Parameterized algorithms for generalized traveling salesman problems in road networks
- 5 November 2013
- conference paper
- conference paper
- Published by Association for Computing Machinery (ACM) in Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Abstract
The Generalized Traveling Salesman (Path) Problem involves finding a minimum-cost tour (or path) through exactly one location from each of a set of generalized location categories (e.g., gas stations, coffee shops). This problem type has many practical applications in personal navigation and logistics. While NP-hard in general, this problem also admits fixed-parameter tractable (FPT) algorithms with run times of the form f(k)nO(1) for some function f (independent of the problem size, n) with respect to the number of location categories, k (typically very small in practice). We present both exact and approximate FPT algorithms for this problem. Experimental results on the road network of North America (with over 50 million edges) show that we can optimally solve nationwide queries with up to 7 categories and millions of optional category locations in sub-second time. Our approximate solutions improve this even further down to millisecond query times, resulting in only negligible relative error with respect to optimality, on average.Keywords
Funding Information
- Division of Information and Intelligent Systems (IIS-1161997)
This publication has 21 references indexed in Scilit:
- A multistart heuristic for the equality generalized traveling salesman problemNetworks, 2010
- Contraction Hierarchies: Faster and Simpler Hierarchical Routing in Road NetworksPublished by Springer Science and Business Media LLC ,2008
- Exact Algorithms for Generalized Combinatorial Optimization ProblemsLecture Notes in Computer Science, 2007
- A random-key genetic algorithm for the generalized traveling salesman problemEuropean Journal of Operational Research, 2006
- On the Complexity of Approximating TSP with Neighborhoods and Related ProblemsLecture Notes in Computer Science, 2003
- An efficient transformation of the generalized traveling salesman problem into the traveling salesman problem on digraphsInformation Sciences, 1997
- Approximation algorithms for the geometric covering salesman problemDiscrete Applied Mathematics, 1994
- Transformation of the generalized traveling-salesman problem into the standard traveling-salesman problemInformation Sciences, 1993
- Generalized travelling salesman problem through n sets of nodes: the asymmetrical caseDiscrete Applied Mathematics, 1987
- A note on two problems in connexion with graphsNumerische Mathematik, 1959