When Trees Collide: An Approximation Algorithm for theGeneralized Steiner Problem on Networks
SIAM Journal on Computing
A threshold of ln n for approximating set cover (preliminary version)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Improved low-degree testing and its applications
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Rounding via trees: deterministic approximation algorithms for group Steiner trees and k-median
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Bicriteria network design problems
Journal of Algorithms
Improved solutions for the traveling purchaser problem
Computers and Operations Research
A polylogarithmic approximation algorithm for the group Steiner tree problem
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Optimizing a mail-order with discount and shipping costs
Information Processing Letters
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
Budget Constrained Minimum Cost Connected Medians
WG '00 Proceedings of the 26th International Workshop on Graph-Theoretic Concepts in Computer Science
Improved heuristics for the traveling purchaser problem
Computers and Operations Research
On the approximability of some network design problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation via cost sharing: Simpler and better approximation algorithms for network design
Journal of the ACM (JACM)
Approximating connected facility location problems via random facility sampling and core detouring
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
On the approximability of some network design problems
ACM Transactions on Algorithms (TALG)
The traveling purchaser problem with budget constraint
Computers and Operations Research
Pricing tree access networks with connected backbones
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Connected facility location via random facility sampling and core detouring
Journal of Computer and System Sciences
Tree embeddings for two-edge-connected network design
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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The traveling purchaser problem is a generalization of the traveling salesman problem with applications in a wide range of areas including network design and scheduling. The input consists of a set of markets and a set of products. Each market offers a price for each product and there is a cost associated with traveling from one market to another. The problem is to purchase all products by visiting a subset of the markets in a tour such that the total travel and purchase costs are minimized. This problem includes many well-known NP-hard problems such as uncapacitated facility location, set cover and group Steiner tree problems as its special cases.We give an approximation algorithm with a poly-logarithmic worst-case ratio for the traveling purchaser problem with metric travel costs. For a special case of the problem that models the ring-star network design problem, we give a constantfactor approximation algorithm. Our algorithms are based on rounding LP relaxation solutions.