Journal Article10.1007/BF02523691
AnO(logk)-approximation algorithm for thek minimum spanning tree problem in the plane
Naveen Garg,Dorit S. Hochbaum +1 more
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TL;DR: The problem of finding the minimum tree spanning anyk points in the Euclidean plane is NP-hard and the anO(logk)-approximation algorithm is given.
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Abstract: Givenn points in the Euclidean plane, we consider the problem of finding the minimum tree spanning anyk points. The problem isNP-hard and we give anO(logk)-approximation algorithm.
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Citations
New metaheuristic approaches for the edge-weighted k -cardinality tree problem
Christian Blum,Maria J. Blesa +1 more
TL;DR: Three metaheuristic approaches are proposed, namely a Tabu Search, an Evolutionary Computation and an Ant Colony Optimization approach, for the edge-weighted k-cardinality tree (KCT) problem, an NP-hard combinatorial optimization problem that generalizes the well-known minimum weight spanning tree problem.
89
An annotated bibliography of combinatorial optimization problems with fixed cardinality constraints
Maurizio Bruglieri,Matthias Ehrgott,Horst W. Hamacher,Francesco Maffioli +3 more
- 01 Jun 2006
TL;DR: This paper formally defines the problem, mentions some examples and summarizes general results, and provides an annotated bibliography of combinatorial optimization problems of which versions with cardinality constraint have been considered in the literature.
74
A hybrid algorithm based on tabu search and ant colony optimization for k-minimum spanning tree problems
TL;DR: An efficient approximate algorithm for solving k-minimum spanning tree problems which is one of the combinatorial optimization in networks and a new hybrid algorithm based on tabu search and ant colony optimization is provided.
48
Local search algorithms for the k -cardinality tree problem
Christian Blum,Matthias Ehrgott +1 more
TL;DR: This paper proves that under the condition that the graph contains exactly one trough, the k-cardinality tree problem in node-weighted graphs can be solved in polynomial time.
32
Revisiting dynamic programming for finding optimal subtrees in trees
TL;DR: An existing dynamic programming algorithm for finding optimal subtrees in edge weighted trees is revisit and the proposed heuristics reach the performance of state-of-the-art metaheuristics for the k-cardinality tree problem in undirected graphs G with node and edge weights.
31
References
•Posted Content
Spanning trees short or small
TL;DR: It is shown that the kMST problem is NP-hard even for points in the Euclidean plane, and a simple technique is used to provide a polynomiM-time solution for finding k-trees of minimum diameter.
Weighted k-cardinality trees: complexity and polyhedral structure
TL;DR: An integer programming formulation of k-CARD TREE and an efficient exact separation routine for a set of generalized subtour elimination constraints are given and the polyhedral structure of the convex hull of the integer solutions is studied.
141
Guillotine subdivisions approximate polygonal subdivisions: a simple new method for the geometric k-MST problem
Joseph S. B. Mitchell
- 28 Jan 1996
TL;DR: A consequence of the main theorem is a very simple proof that the k-MST problem in the plane has a constant factor polynomial-time approximation algorithm, and the constant factor that is obtained is a substantial improvement over all previous bounds.
85
Improved approximation guarantees for minimum-weight k-trees and prize-collecting salesmen
Baruch Awerbuch,Yossi Azar,Avrim Blum,Santosh Vempala +3 more
- 29 May 1995
TL;DR: This paper gives the first approximation algorithms with poly-logarithmic performance guarantees for the k-MST problem, as well as for the slightly more general PCTSP problem of Balas, and a variation the authors call the "bank-robber problem".
78
Facility dispersion problems: Heuristics and special cases
S. S. Ravi,Daniel J. Rosenkrantz,Giri Kumar Tayi +2 more
- 14 Aug 1991
TL;DR: In this paper, the authors considered the problem under two different optimality criteria, namely, maximizing the minimum distance between any pair of facilities and maximizing the average distance (MAX-AVG) between any pairs of facilities.
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