Transitions in geometric minimum spanning trees
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
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
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
A network-flow technique for finding low-weight bounded-degree spanning trees
Journal of Algorithms
Multicasting in heterogeneous networks
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
Improved Steiner tree approximation in graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
The freeze-tag problem: how to wake up a swarm of robots
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Introduction to Algorithms
Low-Degree Spanning Trees of Small Weight
SIAM Journal on Computing
A fast approximation algorithm for TSP with neighborhoods
Nordic Journal of Computing
Analysis of Heuristics for the Freeze-Tag Problem
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Improved approximation algorithms for the freeze-tag problem
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
Euclidean bounded-degree spanning tree ratios
Proceedings of the nineteenth annual symposium on Computational geometry
Some NP-complete geometric problems
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
Approximation algorithms for TSP with neighborhoods in the plane
Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
A New Multilayered PCP and the Hardness of Hypergraph Vertex Cover
SIAM Journal on Computing
On the complexity of approximating tsp with neighborhoods and related problems
Computational Complexity
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
A PTAS for TSP with neighborhoods among fat regions in the plane
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Rapid rumor ramification: approximating the minimum broadcast time
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
TSP with neighborhoods of varying size
Journal of Algorithms
Analysis of Christofides' heuristic: Some paths are more difficult than cycles
Operations Research Letters
| Hi-index | 5.23 |
In this paper we introduce and study cooperative variants of the Traveling Salesperson Problem. In these problems a salesperson has to make deliveries to customers who are willing to help in the process. Customer cooperativeness may be manifested in several modes: they may assist by approaching the salesperson, by reselling the goods they purchased to other customers, or by doing both. Several objectives are of interest: minimizing the total distance traveled by all of the participants, minimizing the maximal distance traveled by a participant and minimizing the total time until all of the deliveries are made. All of the combinations of cooperation modes and objective functions are considered, both in weighted undirected graphs and in Euclidean space. We show that most of the problems have a constant approximation algorithm, many of the others admit a PTAS, and a few are solvable in polynomial time. On the intractability side we provide NP-hardness proofs and inapproximability factors, some of which are tight.