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
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
Approximation algorithms for TSP with neighborhoods in the plane
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Space-efficient approximate Voronoi diagrams
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Introduction to Algorithms
A fast approximation algorithm for TSP with neighborhoods
Nordic Journal of Computing
Polynomial time approximation schemes for Euclidean TSP and other geometric problems
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
A Replacement for Voronoi Diagrams of Near Linear Size
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
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
Improved Approximation Algorithms for Relay Placement
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Survey: A survey on relay placement with runtime and approximation guarantees
Computer Science Review
Hi-index | 0.00 |
We consider a natural generalization of the classical minimum spanning tree problem called Minimum Spanning Tree with Neighborhoods (MSTN)which seeks a tree of minimum length to span a set of 2D regions called neighborhoods. Each neighborhood contributes exact one node to the tree, and the MSTN has the minimum total length among all possible trees spanning the set of nodes. We prove the NP-hardness of this problem for the case in which the neighborhoods are a set of disjoint discs and rectangles. When the regions considered are a set of disjoint 2D unit discs, we present the following approximation results: (1) A simple algorithm that achieves an approximation ratio of 7.4; (2) Lower bounds and two 3-approximation algorithms; (3) A PTAS for this problem. Our algorithms can be easily generalized to higher dimensions.