An optimal synchronizer for the hypercube
PODC '87 Proceedings of the sixth annual ACM Symposium on Principles of distributed computing
On sparse spanners of weighted graphs
Discrete & Computational Geometry
SIAM Journal on Discrete Mathematics
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
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the Hardness of Approximation Spanners
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
Cost, Delay, and Delay Variation Conscious Multicast Routing
Cost, Delay, and Delay Variation Conscious Multicast Routing
Multicast routing with end-to-end delay and delay variation constraints
IEEE Journal on Selected Areas in Communications
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For any fixed parameter k ≥ 1, a tree k-spanner of a graph G is a spanning tree T in G such that the distance between every pair of vertices in T is at most k times their distance in G. In this paper, we generalize on this very restrictive concept, and introduce Steiner tree k-spanners: We are given an input graph consisting of terminals and Steiner vertices, and we are now looking for a tree k-spanner that spans all terminals. The complexity status of deciding the existence of a Steiner tree k- spanner is easy for some k: it is NP-hard for k ≥ 4, and it is in P for k = 1. For the case k = 2, we develop a model in terms of an equivalent tree covering problem, and use this to show NP-hardness. By showing the NP-hardness also for the case k = 3, the complexity results for all k are complete. We also consider the problem of finding a smallest Steiner tree k-spanner (if one exists at all). For any arbitrary k ≥ 2, we prove that we cannot hope to find efficiently a Steiner tree k-spanner that is closer to the smallest one than within a logarithmic factor. We conclude by discussing some problems related to the model for the case k = 2.