ( 1 ) -round O ( Δ ) -coloring algorithm in the MapReduce model. We apply our simulation algorithm to other Congested Clique algorithms including the 2-ruling set and metric facility location algorithms of Berns et al. (ICALP 2012). Our simulation algorithm illustrates a natural correspondence between per-node bandwidth in the Congested Clique model and memory per machine in the MapReduce model. In the Congested Clique (and more generally, any network in the CONGEST model), the major impediment to constructing fast algorithms is the O ( log ⁡ n ) restriction on message sizes. Similarly, in the MapReduce model, the combined restrictions on memory per machine and total system memory have a dominant effect on algorithm design. In showing a fairly general simulation algorithm, we highlight the similarities and differences between these models. [ABSTRACT FROM AUTHOR]

This paper studies two problems of locating two paths in a tree with positive and negative weights. The first problem has objective to minimize the sum of minimum weighted distances from every vertex of the tree to the two paths, while the second is to minimize the sum of the weighted minimum distances from every vertex of the tree to the two paths. We develop an O ( n 2 ) algorithm based on the optimal properties for the first problem, and also an O ( n 3 ) algorithm for the second problem. [ABSTRACT FROM AUTHOR]

We consider the problem of tracking quantiles and range countings in wireless sensor networks. The quantiles and range countings are two important aggregations to characterize a data distribution. Let S ( t ) = ( d 1 , … , d n ) denote the multi-set of sensory data that have arrived until time t , which is a sequence of data orderly collected by nodes s 1 , s 2 , … , s k . One of our goals is to continuously track ϵ -approximate ϕ -quantiles ( 0 ≤ ϕ ≤ 1 ) of S ( t ) for all ϕ 's with efficient total communication cost and balanced individual communication cost. The other goal is to track ( ϵ , δ ) -approximate range countings satisfying the requirement of arbitrary precision specified by different users. In this paper, a deterministic tracking algorithm based on a dynamic binary tree is proposed to track ϵ -approximate ϕ -quantiles, whose total communication cost is O ( k / ϵ ⋅ log ⁡ n ⋅ log 2 ⁡ ( 1 / ϵ ) ) , where k is the number of the nodes in a network, n is the total number of the data, and ϵ is the user-specified approximation error. For range countings, a Bernoulli sampling based algorithm is proposed to track ( ϵ , δ ) -approximate range countings, whose total communication cost is O ( 2 ϵ 2 ln ⁡ 2 1 − 1 − δ + n c ) , where δ is the user-specified error probability, n c is the number of clusters. [ABSTRACT FROM AUTHOR]

We study the Multicut on Trees and the Generalized Multiway Cut on Trees problems. For the Multicut on Trees problem, we present a parameterized algorithm that runs in time O ⁎ ( ρ k ) , where ρ = 2 + 1 < 1.554 is the positive root of the polynomial x 4 − 2 x 2 − 1 . This improves the current-best algorithm of Chen et al. that runs in time O ⁎ ( 1.619 k ) . For the Generalized Multiway Cut on Trees problem, we show that this problem is solvable in polynomial time if the number of terminal sets is fixed; this answers an open question posed in a recent paper by Liu and Zhang. By reducing the Generalized Multiway Cut on Trees problem to the Multicut on Trees problem, our results give a parameterized algorithm that solves the Generalized Multiway Cut on Trees problem in time O ⁎ ( ρ k ) . [ABSTRACT FROM AUTHOR]

In this paper we study the problem of partitioning a convex polygon P of n vertices into m polygons of equal area and perimeter. We give an algorithm for m = 2 that runs in O ( n ) time, and an algorithm for m = 2 k , where k is an integer, that runs in O ( ( 2 n ) k ) time. These are the first algorithms to solve this problem. [ABSTRACT FROM AUTHOR]

A plane graph is a planar graph with a fixed planar embedding. In this paper we define a special spanning tree of a plane graph which we call a good spanning tree. Not every plane graph has a good spanning tree. We show that every connected planar graph has a planar embedding with a good spanning tree. Using a good spanning tree, we show that every connected planar graph G of n vertices has a straight-line monotone grid drawing on an O ( n ) × O ( n 2 ) grid, and such a drawing can be found in O ( n ) time. Our results solve two open problems on monotone drawings of planar graphs posed by Angelini et al. Using good spanning trees, we also give simple linear-time algorithms for finding a 2-visibility representation of a connected planar graph G of n vertices on a ( 2 n − 1 ) × ( 2 n − 1 ) grid and for finding a spike- VPG representation of G on a ( 2 n − 1 ) × n grid. [ABSTRACT FROM AUTHOR]

Suppose that we are given two independent sets I b and I r of a graph such that | I b | = | I r | , and imagine that a token is placed on each vertex in I b . Then, the sliding token problem is to determine whether there exists a sequence of independent sets which transforms I b into I r so that each independent set in the sequence results from the previous one by sliding exactly one token along an edge in the graph. This problem is known to be PSPACE-complete even for planar graphs, and also for bounded treewidth graphs. In this paper, we thus study the problem restricted to trees, and give the following three results: (1) the decision problem is solvable in linear time; (2) for a yes-instance, we can find in quadratic time an actual sequence of independent sets between I b and I r whose length (i.e., the number of token-slides) is quadratic; and (3) there exists an infinite family of instances on paths for which any sequence requires quadratic length. [ABSTRACT FROM AUTHOR]

The Closest String problem asks to find a string s which is not too far from each string in a set of m input strings, where the distance is taken as the Hamming distance. This well-studied problem has various applications in computational biology and drug design. In this paper, we introduce a new variant of Closest String where the input strings can contain wildcards that can match any letter in the alphabet, and the goal is to find a solution string without wildcards. We call this problem the Closest String with Wildcards problem, and we analyze it in the framework of parameterized complexity. Our study determines for each natural parameterization whether this parameterization yields a fixed-parameter algorithm, or whether such an algorithm is highly unlikely to exist. [ABSTRACT FROM AUTHOR]

A 1.5D terrain is a region on a plane determined by an x -monotone polygonal chain. A set G of points on the terrain is called a guarding set if every point on the terrain is seen by some point in G . In the 1.5D terrain guarding problem we are given a 1.5D terrain and the goal is to find the minimum guarding set for the given input terrain. It is proved that this problem is NP-hard and the only previous theoretical results for this problem involve approximation. In this paper, we turn to fixed-parameter tractability. We present “depth of terrain onion peeling” as a new geometric parameter. Based on this parameter, we give an upper bound for the treewidth of the terrain visibility graph. By presenting a dynamic programming algorithm, we show that the 1.5D terrain guarding problem is fixed-parameter tractable with respect to this parameter. [ABSTRACT FROM AUTHOR]

We consider the problem of finding k centers for n weighted points on a real line. This (weighted) k -center problem was solved in O ( n log ⁡ n ) time previously by using Cole's parametric search and other complicated approaches. In this paper, we present an easier O ( n log ⁡ n ) time algorithm that avoids the parametric search, and in certain special cases our algorithm solves the problem in O ( n ) time. In addition, our techniques involve developing interesting data structures for processing queries that find a lowest point in the common intersection of a certain subset of half-planes. This subproblem is interesting in its own right and our solution for it may find other applications as well. [ABSTRACT FROM AUTHOR]

This paper considers the minimax regret 1-sink location problem in dynamic path networks. In our model, a dynamic path network consists of an undirected path with positive edge lengths and uniform edge capacity, and each vertex supply which is nonnegative value is unknown but only the interval of supply is known. A particular assignment of supply to each vertex is called a scenario. Under any scenario, the cost of a sink location is defined as the minimum time to complete the evacuation for all supplies (evacuees), and the regret of a sink location x is defined as the cost of x minus the cost of the optimal sink location. Then, the problem is to find a point as a sink such that the maximum regret for all possible scenarios is minimized. We propose an O ( n log ⁡ n ) time algorithm for the minimax regret 1-sink location problem in dynamic path networks with uniform capacity, where n is the number of vertices in the network. [ABSTRACT FROM AUTHOR]

In this paper, we show the relationship between the two most widely used approaches for the minimization of deterministic finite automata: minimization by split of partitions and minimization by double reversal. Even though the double reversal approach has usually been considered to be unconventional with respect to the more common split approach, we show that any double reversal minimization algorithm can be related to a split minimization algorithm and vice versa. [ABSTRACT FROM AUTHOR]

Given a graph G = ( V , E ) with a positive weight function w on the vertices of G , a global powerful alliance of G is a subset S of V such that for every vertex v at least half of the total weight in the closed neighborhood of v is contributed by the vertices of S . A global offensive alliance is a subset S of V such that the above condition holds for every vertex v not in S . Finding the smallest such set in general graphs is NP-complete for both of these problems, even when the weights are all the same. In this paper, we give linear time algorithms that find the smallest global offensive and global powerful alliance of any weighted tree T = ( V , E ) . [ABSTRACT FROM AUTHOR]

The notion of Shared Risk Link Groups (SRLG) has been introduced to capture survivability issues where some links of a network fail simultaneously. In this context, the k-diverse routing problem is to find a set of k pairwise SRLG-disjoint paths between a given pair of end nodes of the network. This problem has been proven NP-complete in general and some polynomial instances have been characterized. In this paper, we investigate the k -diverse routing problem in networks where the SRLGs are localized and satisfy the star property . This property states that a link may be subject to several SRLGs, but all links subject to a given SRLG are incident to a common node. We first provide counterexamples to the polynomial time algorithm proposed by X. Luo and B. Wang (DRCN'05) for computing a pair of SRLG-disjoint paths in networks with SRLGs satisfying the star property, and then prove that this problem is in fact NP-complete. We then characterize instances that can be solved in polynomial time or are fixed parameter tractable, in particular when the number of SRLGs is constant, the maximum degree of the vertices is at most 4, and when the network is a directed acyclic graph. Finally we consider the problem of finding the maximum number of SRLG-disjoint paths in networks with SRLGs satisfying the star property. We prove that this problem is NP-hard to approximate within O ( | V | 1 − ε ) for any 0 < ε < 1 , where V is the set of nodes in the network. Then, we provide exact and approximation algorithms for relevant subcases. [ABSTRACT FROM AUTHOR]