Proceedings Article10.1109/SFCS.1976.6
Approximation algorithms for some routing problems
Greg N. Frederickson,Matthew S. Hecht,Chul E. Kim +2 more
- 25 Oct 1976
- pp 216-227
335
TL;DR: Several polynomial time approximation algorithms for some NP-complete routing problems are presented, and the worst-case ratios of the cost of the obtained route to that of an optimal are determined.
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Abstract: Several polynomial time approximation algorithms for some NP-complete routing problems are presented, and the worst-case ratios of the cost of the obtained route to that of an optimal are determined. A mixed-strategy heuristic with a bound of 9/5 is presented for the Stacker-Crane problem (a modified Traveling Salesman problem). A tour-splitting heuristic is given for k-person variants of the Traveling Salesman problem, the Chinese Postman problem, and the Stacker-Crane problem, for which a minimax solution is sought. This heuristic has a bound of e + 1 - 1/k, where e is the bound for the corresponding 1-person algorithm.
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Citations
•Posted Content
Complexity Of Vehicle Routing And Scheduling Problems
Jan Karel Lenstra,A. H. G. Rinnooy Kan +1 more
- 01 Jan 1979
TL;DR: The complexity of a class of vehicle routing and scheduling problems is investigated and known NP-hardness results are reviewed and compiled to compile the worst-case performance of approximation algorithms.
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Computational complexity of discrete optimization problems
TL;DR: This paper gives an informal introduction to the theory of NP-completeness and derives some fundamental results, in the hope of stimulating further use of this valuable analytical tool.
Tour Planning for Mobile Data-Gathering Mechanisms in Wireless Sensor Networks
Ming Ma,Yuanyuan Yang,Miao Zhao +2 more
TL;DR: Simulation results demonstrate that the proposed data-gathering algorithm can greatly shorten the moving distance of the collectors compared with the covering line approximation algorithm and is close to the optimal algorithm for small networks.
263
•Journal Article
Approximation algorithms for the geometric covering salesman problem
Esther M. Arkin,Refael Hassin +1 more
TL;DR: In this article, the authors introduce a geometric version of the Covering Salesman Problem, in which each salesman's clients specify a neighborhood in which they are willing to meet the salesman.
260
References
Matching, euler tours and the chinese postman
Jack Edmonds,Ellis L. Johnson +1 more
TL;DR: The solution of the Chinese postman problem using matching theory is given and the convex hull of integer solutions is described as a linear programming polyhedron, used to show that a good algorithm gives an optimum solution.
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Oscar H. Ibarra,Chul Kim +1 more
TL;DR: An algorithm is presented which finds for any 0 < e < 1 an approximate solution P satisfying (P* P)/P* < ~, where P* is the desired optimal sum.
1K
Transformation of Multisalesman Problem to the Standard Traveling Salesman Problem
Mandell Bellmore,Saman Hong +1 more
TL;DR: It is shown that the multisalesmen problem can be solved by solving the standard traveling salesman problem on an expanded graph.
167
Approximate algorithms for the traveling salesperson problem
Daniel J. Rosenkrantz,Richard Edwin Stearns,P. M. Lewis +2 more
- 14 Oct 1974
TL;DR: Several polynomial time algorithms finding "good," but not necessarily optimal, tours for the traveling salesman problem are considered, and the worst case ratio of the obtained tour to the optimal tour is shown to increase logarithmically with the number of cities.