TY - GEN
T1 - Fast approximate shortest paths in the congested clique
AU - Censor-Hillel, Keren
AU - Dory, Michal
AU - Korhonen, Janne H.
AU - Leitersdorf, Dean
N1 - Publisher Copyright: © 2019 ACM.
PY - 2019/7/16
Y1 - 2019/7/16
N2 - We design fast deterministic algorithms for distance computation in the CONGESTED CLIQUE model. Our key contributions include: A (2+)-approximation for all-pairs shortest paths problem in O(log2n / ) rounds on unweighted undirected graphs. With a small additional additive factor, this also applies for weighted graphs. This is the first sub-polynomial constant-factor approximation for APSP in this model. A (1+)-approximation for multi-source shortest paths problem from O(n) sources in O(log2 n / ) rounds on weighted undirected graphs. This is the first sub-polynomial algorithm obtaining this approximation for a set of sources of polynomial size. Our main techniques are new distance tools that are obtained via improved algorithms for sparse matrix multiplication, which we leverage to construct efficient hopsets and shortest paths. Furthermore, our techniques extend to additional distance problems for which we improve upon the state-of-the-art, including diameter approximation, and an exact single-source shortest paths algorithm for weighted undirected graphs in (n1/6) rounds.
AB - We design fast deterministic algorithms for distance computation in the CONGESTED CLIQUE model. Our key contributions include: A (2+)-approximation for all-pairs shortest paths problem in O(log2n / ) rounds on unweighted undirected graphs. With a small additional additive factor, this also applies for weighted graphs. This is the first sub-polynomial constant-factor approximation for APSP in this model. A (1+)-approximation for multi-source shortest paths problem from O(n) sources in O(log2 n / ) rounds on weighted undirected graphs. This is the first sub-polynomial algorithm obtaining this approximation for a set of sources of polynomial size. Our main techniques are new distance tools that are obtained via improved algorithms for sparse matrix multiplication, which we leverage to construct efficient hopsets and shortest paths. Furthermore, our techniques extend to additional distance problems for which we improve upon the state-of-the-art, including diameter approximation, and an exact single-source shortest paths algorithm for weighted undirected graphs in (n1/6) rounds.
KW - All-pairs shortest paths
KW - Congested clique
KW - Diameter
KW - Distributed computing
KW - Hopsets
KW - Matrix multiplication
KW - Single-source shortest paths
KW - approximation algorithms
UR - http://www.scopus.com/inward/record.url?scp=85070984640&partnerID=8YFLogxK
U2 - 10.1145/3293611.3331633
DO - 10.1145/3293611.3331633
M3 - منشور من مؤتمر
T3 - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing
SP - 74
EP - 83
BT - PODC 2019 - Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing
T2 - 38th ACM Symposium on Principles of Distributed Computing, PODC 2019
Y2 - 29 July 2019 through 2 August 2019
ER -