In this paper, we explore problems and algorithms related to the optimisation of locks, as used in inland shipping. We define several optimisation problems associated with inland shipping. We prove that the problem of...
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In this paper, we explore problems and algorithms related to the optimisation of locks, as used in inland shipping. We define several optimisation problems associated with inland shipping. We prove that the problem of scheduling a lock is NP-hard if one allows multiple ships to go through in the same lock operation. The single-ship lock optimization problem can, however, be solved in polynomialtime and a novel deterministic scheduling algorithm for solving this problem is presented in this paper.
The feasible minimum cover problem is that of finding a minimum vertex cover S for a bipartite graph G = (X, Y, E) such that S contains no more than cr vertices from X and no more than B vertices from Y, where cr and ...
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The feasible minimum cover problem is that of finding a minimum vertex cover S for a bipartite graph G = (X, Y, E) such that S contains no more than cr vertices from X and no more than B vertices from Y, where cr and B are constants such that 0 less than or equal to ct less than or equal to \X\ and 0 less than or equal to B less than or equal to \Y\. This problem is closely related to the problem of reconfiguring defective VLSI arrays, such as the random access memories and is known to be NP-complete. In this paper, we present a nontrivial polynomialtime solvable instance of the feasible minimum cover problem that is based on the unique decomposition of a given bipartite graph into three vertex disjoint subgraphs. (C) 1998 Elsevier Science B.V. All rights reserved.
Let G = (V, E) be a finite undirected graph. An edge set E' subset of E is a dominating induced matching (d.i.m.) in G if every edge in E is intersected by exactly one edge of E'. The Dominating Induced Matchi...
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Let G = (V, E) be a finite undirected graph. An edge set E' subset of E is a dominating induced matching (d.i.m.) in G if every edge in E is intersected by exactly one edge of E'. The Dominating Induced Matching (DIM) problem asks for the existence of a d.i.m. in G;this problem is also known as the Efficient Edge Domination problem;it is the Efficient Domination problem for line graphs. The DIM problem is NP-complete even for very restricted graph classes such as planar bipartite graphs with maximum degree 3 but is solvable in linear time for P-7-free graphs, and in polynomialtime for S-1,S-2,S-4-free graphs as well as for S-2,S-2,S-2-free graphs and for S-2,S-2,S-3-free graphs. In this paper, combining two distinct approaches, we solve it in polynomialtime for S-1,S-1,S-5-free graphs. (C) 2020 Elsevier B.V. All rights reserved.
Let be a finite undirected graph. An edge set is a dominating induced matching (d.i.m.) in G if every edge in E is intersected by exactly one edge of . The Dominating Induced Matching (DIM) problem asks for the existe...
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Let be a finite undirected graph. An edge set is a dominating induced matching (d.i.m.) in G if every edge in E is intersected by exactly one edge of . The Dominating Induced Matching (DIM) problem asks for the existence of a d.i.m. in G;this problem is also known as the Efficient Edge Domination problem. The DIM problem is related to parallel resource allocation problems, encoding theory and network routing. It is -complete even for very restricted graph classes such as planar bipartite graphs with maximum degree three and is solvable in linear time for -free graphs. However, its complexity was open for -free graphs for any;denotes the chordless path with k vertices and edges. We show in this paper that the weighted DIM problem is solvable in polynomialtime for -free graphs.
This paper proposes a modification of the algorithm of de Ghellinck and Vial, which keeps the size of the numbers occurring in the calculation by a fixed bound, independently of the number of iterations. This algorith...
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This paper proposes a modification of the algorithm of de Ghellinck and Vial, which keeps the size of the numbers occurring in the calculation by a fixed bound, independently of the number of iterations. This algorithm is fully polynomial in time.
The Maximum Weight Independent Set (MWIS) problem on finite undirected graphs with vertex weights asks for a set of pairwise nonadjacent vertices of maximum weight sum. MWIS is one of the most investigated and most im...
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The Maximum Weight Independent Set (MWIS) problem on finite undirected graphs with vertex weights asks for a set of pairwise nonadjacent vertices of maximum weight sum. MWIS is one of the most investigated and most important algorithmic graph problems;it is well known to be NP-complete, and it remains NP-complete even under various strong restrictions such as for triangle-free graphs. Its complexity for P-k-free graphs, k >= 7, is an open problem. In [7], it is shown that MWIS can be solved in polynomialtime for (P-7,triangle)-free graphs. This result is extended by Maffray and Pastor [22] showing that MWIS can be solved in polynomialtime for (P-7,bull)-free graphs. In the same paper, they also showed that MWIS can be solved in polynomialtime for (S-1,S-2,S-3,bull)-free graphs. In this paper, using a similar approach as in [7], we show that MWIS can be solved in polynomialtime for (S-1,S-2,S-4,triangle)-free graphs which generalizes the result for (P-7,triangle)-free graphs. (C) 2021 Elsevier B.V. All rights reserved.
In this paper, we consider the optimal (i.e., minimum length) time slot assignment problem for variable bandwidth switching systems. Existing algorithms for this problem are known to be pseudo-polynomial. The practica...
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In this paper, we consider the optimal (i.e., minimum length) time slot assignment problem for variable bandwidth switching systems. Existing algorithms for this problem are known to be pseudo-polynomial. The practical question of finding a fast optimal algorithm, as well as the theoretical question of whether the above problem is NP-complete were left open. We present here a technique to show polynomialtime complexity of some time slot assignment algorithms. Such a technique applies to an algorithm proposed by Chalasani and Varma in 1991 (called CV algorithm), as well as to a network how based optimal algorithm, proposed here for the first time. CV algorithm and the one proposed here are slightly different. Thus, we give an answer to both the above questions, by establishing that the problem is in P, and by showing effective algorithms for it.
For a graph let and denote respectively the cardinality of a maximum stable set and of a maximum matching of . It is well-known that computing is NP-hard and that computing can be done in polynomialtime. In particula...
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For a graph let and denote respectively the cardinality of a maximum stable set and of a maximum matching of . It is well-known that computing is NP-hard and that computing can be done in polynomialtime. In particular checking if is NP-complete and relies on the fact that computing is NP-hard (Mosca, Graphs Combinat 18:367-379, 2002). A well known result of Hammer et al. (SIAM J Alg Disc Math 3(4):511-522, 1982). states that the vertex-set of a graph can be efficiently and uniquely partitioned in two subsets (possibly empty) and , such that has the Konig-Egervary property while can be covered by pairwise disjoint edges and odd cycles: furthermore, one has , where computing can be done in polynomialtime. For that let us call those graphs which can be covered by pairwise disjoint edges and odd cycles (in particular computing remains NP-hard for such graphs). This paper shows that: (i) for every essential graph , checking if can be done in polynomialtime;(ii) essential graphs for which can be recognized in polynomialtime and for such graph a maximum stable set can be computed in polynomialtime;(iii) a new characterization of graphs which have the Konig-Egervary property can be derived in that context.
Permutations that can be sorted greedily by one or more stacks having various constraints have been studied by a number of authors. A pop-stack is a greedy stack that must empty all entries whenever popped. Permutatio...
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Permutations that can be sorted greedily by one or more stacks having various constraints have been studied by a number of authors. A pop-stack is a greedy stack that must empty all entries whenever popped. Permutations in the image of the pop-stack operator are said to be pop-stacked. Asinowki, Banderier, Billey, Hackl, and Linusson recently investigated these permutations and calculated their number up to length 16. We give a polynomial-timealgorithm to count pop-stacked permutations up to a fixed length and we use it to compute the first 1000 terms of the corresponding counting sequence. With the 1000 terms, we apply a pair of computational methods to prove some negative results concerning the nature of the generating function for pop-stacked permutations and to empirically predict the asymptotic behavior of the counting sequence using differential approximation.
Response property is a kind of liveness property. Response property problem is defined as follows: Given two activities alpha and beta whenever alpha is executed, is beta always executed after that? In this paper, we ...
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Response property is a kind of liveness property. Response property problem is defined as follows: Given two activities alpha and beta whenever alpha is executed, is beta always executed after that? In this paper, we tackled the problem in terms of Workflow Petri nets (WF-nets for short). Our results are (i) the response property problem for acyclic WF-nets is decidable, (ii) the problem is intractable for acyclic asymmetric choice (AC) WF-nets, and (iii) the problem for acyclic bridge-less well-structured WF-nets is solvable in polynomialtime. We illustrated the usefulness of the procedure with an application example.
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