The problem of scheduling a collection of different jobs on identical parallel machines is investigated. For each job a number of unit processing time tasks, a given deadline and an upper bound on inventory are known....
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The problem of scheduling a collection of different jobs on identical parallel machines is investigated. For each job a number of unit processing time tasks, a given deadline and an upper bound on inventory are known. The optimality criterion is changeover cost which occur if different types of jobs are processed in sequence. Only unit cost are to be considered. For two job types, an efficient algorithm is presented considering only tight schedules;if more job types have to be considered the problem becomes NP-hard.
For an edge-weighted graph G with n vertices and m edges, the minimum k-way cut problem is to find a partition of the vertex set into k non-empty subsets so that the weight sum of edges between different subsets is mi...
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For an edge-weighted graph G with n vertices and m edges, the minimum k-way cut problem is to find a partition of the vertex set into k non-empty subsets so that the weight sum of edges between different subsets is minimized. For this problem with k = 5 and 6, we present a deterministic algorithm that runs in O(n(k-1)F(n, m)) = O(mn(k) log (n(2)/m)) time, where F(n, m) denotes the time bound required to solve the maximum flow problem in G. The bounds (O) over tilde(mn(5)) for k = 5 and (O) over tilde(mn(6)) for k = 6 improve the previous best randomized bounds (O) over tilde(n(8)) and (O) over tilde(n(10)), respectively.
Let k be a fixed integer. We determine the complexity of finding a p-partition (V-1 , . . . ,V-p) of the vertex set of a given digraph such that the maximum out-degree of each of the digraphs induced by V-i, (1 = 2k a...
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Let k be a fixed integer. We determine the complexity of finding a p-partition (V-1 , . . . ,V-p) of the vertex set of a given digraph such that the maximum out-degree of each of the digraphs induced by V-i, (1 <= i <= p) is at least k smaller than the maximum out-degree of D. We show that this problem is polynomial-time solvable when p >= 2k and NP-complete otherwise. The result for k = 1 and p = 2 answers a question posed in [3]. We also determine, for all fixed non-negative integers k(1), k(2), p, the complexity of deciding whether a given digraph of maximum out-degree p has a 2-partition (V-1, V-2) such that the digraph induced by Vi has maximum out-degree at most k(i);for i is an element of [2]. It follows from this characterization that the problem of deciding whether a digraph has a 2-partition (V-1, V-2) such that each vertex nu is an element of V-i has at least as many neighbours in the set V3-i as in V-i, for i = 1, 2 is NP-complete. This solves a problem from [6] on majority colourings. (C) 2017 Elsevier By. All rights reserved.
This article considers the continuous version of the refueling station location problem on a tree network, which is a common structure in numerous toll roads worldwide, so as to locate a single alternative-fuel refuel...
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This article considers the continuous version of the refueling station location problem on a tree network, which is a common structure in numerous toll roads worldwide, so as to locate a single alternative-fuel refueling station to maximize the traffic flow covered in round trips/day. Two reduction properties regarding the problem size and some optimality conditions are derived. Based on these conditions, an exact polynomial algorithm is developed to determine the set of optimal locations for the refueling station. A small tree network example is solved to illustrate the algorithm. (C) 2014 Elsevier Ltd. All rights reserved.
The paper is concerned with scheduling the two-way traffic between two stations connected by a single-track railway with a siding. It is shown that if, for each station, the order in which trains leave this station is...
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The paper is concerned with scheduling the two-way traffic between two stations connected by a single-track railway with a siding. It is shown that if, for each station, the order in which trains leave this station is known or can be found, then for various objective functions an optimal schedule can be constructed in polynomial time using the method of dynamic programming. Based on this result, the paper also presents a polynomial-time algorithm minimising the weighted number of late trains.
In this paper we present a log-barrier method for solving two-stage quadratic stochastic programs. The mathematical model considered here can be used to present several real world applications, including financial and...
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In this paper we present a log-barrier method for solving two-stage quadratic stochastic programs. The mathematical model considered here can be used to present several real world applications, including financial and production planning problems. We discuss fundamental properties associated with the proposed algorithm and analyze the convergence and complexity of the algorithm. (c) 2004 Elsevier Inc. All rights reserved.
In the paper we consider the problem of scheduling n identical jobs on 3 uniform machines with speeds s(1),s(2), and s(3) to minimize the ***. We assume that jobs are subjected to some kind of mutual exclusion constra...
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In the paper we consider the problem of scheduling n identical jobs on 3 uniform machines with speeds s(1),s(2), and s(3) to minimize the ***. We assume that jobs are subjected to some kind of mutual exclusion constraints, modeled by a cubic incompatibility graph. We show that if the graph is 2-chromatic then. the problem can be solved in 0(n(2)) time. If the graph is 3-chromatic, the problem becomes NP-hard even if s1 > s(2) = s(3). However, in this case there exists a 10/7-approximation algorithm running in 0(n(3)) time. Moreover, this algorithm solves the problem almost surely to optimality if 3(s1)/4 <= s(2) = s(3). (C) 2016 Elsevier B.V. All rights reserved.
This paper is concerned with algorithms and applications of decreasing minimization on an M-convex set, which is the set of integral elements of an integral base-polyhedron. Based on a recent characterization of decre...
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This paper is concerned with algorithms and applications of decreasing minimization on an M-convex set, which is the set of integral elements of an integral base-polyhedron. Based on a recent characterization of decreasingly minimal (dec-min) elements, we develop a strongly polynomial algorithm for computing a dec-min element of an M-convex set. The matroidal feature of the set of dec-min elements makes it possible to compute a minimum cost dec-min element, as well. Our second goal is to exhibit various applications in matroid and network optimization, resource allocation, and (hyper)graph orientation. We extend earlier results on semi-matchings to a large degree by developing a structural description of dec-min in-degree bounded orientations of a graph. This characterization gives rise to a strongly polynomial algorithm for finding a minimum edge-cost dec-min orientation.
Primal-dual interior-point methods (IPMs) are the most efficient methods for a computational point of view. At present the theoretical iteration bound for small-update IPMs is better than the one for large-update IPMs...
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Primal-dual interior-point methods (IPMs) are the most efficient methods for a computational point of view. At present the theoretical iteration bound for small-update IPMs is better than the one for large-update IPMs. However, in practice, large-update IPMs are much more efficient than small-update IPMs. Peng et al. [14,15] proposed new variants of IPMs based on self-regular barrier functions and proved so far the best known complexity, e. g. O(root n log n log n/epsilon), for large-update IPMs with some specific self-regular barrier functions. Recently, Roos et al. [2-9] proposed new primal-dual IPMs based on various barrier functions to improve the iteration bound for large-update methods from O(n log n/epsilon) to O(root n log n log n/epsilon). Motivated by their works we define a new barrier function and propose a new primal-dual interior point algorithm based on this function for linear optimization (LO) problems. We show that the new algorithm has O(root n log n log n/epsilon) iteration bound for large-update and O(root n log n/epsilon) for small-update methods which are currently the best known bounds, respectively. (C) 2011 Elsevier Inc. All rights reserved.
The polynomial algorithms of determining Bayesian network structure are described as "tree" or "polytree". In the known Bayesian network structure consideration is given to Bayesian recognition pro...
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The polynomial algorithms of determining Bayesian network structure are described as "tree" or "polytree". In the known Bayesian network structure consideration is given to Bayesian recognition procedures built on learning samples by estimations of transition probabilities.
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