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A greedy randomized adaptive search procedure for the 2partition problem
 Operations Research
, 1994
"... Abstract. Today, a variety of heuristic approaches are available to the operations research practitioner. One methodology that has a strong intuitive appeal, a prominent empirical track record, and is trivial to efficiently implement on parallel processors is GRASP (Greedy Randomized Adaptive Search ..."
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Cited by 526 (79 self)
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Abstract. Today, a variety of heuristic approaches are available to the operations research practitioner. One methodology that has a strong intuitive appeal, a prominent empirical track record, and is trivial to efficiently implement on parallel processors is GRASP (Greedy Randomized Adaptive Search Procedures). GRASP is an iterative randomized sampling technique in which each iteration provides a solution to the problem at hand. The incumbent solution over all GRASP iterations is kept as the final result. There are two phases within each GRASP iteration: the first intelligently constructs an initial solution via an adaptive randomized greedy function; the second applies a local search procedure to the constructed solution in hope of finding an improvement. In this paper, we define the various components comprising a GRASP and demonstrate, step by step, how to develop such heuristics for combinatorial optimization problems. Intuitive justifications for the observed empirical behavior of the methodology are discussed. The paper concludes with a brief literature review of GRASP implementations and mentions two industrial applications.
Approximating the Throughput of Multiple Machines in RealTime Scheduling
"... We consider the following fundamental scheduling problem. The input to the problem consists of n jobs and k machines. Each of the jobs is associated with a release time, a deadline, a weight, and a processing time on each of the machines. The goal is to find a schedule that maximizes the weight of j ..."
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Cited by 61 (6 self)
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We consider the following fundamental scheduling problem. The input to the problem consists of n jobs and k machines. Each of the jobs is associated with a release time, a deadline, a weight, and a processing time on each of the machines. The goal is to find a schedule that maximizes the weight of jobs that meet their deadline. We give constant factor approximation algorithms for four variants of the problem, depending on the type of the machines (identical vs. unrelated), and the weight of the jobs (identical vs. arbitrary). All these variants are known to be NPHard, and we observe that the two variants involving unrelated machines are also MAXSNP hard. To the best of our knowledge, these are the first approximation algorithms for such problems in the nonpreemptive o line setting. The specific results obtained are:  For identical job weights and unrelated machines: a greedy 2approximation algorithm.  For identical job weights and k identical machines: the same greedy alg...
Approximation Algorithms for the Job Interval Selection Problem and Related Scheduling Problems
"... In this paper we consider the job interval selection problem (JISP), a simple scheduling model with a rich history and numerous applications. Special cases of this problem include the socalled realtime scheduling problem (also known as the throughput maximization problem) in single and multiple ma ..."
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Cited by 30 (3 self)
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In this paper we consider the job interval selection problem (JISP), a simple scheduling model with a rich history and numerous applications. Special cases of this problem include the socalled realtime scheduling problem (also known as the throughput maximization problem) in single and multiple machine environments. In these special cases we have to maximize the number of jobs scheduled between their release date and deadline (preemption is not allowed). Even the single machine case is NPhard. The unrelated machines case, as well as other special cases of JISP, are MAX SNPhard. A simple greedy algorithm gives a 2approximation for JISP. Despite many efforts, this was the best approximation guarantee known, even for throughput maximization on a single machine. In this paper, we break this barrier and show an approximation guarantee of less than 1.582 for arbitrary instances of JISP. For some special cases, we show better results.
Approximation Results for the Optimum Cost Chromatic Partition Problem
 J. Algorithms
"... . In this paper, we study the optimum cost chromatic partition (OCCP) problem for several graph classes. The OCCP problem is the problem of coloring the vertices of a graph such that adjacent vertices get different colors and that the total coloring costs are minimum. We prove several approximation ..."
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Cited by 28 (0 self)
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. In this paper, we study the optimum cost chromatic partition (OCCP) problem for several graph classes. The OCCP problem is the problem of coloring the vertices of a graph such that adjacent vertices get different colors and that the total coloring costs are minimum. We prove several approximation results for the OCCP problem restricted to bipartite, chordal, comparability, interval, permutation, split and unimodular graphs. We prove that there exists no polynomial approximation algorithm with ratio O(jV j 0:5 ) for the OCCP problem restricted to bipartite and interval graphs, unless P = NP . Furthermore, we propose approximation algorithms with ratio O(jV j 0:5 ) for bipartite, interval and unimodular graphs. Finally, we prove that there exists no polynomial approximation algorithm with ratio O(jV j 1 ) for the OCCP problem restricted to split, chordal, permutation and comparability graphs, unless P = NP .
The Optimal Cost Chromatic Partition Problem for Trees and Interval Graphs
 GraphTheoretic Concepts in Computer Science (Cadenabbia, 1996), Lecture Notes in Computer Science
, 1996
"... In this paper we study the Optimal Cost Chromatic Partition (OCCP) problem for trees and interval graphs. The OCCP problem is the problem of coloring the nodes of a graph in such a way that adjacent nodes obtain different colors and that the total coloring costs are minimum. ..."
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Cited by 18 (0 self)
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In this paper we study the Optimal Cost Chromatic Partition (OCCP) problem for trees and interval graphs. The OCCP problem is the problem of coloring the nodes of a graph in such a way that adjacent nodes obtain different colors and that the total coloring costs are minimum.
Ordering heuristics for parallel graph coloring
 In SPAA
, 2014
"... This paper introduces the largestlogdegreefirst (LLF) and smallestlogdegreelast (SLL) ordering heuristics for parallel greedy graphcoloring algorithms, which are inspired by the largestdegreefirst (LF) and smallestdegreelast (SL) serial heuristics, respectively. We show that although LF ..."
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Cited by 3 (1 self)
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This paper introduces the largestlogdegreefirst (LLF) and smallestlogdegreelast (SLL) ordering heuristics for parallel greedy graphcoloring algorithms, which are inspired by the largestdegreefirst (LF) and smallestdegreelast (SL) serial heuristics, respectively. We show that although LF and SL, in practice, generate colorings with relatively small numbers of colors, they are vulnerable to adversarial inputs for which any parallelization yields a poor parallel speedup. In contrast, LLF and SLL allow for provably good speedups on arbitrary inputs while, in practice, producing colorings of competitive quality to their serial analogs. We applied LLF and SLL to the parallel greedy coloring algorithm introduced by Jones and Plassmann, referred to here as JP. Jones and Plassman analyze the variant of JP that processes the vertices of a graph in a random order, and show that on an O(1)degree graph G = (V,E), this JPR variant has an expected parallel running time of O(lgV / lg lgV) in a PRAM model. We improve this bound to show, using workspan analysis, that JPR, augmented to handle arbitrarydegree graphs, colors a graph G = (V,E) with degree ∆ using Θ(V +E) work and O(lgV + lg ∆ ·min{√E,∆+ lg ∆ lgV / lg lgV}) expected span. We prove that JPLLF and JPSLL — JP using the LLF and SLL heuristics, respectively — execute with the same asymptotic work as JPR and only logarithmically more span while producing higherquality colorings than JPR in practice. We engineered an efficient implementation of JP for modern sharedmemory multicore computers and evaluated its performance on a machine with 12 Intel Corei7 (Nehalem) processor cores. Our implementation of JPLLF achieves a geometricmean speedup of 7.83 on eight realworld graphs and a geometricmean speedup of 8.08 on ten synthetic graphs, while our implementation using SLL achieves a geometricmean speedup of 5.36 on these realworld graphs and a geometricmean speedup of 7.02 on these synthetic graphs. Furthermore, on one processor, JPLLF is slightly faster than a wellengineered serial greedy algorithm using LF, and likewise, JPSLL is slightly faster than the greedy algorithm using SL.
Cost Constrained Fixed Job Scheduling
"... Abstract. In this paper, we study the problem of cost constrained fixed job scheduling (CCFJS). In this problem, there are a number of processors, each of which belongs to one of several classes. The unit time processing cost for a processor varies with the class to which the processor belongs. Ther ..."
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Abstract. In this paper, we study the problem of cost constrained fixed job scheduling (CCFJS). In this problem, there are a number of processors, each of which belongs to one of several classes. The unit time processing cost for a processor varies with the class to which the processor belongs. There are N jobs, each of which must be processed from a given start time to a given finish time without preemption. A job can be processed by any processor, and the cost of that processing is the product of the processing time and the processor’s unit time processing cost. The problem is to find a feasible scheduling of the jobs such that the total processing cost is within a given cost bound. This problem (CCFJS) arises in several applications, including offline multimedia gateway call routing. We show that CCFJS can be solved by a network flow based algorithm when there are only two classes of processors. For more than two classes of processors, we prove that CCFJS is not only NPComplete, but also that there is no constant ratio approximation algorithm. Finally, we present an approximation algorithm, derive its worstcase performance ratio (non constant), and show that it has a constant approximation ratio in several special cases. 1
« Évaluation et optimisation des systèmes innovants de production de biens et de services » PLANIFICATION DE FLUX LOGISTIQUES HOSPITALIERS, DIMENSIONNEMENT D’EQUIPES DE MANUTENTION ET
"... RÉSUMÉ: Dans le cadre d’une étude sur la réorganisation de la logistique hospitalière des hôpitaux de Tours, nous nous intéressons à la planification des tournées de véhicules entre les différents hôpitaux et à la création d’une équipe manutentionnaire dans un hôpital de taille importante. Le nombre ..."
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RÉSUMÉ: Dans le cadre d’une étude sur la réorganisation de la logistique hospitalière des hôpitaux de Tours, nous nous intéressons à la planification des tournées de véhicules entre les différents hôpitaux et à la création d’une équipe manutentionnaire dans un hôpital de taille importante. Le nombre de manutentionnaires et la définition de leurs tournées dans les différents services sont fortement liés à la planification des tournées entre les hôpitaux. Les circuits pris en compte dans cette étude sont les sept plus importants du groupe hospitalier: pharmaceutique, logistique hôtelière, blanchisserie (linge propre et sale), restauration, archives, et salubrité. La spécificité et l’originalité de cette étude résident dans le fait que deux problèmes de tournées de véhicules multiproduits interagissent. Etant donnée l’ampleur du problème, nous proposons un algorithme génétique, pour résoudre ce problème sous sa forme déterministe. Nous avons également conçu un moteur de simulation pour évaluer et valider dans un environnement incertain (quantités des demandes et temps des livraisons variables) la solution renvoyée. Les premiers résultats obtenus lors de cette étude sont présentés. MOTSCLÉS: Logistique hospitalière; tournées de véhicules; algorithme génétique; simulation. 1