We study the problem of minimizing total completion time in two-machine job shop with unit-time operations. We propose an efficient algorithm for the problem. The algorithm is polynomial with respect to a succinct enc...
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We study the problem of minimizing total completion time in two-machine job shop with unit-time operations. We propose an efficient algorithm for the problem. The algorithm is polynomial with respect to a succinct encoding of the problem instances, where the number of bits necessary to encode a job with k operations is O(log(k + 1)). This result answers a long standing open question about the complexity of the problem.
In this paper we introduce the concept of ordered graph and ordered graph isomorphism that provides a natural representation of many objects in applications such as computer vision and pattern recognition. While no ef...
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In this paper we introduce the concept of ordered graph and ordered graph isomorphism that provides a natural representation of many objects in applications such as computer vision and pattern recognition. While no efficient (polynomial-bound) isomorphism algorithm for general graphs exists today, we show that the ordered graph isomorphism problem can be optimally solved in quadratic time. An experimental evaluation demonstrates the superior performance of the new method. Our ordered graph isomorphism algorithm is simple and can be easily implemented. It is therefore expected to be practically useful in many applications. (C) 1999 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.
Bubble-sort graphs are variants of Cayley graphs. A bubble-sort graph is suitable as a topology for massively parallel systems because of its simple and regular structure. Therefore, in this study, we focus on n-bubbl...
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Bubble-sort graphs are variants of Cayley graphs. A bubble-sort graph is suitable as a topology for massively parallel systems because of its simple and regular structure. Therefore, in this study, we focus on n-bubble-sort graphs and propose an algorithm to obtain n - 1 disjoint paths between two arbitrary nodes in time bounded by a polynomial in n, the degree of the graph plus one. We estimate the time complexity of the algorithm and the sum of the path lengths after proving the correctness of the algorithm. In addition, we report the results of computer experiments evaluating the average performance of the algorithm.
We consider the following problem: Given a finite set of straight line segments in the plane, find a set of points of minimum size, so that every segment contains at least one point in the set. This problem can be int...
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We consider the following problem: Given a finite set of straight line segments in the plane, find a set of points of minimum size, so that every segment contains at least one point in the set. This problem can be interpreted as looking for a minimum number of locations of policemen, guards, cameras or other sensors, that can observe a network of streets, corridors, tunnels, tubes, etc. We show that the problem is strongly NP-complete even for a set of segments with a cubic graph structure, but in P for tree structures. Published by Elsevier B.V.
This paper deals with the problem of finding a minimum cost schedule for a set of dependent activities when a convex cost function is attached to the starting time of each activity. A first optimality necessary and su...
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This paper deals with the problem of finding a minimum cost schedule for a set of dependent activities when a convex cost function is attached to the starting time of each activity. A first optimality necessary and sufficient condition bearing on the head and tail blocks of a schedule is first established. A second such condition that uses the spanning active equality trees of a schedule leads to design a generic algorithm for the general case. When the cost function is the usual earliness-tardiness linear function with assymetric and independent penalty coefficients, the problem is shown to be solved in O(nmax{n,m}). Finally, the special cases when the precedence graph is an intree or a family of chains are then also shown to be solved by efficient polynomial algorithms. (C) 2002 Elsevier Science B.V. All rights reserved.
In this article, we define two different workforce leveling objectives for serial transfer lines. Each job is to be processed on each transfer station for c time periods (e.g., hours). We assume that the number of wor...
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In this article, we define two different workforce leveling objectives for serial transfer lines. Each job is to be processed on each transfer station for c time periods (e.g., hours). We assume that the number of workers needed to complete each operation of a job in precisely c periods is given. Jobs transfer forward synchronously after every production cycle (i.e., c periods). We study two leveling objectives: maximin workforce size (W-m) and min range (R). Leveling objectives produce schedules where the cumulative number of workers needed in all stations of a transfer line does not experience dramatic changes from one production cycle to the next. For W-m and a two-station system, we develop a fast polynomial algorithm. The range problem is known to be NP-complete. For the two-station system, we develop a very fast optimal algorithm that uses a tight lower bound and an efficient procedure for finding complementary Hamiltonian cycles in bipartite graphs. Via a computational experiment, we demonstrate that range schedules are superior because not only do they limit the workforce fluctuations from one production cycle to the next, but they also do so with a minor increase in the total workforce size. We extend our results to the m-station system and develop heuristic algorithms. We find that these heuristics work poorly for min range (R), which indicates that special structural properties of the m-station problem need to be identified before we can develop efficient algorithms. (C) 2016 Wiley Periodicals, Inc.
We present a polynomial time solution algorithm for the so-called Convex-hull-and-k-line TSP: This is a special case of the Euclidean TSP where n - m of the cities lie on the convex hull and m of the cities lie on k a...
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We present a polynomial time solution algorithm for the so-called Convex-hull-and-k-line TSP: This is a special case of the Euclidean TSP where n - m of the cities lie on the convex hull and m of the cities lie on k almost parallel line segments in the interior of the hull such that the carrying lines of all these segments intersect the hull in two common edges. Our result contains and generalizes three earlier results that are due to Cutler (1980),to Rote (1992), and to Deineko, Van Dal and Rote (1994).
Hoist scheduling is a typical problem in the operation of electroplating systems. The cyclic scheduling policy is widely used in these systems in industry. Research on hoist scheduling has focused on the cyclic proble...
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Hoist scheduling is a typical problem in the operation of electroplating systems. The cyclic scheduling policy is widely used in these systems in industry. Research on hoist scheduling has focused on the cyclic problem to minimize the cycle length. Most previous studies consider the single-hoist case. In practice, however, more than one hoist is often used in an electroplating line. This paper addresses the two-hoist, no-wait cyclic scheduling problem, in which the tank-processing times are constants and, upon completion of processing in a tank, the parts have to be moved to the next tank immediately. Based on the analysis of the problem properties, a polynomial algorithm is developed to obtain an optimal schedule. This algorithm first identifies a set of thresholds, which are special values of the cycle length, so that the feasibility property may change only at these thresholds. Feasibility checking is then carried out on each individual threshold in ascending order. The first feasible threshold found will be the optimal cycle length, and the corresponding feasible schedule is an optimal hoist schedule.
In this paper we present two new polynomial algorithms for the asymmetric version of the m-Peripatetic Salesman Problem (m-APSP) which consists in finding m edge-disjoint Hamiltonian circuits of extremal total weight ...
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In this paper we present two new polynomial algorithms for the asymmetric version of the m-Peripatetic Salesman Problem (m-APSP) which consists in finding m edge-disjoint Hamiltonian circuits of extremal total weight in a complete weighted digraph. The first algorithm solves the asymmetric 2-PSP on maximum. Its approximation ratio is equal to 2/3. The second algorithm deals with the minimization version of the asymmetric m-PSP on random instances. For this algorithm conditions for asymptotically exactness are presented. (C) 2015 Elsevier B.V. All rights reserved.
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.
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