Results 1  10
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13
Greedy Randomized Adaptive Search Procedures
, 2002
"... GRASP is a multistart metaheuristic for combinatorial problems, in which each iteration consists basically of two phases: construction and local search. The construction phase builds a feasible solution, whose neighborhood is investigated until a local minimum is found during the local search phas ..."
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Cited by 647 (82 self)
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GRASP is a multistart metaheuristic for combinatorial problems, in which each iteration consists basically of two phases: construction and local search. The construction phase builds a feasible solution, whose neighborhood is investigated until a local minimum is found during the local search phase. The best overall solution is kept as the result. In this chapter, we first describe the basic components of GRASP. Successful implementation techniques and parameter tuning strategies are discussed and illustrated by numerical results obtained for different applications. Enhanced or alternative solution construction mechanisms and techniques to speed up the search are also described: Reactive GRASP, cost perturbations, bias functions, memory and learning, local search on partially constructed solutions, hashing, and filtering. We also discuss in detail implementation strategies of memorybased intensification and postoptimization techniques using pathrelinking. Hybridizations with other metaheuristics, parallelization strategies, and applications are also reviewed.
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 75 (7 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 36 (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 31 (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 .
Pipeline scheduling: A survey
 Tech. Rep. RJ 5738, IBM Research Div
, 1987
"... In interval scheduling, not only the processing times of the jobs but also their starting times are given. This paper surveys the area of interval scheduling and presents proofs of results that have been known within the community for some time. We first review the complexity and approximability of ..."
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Cited by 22 (1 self)
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In interval scheduling, not only the processing times of the jobs but also their starting times are given. This paper surveys the area of interval scheduling and presents proofs of results that have been known within the community for some time. We first review the complexity and approximability of different variants of interval scheduling problems. Next, we motivate the relevance of interval scheduling problems by providing an overview of applications that have appeared in literature. Finally, we focus on algorithmic results for two important variants of interval scheduling problems. In one variant we deal with nonidentical machines: instead of each machine being continuously available, there is a given interval for each machine in which it is available. In another variant, the machines are continuously available but they are ordered, and each job has a given ‘maximal ’ machine on which it can be processed. We investigate the complexity of these problems and describe algorithms for their solution. Analysis of algorithms, computational complexity: exact algorithms. Production/scheduling, sequencing, deterministic: interval scheduling ∗Antoon Kolen sadly passed away on October 3, 2004. His coauthors dedicate their contribution to this paper to his memory.
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 22 (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.
An analysis of shift class design problems
, 1994
"... In this paper we consider a generalization of the Fixed Job Schedule Problem (FJSP) which appears in the aircraft maintenance process at an airport. A number of jobs must be carried out where each job requires processing from a fixed start time to a fixed finish time. These jobs must be carried ou ..."
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Cited by 6 (2 self)
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In this paper we consider a generalization of the Fixed Job Schedule Problem (FJSP) which appears in the aircraft maintenance process at an airport. A number of jobs must be carried out where each job requires processing from a fixed start time to a fixed finish time. These jobs must be carried out by a number of machines which are available in specific shifts only. The jobs must be carried out in a nonpreemptive way, although at the end of a shift preemption of a job is allowed sometimes. The problem is to choose the number of machines in each of the shifts in such a way that all jobs can be carried out and that the total costs of the machines or the total number of machines are minimum. In this paper we present an analysis of the computational complexity of these problems. We also analyse the worst case behaviour of the preemptive variant versus the nonpreemptive variant.
Combinatorics in operations research
, 1990
"... This is a collection of examples of the use of combinatorial techniques in practical decision situations. The emphasis is on the description of realworld problems, the formulation of mathematical models, and the development of algorithms for their solution. We survey related models and applications ..."
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Cited by 5 (3 self)
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This is a collection of examples of the use of combinatorial techniques in practical decision situations. The emphasis is on the description of realworld problems, the formulation of mathematical models, and the development of algorithms for their solution. We survey related models and applications.
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 5 (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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Cited by 4 (0 self)
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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