Minimum diameter spanning trees and related problems
SIAM Journal on Computing
Designing multi-commodity flow trees
Information Processing Letters
A Graph-Theoretic Game and its Application to the $k$-Server Problem
SIAM Journal on 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
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Steiner points in tree metrics don't (really) help
SODA '01 Proceedings of the twelfth 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
Deterministic Polylog Approximation for Minimum Communication Spanning Trees
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
On the minimum diameter spanning tree problem
Information Processing Letters
Approximating Minimum Max-Stretch spanning Trees on unweighted graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
The zoo of tree spanner problems
Discrete Applied Mathematics
Approximating buy-at-bulk and shallow-light k-Steiner trees
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
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Let G = (V, E) be a requirements graph. Let d = (dij)i,j=1n be a length metric. For a tree T denote by dT (i,j) the distance between i and j in T (the length according to d of the unique i - j path in T). The restricted diameter of T, DT, is the maximum distance in T between pair of vertices with requirement between them. The minimum restricted diameter spanning tree problem is to find a spanning tree T such that the minimum restricted diameter is minimized. We prove that the minimum restricted diameter spanning tree problem is NP- hard and that unless P = NP there is no polynomial time algorithm with performance guarantee of less than 2. In the case that G contains isolated vertices and the length matrix is defined by distances over a tree we prove that there exist a tree over the non-isolated vertices such that its restricted diameter is at most 4 times the minimum restricted diameter and that this constant is at least 3 1/2. We use this last result to present an O(log(n))-approximation algorithm.