Information Sciences: an International Journal
Approximation algorithms for the geometric covering salesman problem
Discrete Applied Mathematics
Approximation algorithms for geometric tour and network design problems (extended abstract)
Proceedings of the eleventh annual symposium on Computational geometry
Information Sciences: an International Journal
Approximation algorithms for TSP with neighborhoods in the plane
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Bi-directional and heuristic search in path problems
Bi-directional and heuristic search in path problems
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
A fast approximation algorithm for TSP with neighborhoods and red-blue separation
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Exact algorithms for generalized combinatorial optimization problems
COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
Contraction hierarchies: faster and simpler hierarchical routing in road networks
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
On trip planning queries in spatial databases
SSTD'05 Proceedings of the 9th international conference on Advances in Spatial and Temporal Databases
Exact graph search algorithms for generalized traveling salesman path problems
SEA'12 Proceedings of the 11th international conference on Experimental Algorithms
Engineering Generalized Shortest Path queries
ICDE '13 Proceedings of the 2013 IEEE International Conference on Data Engineering (ICDE 2013)
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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.