Abstract
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 e (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 e (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.
Original language | English |
---|---|
Title of host publication | 32nd International Symposium on Distributed Computing, DISC 2018 |
Editors | Ulrich Schmid, Josef Widder |
Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |
ISBN (Electronic) | 9783959770927 |
DOIs | |
State | Published - 1 Oct 2018 |
Externally published | Yes |
Event | 32nd International Symposium on Distributed Computing, DISC 2018 - New Orleans, United States Duration: 15 Oct 2018 → 19 Oct 2018 |
Publication series
Name | Leibniz International Proceedings in Informatics, LIPIcs |
---|---|
Volume | 121 |
ISSN (Print) | 1868-8969 |
Conference
Conference | 32nd International Symposium on Distributed Computing, DISC 2018 |
---|---|
Country/Territory | United States |
City | New Orleans |
Period | 15/10/18 → 19/10/18 |
Bibliographical note
Publisher Copyright:© Merav Parter and Eylon Yogev.
Keywords
- And phrases Distributed Graph Algorithms
- Congested Clique
- Spanner