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224
Exact algorithms for NPhard problems: a survey, in: Combinatorial Optimization—Eureka, you shrink!”,
 Lecture Notes in Computer Science,
, 2003
"... Abstract. We discuss fast exponential time solutions for NPcomplete problems. We survey known results and approaches, we provide pointers to the literature, and we discuss several open problems in this area. The list of discussed NPcomplete problems includes the travelling salesman problem, sched ..."
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Cited by 151 (4 self)
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Abstract. We discuss fast exponential time solutions for NPcomplete problems. We survey known results and approaches, we provide pointers to the literature, and we discuss several open problems in this area. The list of discussed NPcomplete problems includes the travelling salesman problem, scheduling under precedence constraints, satisfiability, knapsack, graph coloring, independent sets in graphs, bandwidth of a graph, and many more.
Decoding Complexity in WordReplacement Translation Models
 Computational Linguistics
, 1999
"... This paper looks at decoding complexity. ..."
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SCIP: solving constraint integer programs
, 2009
"... Constraint integer programming (CIP) is a novel paradigm which integrates constraint programming (CP), mixed integer programming (MIP), and satisfiability (SAT) modeling and solving techniques. In this paper we discuss the software framework and solver SCIP (Solving Constraint Integer Programs), wh ..."
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Cited by 122 (0 self)
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Constraint integer programming (CIP) is a novel paradigm which integrates constraint programming (CP), mixed integer programming (MIP), and satisfiability (SAT) modeling and solving techniques. In this paper we discuss the software framework and solver SCIP (Solving Constraint Integer Programs), which is free for academic and noncommercial use and can be downloaded in source code. This paper gives an overview of the main design concepts of SCIP and how it can be used to solve constraint integer programs. To illustrate the performance and flexibility of SCIP, we apply it to two different problem classes. First, we consider mixed integer programming and show by computational experiments that SCIP is almost competitive to specialized commercial MIP solvers, even though SCIP supports the more general constraint integer programming paradigm. We develop new ingredients that improve current MIP solving technology. As a second application, we employ SCIP to solve chip design verification problems as they arise in the logic design of integrated circuits. This application goes far beyond traditional MIP solving, as it includes several highly nonlinear constraints, which can be handled nicely within the constraint integer programming framework. We show anecdotally how the different solving techniques from MIP, CP, and SAT work together inside SCIP to deal with such constraint classes. Finally, experimental results show that our approach outperforms current stateoftheart techniques for proving the validity of properties on circuits containing arithmetic.
A Theoretician's Guide to the Experimental Analysis of Algorithms
, 1996
"... This paper presents an informal discussion of issues that arise when one attempts to analyze algorithms experimentally. It is based on lessons learned by the author over the course of more than a decade of experimentation, survey paper writing, refereeing, and lively discussions with other experimen ..."
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Cited by 105 (0 self)
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This paper presents an informal discussion of issues that arise when one attempts to analyze algorithms experimentally. It is based on lessons learned by the author over the course of more than a decade of experimentation, survey paper writing, refereeing, and lively discussions with other experimentalists. Although written from the perspective of a theoretical computer scientist, it is intended to be of use to researchers from all fields who want to study algorithms experimentally. It has two goals: first, to provide a useful guide to new experimentalists about how such work can best be performed and written up, and second, to challenge current researchers to think about whether their own work might be improved from a scientific point of view. With the latter purpose in mind, the author hopes that at least a few of his recommendations will be considered controversial.
Chained LinKernighan for large traveling salesman problems
, 2000
"... We discuss several issues that arise in the implementation of Martin, Otto, and Felten's Chained LinKernighan heuristic for largescale traveling salesman problems. Computational results are presented for TSPLIB instances ranging in size from 11,849 cities up to 85,900 cities; for each of t ..."
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Cited by 74 (1 self)
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We discuss several issues that arise in the implementation of Martin, Otto, and Felten's Chained LinKernighan heuristic for largescale traveling salesman problems. Computational results are presented for TSPLIB instances ranging in size from 11,849 cities up to 85,900 cities; for each of these instances, solutions within 1% of the optimal value can be found in under 1 CPU minute on a 300 Mhz Pentium II workstation, and solutions within 0.5% of optimal can be found in under 10 CPU minutes. We also demonstrate the scalability of the heuristic, presenting results for randomly generated Euclidean instances having up to 25,000,000 cities. For the largest of these random instances, a tour within 1% of an estimate of the optimal value can be obtained in under 1 CPU day on a 64bit IBM RS6000 workstation.
On the pointtopoint and traveling salesperson problems for Dubins’ vehicle,”
 in American Control Conference,
, 2005
"... AbstractIn this paper we propose some novel planning and routing strategies for Dubins' vehicle, i.e., for a nonholonomic vehicle moving along paths with bounded curvature, without reversing direction. First, we study a stochastic version of the Traveling Salesperson Problem (TSP): given n ta ..."
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Cited by 73 (18 self)
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AbstractIn this paper we propose some novel planning and routing strategies for Dubins' vehicle, i.e., for a nonholonomic vehicle moving along paths with bounded curvature, without reversing direction. First, we study a stochastic version of the Traveling Salesperson Problem (TSP): given n targets randomly sampled from a uniform distribution in a rectangle, what is the shortest Dubins' tour through the targets and what is its length? We show that the expected length of such a tour is Ω(n 2/3 ) and we propose a novel algorithm that generates a tour of length O(n 2/3 log(n) 1/3 ) with high probability. Second, we study a dynamic version of the TSP (known as "Dynamic Traveling Repairperson Problem" in the Operations Research literature): given a stochastic process that generates targets, is there a policy that allows a Dubins vehicle to stabilize the system, in the sense that the number of unvisited targets does not diverge over time? If such policies exist, what is the minimum expected waiting period between the time a target is generated and the time it is visited? We propose a novel recedinghorizon algorithm whose performance is almost within a constant factor from the optimum.
Experimental Analysis of Heuristics for the STSP
 Local Search in Combinatorial Optimization
, 2001
"... In this and the following chapter, we consider what approaches one should take when one is confronted with a realworld application of the TSP. What algorithms should be used under which circumstances? We ..."
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Cited by 68 (1 self)
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In this and the following chapter, we consider what approaches one should take when one is confronted with a realworld application of the TSP. What algorithms should be used under which circumstances? We
Automatic Data Layout Using 01 Integer Programming
 In Proceedings of the International Conference on Parallel Architectures and Compilation Techniques (PACT94
, 1994
"... : The goal of languages like Fortran D or High Performance Fortran (HPF) is to provide a simple yet efficient machineindependent parallel programming model. By shifting much of the burden of machinedependent optimization to the compiler, the programmer is able to write dataparallel programs that ..."
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Cited by 65 (5 self)
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: The goal of languages like Fortran D or High Performance Fortran (HPF) is to provide a simple yet efficient machineindependent parallel programming model. By shifting much of the burden of machinedependent optimization to the compiler, the programmer is able to write dataparallel programs that can be compiled and executed with good performance on many different architectures. However, the choice of a good data layout is still left to the programmer. Even the most sophisticated compiler may not be able to compensate for a poorly chosen data layout since many compiler decisions are driven by the data layout specified in the program. The choice of a good data layout depends on many factors, including the target machine architecture, the compilation system, the problem size, and the number of processors available. The option of remapping arrays at specific points in the program makes the choice even harder. Current programming tools provide little or no support for this difficult sele...
The sample average approximation method applied to stochastic routing problems: a computational study
 Computational Optimization and Applications
"... Abstract. The sample average approximation (SAA) method is an approach for solving stochastic optimization problems by using Monte Carlo simulation. In this technique the expected objective function of the stochastic problem is approximated by a sample average estimate derived from a random sample. ..."
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Cited by 65 (7 self)
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Abstract. The sample average approximation (SAA) method is an approach for solving stochastic optimization problems by using Monte Carlo simulation. In this technique the expected objective function of the stochastic problem is approximated by a sample average estimate derived from a random sample. The resulting sample average approximating problem is then solved by deterministic optimization techniques. The process is repeated with different samples to obtain candidate solutions along with statistical estimates of their optimality gaps. We present a detailed computational study of the application of the SAA method to solve three classes of stochastic routing problems. These stochastic problems involve an extremely large number of scenarios and firststage integer variables. For each of the three problem classes, we use decomposition and branchandcut to solve the approximating problem within the SAA scheme. Our computational results indicate that the proposed method is successful in solving problems with up to 21694 scenarios to within an estimated 1.0 % of optimality. Furthermore, a surprising observation is that the number of optimality cuts required to solve the approximating problem to optimality does not significantly increase with the size of the sample. Therefore, the observed computation times needed to find optimal solutions to the approximating problems grow only linearly with the sample size. As a result, we are able to find provably nearoptimal solutions to these difficult stochastic programs using only a moderate amount of computation time. Keywords: salesman stochastic optimization, stochastic programming, stochastic routing, shortest path, traveling 1.
The Traveling Tournament Problem Description and Benchmarks
, 2001
"... The Traveling Tournament Problem is a sports timetabling problem that abstracts the important issues in creating timetables where team travel is an important issue. Instances of this problem seem to be very difficult to solve even for very small cases. Given the practical importance of solving i ..."
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Cited by 60 (5 self)
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The Traveling Tournament Problem is a sports timetabling problem that abstracts the important issues in creating timetables where team travel is an important issue. Instances of this problem seem to be very difficult to solve even for very small cases. Given the practical importance of solving instances similar to these, this makes this problem an interesting challenge for combinatorial optimization techniques. We introduce this problem, give some interesting classes of instances and give some base computational results.