eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-10-04
40:1
40:18
10.4230/LIPIcs.DISC.2018.40
article
Congested Clique Algorithms for Graph Spanners
Parter, Merav
1
Yogev, Eylon
1
Weizmann IS, Rehovot, Israel
Graph spanners are sparse subgraphs that faithfully preserve the distances in the original graph up to small stretch. Spanner have been studied extensively as they have a wide range of applications ranging from distance oracles, labeling schemes and routing to solving linear systems and spectral sparsification. A k-spanner maintains pairwise distances up to multiplicative factor of k. It is a folklore that for every n-vertex graph G, one can construct a (2k-1) spanner with O(n^{1+1/k}) edges. In a distributed setting, such spanners can be constructed in the standard CONGEST model using O(k^2) rounds, when randomization is allowed.
In this work, we consider spanner constructions in the congested clique model, and show:
- a randomized construction of a (2k-1)-spanner with O~(n^{1+1/k}) edges in O(log k) rounds. The previous best algorithm runs in O(k) rounds;
- a deterministic construction of a (2k-1)-spanner with O~(n^{1+1/k}) edges in O(log k +(log log n)^3) rounds. The previous best algorithm runs in O(k log n) rounds. This improvement is achieved by a new derandomization theorem for hitting sets which might be of independent interest;
- a deterministic construction of a O(k)-spanner with O(k * n^{1+1/k}) edges in O(log k) rounds.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol121-disc2018/LIPIcs.DISC.2018.40/LIPIcs.DISC.2018.40.pdf
Distributed Graph Algorithms
Spanner
Congested Clique