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Results 1 - 10
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92
Universal approximations for TSP, Steiner tree, and set cover
- In Proceedings of the 37th Annual ACM Symposium on Theory of Computing (STOC’05
, 2005
"... We introduce a notion of universality in the context of optimization problems with partial information. Universality is a framework for dealing with uncertainty by guaranteeing a certain quality of goodness for all possible completions of the partial information set. Universal variants of optimizati ..."
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Cited by 34 (3 self)
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of optimization problems can be defined that are both natural and well-motivated. We consider universal versions of three classical problems: TSP, Steiner Tree and Set Cover. We present a polynomial-time algorithm to find a universal tour on a given metric space over vertices such that for any subset
Finding the Population Variance of Costs over the Solution Space of the TSP in Polynomial Time
"... Abstract: We give a polynomial time algorithm to find the population variance of tour costs over the solution space of the symmetric Traveling Salesman Problem (TSP). In practical terms the algorithm provides a linear time method, on the number of edges of the problem, for determining the standard d ..."
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Cited by 1 (1 self)
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Abstract: We give a polynomial time algorithm to find the population variance of tour costs over the solution space of the symmetric Traveling Salesman Problem (TSP). In practical terms the algorithm provides a linear time method, on the number of edges of the problem, for determining the standard
Bypassing the embedding: Algorithms for low-dimensional metrics
- In Proceedings of the 36th ACM Symposium on the Theory of Computing (STOC
, 2004
"... The doubling dimension of a metric is the smallest k such that any ball of radius 2r can be covered using 2 k balls of radius r. This concept for abstract metrics has been proposed as a natural analog to the dimension of a Euclidean space. If we could embed metrics with low doubling dimension into l ..."
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Cited by 77 (3 self)
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the embedding. In particular we show the following for low dimensional metrics: • Quasi-polynomial time (1+ɛ)-approximation algorithm for various optimization problems such as TSP, k-median and facility location. • (1 + ɛ)-approximate distance labeling scheme with optimal label length. • (1+ɛ
Double-Tree Approximations for Metric TSP: Is the Best One Good Enough?
, 2004
"... The Metric Travelling Salesman Problem (TSP) is a classical NP-hard optimisation problem. The double-tree heuristic for Metric TSP yields a space of approximate solutions, each of which is within a factor of 2 from the optimum. Such an approach raises two natural questions: can we nd eciently a ..."
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Cited by 1 (0 self)
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a solution that is optimal for the approximation space? will this optimal solution provide a better approximation ratio than an arbitrary solution from the space? Paper [3] answers the rst question in the armative, by presenting an algorithm that nds the optimal doubletree solution to Metric
Fast minimum-weight double-tree shortcutting for Metric TSP
- In Proceedings of the 6th WEA. Lecture Notes in Computer Science
"... Abstract. The Metric Traveling Salesman Problem (TSP) is a classical NP-hard optimization problem. The double-tree shortcutting method for Metric TSP yields an exponentially-sized space of TSP tours, each of which approximates the optimal solution within at most a factor of 2. We consider the proble ..."
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Cited by 4 (2 self)
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Abstract. The Metric Traveling Salesman Problem (TSP) is a classical NP-hard optimization problem. The double-tree shortcutting method for Metric TSP yields an exponentially-sized space of TSP tours, each of which approximates the optimal solution within at most a factor of 2. We consider
An Optimized NoC Architecture for Accelerating TSP Kernels in Breakpoint Median Problem
"... Traveling Salesman Problem (TSP) is a classical NP-complete problem in graph theory. It aims at finding a least-cost Hamiltonian cycle that traverses all vertices of an input edge-weighted graph. One application of TSP is in breakpoint median-based Maximum Parsimony phylogenetic tree reconstruction, ..."
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, wherein a bounded edge-weight model is used. Exponential algorithms that apply efficient heuristics, such as branch-and-bound, to dynamically prune the search space are used. We adopted this approach in an NoC-based implementation for solving TSP targeted towards phylogenetics taking advantage of the fine
An Improved Adaptive Multi-Start Approach to Finding Near-Optimal Solutions to the Euclidean TSP
- in Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2000
, 2000
"... We present an "adaptive multi-start" genetic algorithm for the Euclidean traveling salesman problem that uses a population of tours locally optimized by the Lin-Kernighan algorithm. An all-parent cross-breeding technique, chosen to exploit the structure of the search space, generates bette ..."
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Cited by 3 (0 self)
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tsplib [5] instances, it is able to find nearly optimal (or optimal) tours for problems of several thousand cities in a few minutes on a Pentium Pro workstation. We nd these results are competitive both in time and tour length with one of the most successful TSP algorithms, Iterated Lin-Kernighan.
Advanced OR and AI Methods in Transportation PATH RELINKING FOR MULTIPLE OBJECTIVE COMBINATORIAL OPTIMIZATION. TSP CASE STUDY
"... Abstract. The paper presents a new metaheuristic algorithm for multiple objective combinatorial optimization based on the idea of path relinking. The algorithm is applied to the traveling salesperson problem with multiple link (arc) costs, corresponding to multiple objectives. The multiple costs may ..."
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may for example correspond to financial cost of travel along a link, time of travel, or risk in case of hazardous materials. The algorithm searches for new good solutions along paths in the decision space connecting two other good solutions. It is compared experimentally to state of the art algorithms
Traveling Salesman Problem with Time Windows Solved with Genetic Algorithms
"... The Traveling Salesman Problem (TSP) is a very common problem in many applications. It appears in the transportation of goods and not only. As we know this problem is NP hard. Time Windows (TW) brings us some additional constraints to solve. In case there are many Time Windows the problem constraint ..."
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The Traveling Salesman Problem (TSP) is a very common problem in many applications. It appears in the transportation of goods and not only. As we know this problem is NP hard. Time Windows (TW) brings us some additional constraints to solve. In case there are many Time Windows the problem
Polynomial Time Approximation Schemes for Geometric Optimization Problems in Euclidean Metric Spaces
"... Introduction Many geometric optimization problems which are interesting and important in practice have been shown to be NP-hard. However, for some cases it is possible to compute approximate solutions in polynomial time. This chapter describes approaches to find polynomial time algorithms that com ..."
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Introduction Many geometric optimization problems which are interesting and important in practice have been shown to be NP-hard. However, for some cases it is possible to compute approximate solutions in polynomial time. This chapter describes approaches to find polynomial time algorithms
Results 1 - 10
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92
