This paper addresses the 2-cyclic identical part scheduling in a no-wait robotic flowshop where exactly two parts enter and two parts leave the production line during each cycle. This problem was previously proved to ...
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This paper addresses the 2-cyclic identical part scheduling in a no-wait robotic flowshop where exactly two parts enter and two parts leave the production line during each cycle. This problem was previously proved to be polynomially solvable in O(N-8 log N) time, where N is the number of tanks in the production line. This paper proposes an improved algorithm with reduced complexity O(N-5 log N).
This paper considers the no-wait scheduling of n jobs, where each job is a chain of unit processing time operations to be processed alternately on two machines. The objective is to minimize the mean flow time. We prop...
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This paper considers the no-wait scheduling of n jobs, where each job is a chain of unit processing time operations to be processed alternately on two machines. The objective is to minimize the mean flow time. We propose an O(n(6))-time algorithm to produce an optimal schedule. It is also shown that if zero processing time operations are allowed, then the problem is NP-hard in the strong sense. (C) 1998 Elsevier Science B.V.
We consider the problem of maximizing total tardiness on a single machine, where the first job starts at time zero and idle times between the processing of jobs are not allowed. We present a modification of an exact p...
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We consider the problem of maximizing total tardiness on a single machine, where the first job starts at time zero and idle times between the processing of jobs are not allowed. We present a modification of an exact pseudo-polynomial algorithm based on a graphical approach, which has a polynomial running time. This result settles the complexity status of the problem under consideration which was open.
The paper considers the three-machine open shop scheduling problem to minimize the makespan. It is assumed that each job consists of at most two operations, one of which is to be processed on the bottleneck machine, t...
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The paper considers the three-machine open shop scheduling problem to minimize the makespan. It is assumed that each job consists of at most two operations, one of which is to be processed on the bottleneck machine, the same for all jobs. A new lower bound on the optimal makespan is derived, and a linear-time algorithm for finding an optimal non-preemptive schedule is presented.
An algorithm is described that constructs, in polynomial time, a Nash equilibrium in a finite game with additive aggregation and decreasing best responses. (C) 2013 Elsevier B.V. All rights reserved.
An algorithm is described that constructs, in polynomial time, a Nash equilibrium in a finite game with additive aggregation and decreasing best responses. (C) 2013 Elsevier B.V. All rights reserved.
The edge-neighbor-scattering number (ENS) is an alternative invulnerability measure of networks such as the vertices represent spies or virus carriers. Let G = (V, E) be a graph and e be any edge in G. The open edge-n...
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The edge-neighbor-scattering number (ENS) is an alternative invulnerability measure of networks such as the vertices represent spies or virus carriers. Let G = (V, E) be a graph and e be any edge in G. The open edge-neighborhood of e is N(e) = {f is an element of E(G)|f not equal e, e and f are adjacent}, and the closed edge-neighborhood of e is N[e] = N(e)boolean OR{e}. An edge e in G is said to be subverted when N [e] is deleted from G. An edge set X subset of E (G) is called an edge subversion strategy of G if each of the edges in X has been subverted from G. The survival subgraph is denoted by G/X. An edge subversion strategy X is called an edge-cut-strategy of G if the survival subgraph G/X is disconnected, or is a single vertex, or is phi. The ENS of a graph G is defined as ENS(G) = max(X subset of E(G)) {omega(G/X)-|X|}, where X is any edge-cut-strategy of G,omega(G/X) is the number of the components of G/X. It is proved that the problem of computing the ENS of a graph is NP-complete. In this paper, we give a polynomial algorithm of ENS of trees. (c) 2016 Elsevier Inc. All rights reserved.
Given a graph G, the longest path problem asks to compute a simple path of G with the largest number of vertices. This problem is the most natural optimization version of the well-known and well-studied Hamiltonian pa...
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Given a graph G, the longest path problem asks to compute a simple path of G with the largest number of vertices. This problem is the most natural optimization version of the well-known and well-studied Hamiltonian path problem, and thus it is NP-hard on general graphs. However, in contrast to the Hamiltonian path problem, there are only a few restricted graph families, such as trees, and some small graph classes where polynomial algorithms for the longest path problem have been found. Recently it has been shown that this problem can be solved in polynomial time on interval graphs by applying dynamic programming to a characterizing ordering of the vertices of the given graph [K. Ioannidou, G. B. Mertzios, and S. D. Nikolopoulos, algorithmica, 61 (2011), pp. 320-341], thus answering an open question. In the present paper, we provide the first polynomial algorithm for the longest path problem on a much greater class, namely on co-comparability graphs. Our algorithm uses a similar, but essentially simpler, dynamic programming approach, which is applied to a lexicographic depth first search (LDFS) characterizing ordering of the vertices of a cocomparability graph. Therefore, our results provide evidence that this general dynamic programming approach can be used in a more general setting, leading to efficient algorithms for the longest path problem on greater classes of graphs. LDFS has recently been introduced in [D. G. Corneil and R. M. Krueger, SIAM J. Discrete Math., 22 (2008), pp. 1259-1276]. Since then, a similar phenomenon of extending an existing interval graph algorithm to cocomparability graphs by using an LDFS preprocessing step has also been observed for the minimum path cover problem [D. G. Corneil, B. Dalton, and M. Habib, submitted]. Therefore, more interestingly, our results also provide evidence that cocomparability graphs present an interval graph structure when they are considered using an LDFS ordering of their vertices, which may lead to other new an
It is shown that the job-shop problem with two machines and a fixed number of k jobs with makespan criterion J2\n = k\C(max) is polynomially solvable. Sotskov and Shakhlevich (1993) have shown that problem J3\n = 3\C(...
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It is shown that the job-shop problem with two machines and a fixed number of k jobs with makespan criterion J2\n = k\C(max) is polynomially solvable. Sotskov and Shakhlevich (1993) have shown that problem J3\n = 3\C(max) is NP-hard. Furthermore it is well known that J\n=2\C(max) in polynomially solvable. Thus, our result settles the remaining open question concerning the complexity status of job-shop problems with fixed numbers of jobs and machines.
We consider the problem of balancing reconfigurable transfer lines. The problem is quite recent and motivated by the growing need of reconfigurability in the industry. The problem consists into allocating a set of ope...
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We give a polynomial-time algorithm for finding a solution to the Traveling Salesman Problem when the points given are constrained to lie on a fixed set of smooth curves of finite length. (C) 2007 John Wiley & Son...
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We give a polynomial-time algorithm for finding a solution to the Traveling Salesman Problem when the points given are constrained to lie on a fixed set of smooth curves of finite length. (C) 2007 John Wiley & Sons, Inc.
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