A cycle base of a permutation group is defined to be a maximal set of its pairwise non-conjugate regular cyclic subgroups. It is proved in this paper that a cycle base of a permutation group of degree n can be constru...
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A cycle base of a permutation group is defined to be a maximal set of its pairwise non-conjugate regular cyclic subgroups. It is proved in this paper that a cycle base of a permutation group of degree n can be constructed in polynomialtime in n. (C) 2018 Elsevier Inc. All rights reserved.
We obtain a polynomial-time algorithm to compute the supremum of the max-min powers of a map from the Cartesian product of a set to a bounded subset of the real numbers. It is also shown that the value at a pair (x, y...
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We obtain a polynomial-time algorithm to compute the supremum of the max-min powers of a map from the Cartesian product of a set to a bounded subset of the real numbers. It is also shown that the value at a pair (x, y) is equal to the maximum of the first k powers of the map where k is the diameter between x and y in a graph corresponding to the map. A characterization is obtained of the metric introduced by Rosenfeld (1975) for a fuzzy graph.
We consider a communication network where there exist wiretappers who can access a subset of channels, called a wiretap set, which is chosen from a given collection of wiretap sets. The collection of wiretap sets can ...
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We consider a communication network where there exist wiretappers who can access a subset of channels, called a wiretap set, which is chosen from a given collection of wiretap sets. The collection of wiretap sets can be arbitrary. Secure network coding is applied to prevent the source information from being leaked to the wiretappers. In secure network coding, the required alphabet size is an open problem not only of theoretical interest but also of practical importance, because it is closely related to the implementation of such coding schemes in terms of computational complexity and storage requirement. In this paper, we develop a systematic graph-theoretic approach for improving Cai and Yeung's lower bound on the required alphabet size for the existence of secure network codes. The new lower bound thus obtained, which depends only on the network topology and the collection of wiretap sets, can be significantly smaller than Cai and Yeung's lower bound. A polynomial-time algorithm is devised for efficient computation of the new lower bound.
A pure morphic sequence is a right-infinite, symbolic sequence obtained by iterating a letter-to-word substitution. For instance, the Fibonacci sequence and the Thue-Morse sequence, which play an important role in the...
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A pure morphic sequence is a right-infinite, symbolic sequence obtained by iterating a letter-to-word substitution. For instance, the Fibonacci sequence and the Thue-Morse sequence, which play an important role in theoretical computer science, are pure morphic. Define a coding as a letter-to-letter substitution. The image of a pure morphic sequence under a coding is called a morphic sequence. A sequence x is called uniformly recurrent if for each finite subword u of x there exists an integer l such that u occurs in every l-length subword of x. The paper mainly focuses on the problem of deciding whether a given morphic sequence is uniformly recurrent. Although the status of the problem remains open, we show some evidence for its decidability: in particular, we prove that it can be solved in polynomialtime on pure morphic sequences and on automatic sequences. In addition, we prove that the complexity of every uniformly recurrent, morphic sequence has at most linear growth: here, complexity is understood as the function that maps each positive integer n to the number of distinct n-length subwords occurring in the sequence.
This paper provides a fast computational algorithm for carrying out the performance analysis DEA technique, which reduces the computational requirements. The provided tests reduce the computational complexity when usi...
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This paper provides a fast computational algorithm for carrying out the performance analysis DEA technique, which reduces the computational requirements. The provided tests reduce the computational complexity when using the DEA technique to specify the efficiency position, the rank, and the returns-to-scale classification of DMUs under assessment.
We study the scheduling of m-machine reentrant robotic cells, in which parts need to reenter machines several times before they are finished. The problem is to find the sequence of 1-unit robot move cycles and the par...
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We study the scheduling of m-machine reentrant robotic cells, in which parts need to reenter machines several times before they are finished. The problem is to find the sequence of 1-unit robot move cycles and the part processing sequence which jointly minimize the cycle time or the makespan. When m = 2, we show that both the cycle time and the makespan minimization problems are polynomially solvable. When m = 3, we examine a special class of reentrant robotic cells with the cycle time objective. We show that in a three-machine loop-reentrant robotic cell, the part sequencing problem under three out of the four possible robot move cycles for producing one unit is strongly NP-hard. The part sequencing problem under the remaining robot move cycle can be solved easily. Finally, we prove that the general problem, without restriction to any robot move cycle, is also intractable.
We give a linear-timealgorithm for computing the edge search number of cographs, thereby resolving the computational complexity of edge searching on this graph class. To achieve this we give a characterization of the...
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We give a linear-timealgorithm for computing the edge search number of cographs, thereby resolving the computational complexity of edge searching on this graph class. To achieve this we give a characterization of the edge search number of the join of two graphs. With our result, the knowledge on graph searching of cographs is now complete: node, mixed, and edge search numbers of cographs can all be computed efficiently. Furthermore, we are one step closer to computing the edge search number of permutation graphs. (C) 2011 Elsevier B.V. All rights reserved.
An induced matching in a graph G is a set of edges, no two of which meet a common vertex or are joined by an edge of G;that is, an induced matching is a matching which forms an induced subgraph. It is known that findi...
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An induced matching in a graph G is a set of edges, no two of which meet a common vertex or are joined by an edge of G;that is, an induced matching is a matching which forms an induced subgraph. It is known that finding an induced matching of maximum cardinality in a graph is NP-hard. We show that a maximum induced matching in a weakly chordal graph can be found in polynomialtime. This generalizes previously known results for the induced matching problem. This also demonstrates that the maximum induced matching problem in chordal bipartite graphs can be solved in polynomialtime while the problem is known to be NP-hard for bipartite graphs in general. (C) 2003 Elsevier Science B.V. All rights reserved.
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 pr...
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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 polynomialtime 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. (C) 2013 Elsevier B.V. All rights reserved.
A class of graphs is called alpha-polynomial if there exists a polynomial-time algorithm for finding the stability number alpha(G) for all graphs G in the class. We define a set Stabex(F, v) associated with a graph F ...
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A class of graphs is called alpha-polynomial if there exists a polynomial-time algorithm for finding the stability number alpha(G) for all graphs G in the class. We define a set Stabex(F, v) associated with a graph F and a vertex v is an element of V(F). Let F be a minimal forbidden induced subgraph for an alpha-polynomial hereditary class P. It is shown that if we change F with Stabex(F, v) in the list of forbidden induced subgraphs for P, then we obtain an alpha-polynomial extension of P. We obtain a generalization of Sbihi's theorem [Discrete Math. 28(3) (1980) 53] on the stability number problem in claw-free graphs. Also, a recent result of Lozin [Eur. J. Oper. Res. 125 (2000) 292] on stability in (P-5, P)-free graphs is a corollary of our result. (C) 2003 Elsevier B.V. All rights reserved.
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