A note on the prize collecting traveling salesman problem
Mathematical Programming: Series A and B
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
A polylogarithmic approximation algorithm for the group Steiner tree problem
Journal of Algorithms
An approximation algorithm for the group Steiner problem
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Beyond Steiner's Problem: A VLSI Oriented Generalization
WG '89 Proceedings of the 15th International Workshop on Graph-Theoretic Concepts in Computer Science
Polylogarithmic inapproximability
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Transformations of generalized ATSP into ATSP
Operations Research Letters
Approximation Algorithms for Capacitated Location Routing
Transportation Science
Hi-index | 0.04 |
In this paper we develop approximation algorithms for generalizations of the following three known combinatorial optimization problems, the Prize-Collecting Steiner Tree problem, the Prize-Collecting Travelling Salesman Problem and a Location-Routing problem. Given a graph G=(V,E) on n vertices and a length function on its edges, in the grouped versions of the above mentioned problems we assume that V is partitioned into k+1 groups, {V"0,V"1,...,V"k}, with a penalty function on the groups. In the Group Prize-Collecting Steiner Tree problem the aim is to find S, a collection of groups of V and a tree spanning the rest of the groups not in S, so as to minimize the sum of the costs of the edges in the tree and the costs of the groups in S. The Group Prize-Collecting Travelling Salesman Problem, is defined analogously. In the Group Location-Routing problem the customer vertices are partitioned into groups and one has to select simultaneously a subset of depots to be opened and a collection of tours that covers the customer groups. The goal is to minimize the costs of the tours plus the fixed costs of the opened depots. We give a (2-1n-1)I-approximation algorithm for each of the three problems, where I is the cardinality of the largest group.