Near-linear cost sequential and distributed constructions of sparse neighborhood covers

Authors:
B. Awerbuch;B. Berger;L. Cowen;D. Peleg
Affiliations:
Lab. for Comput. Sci., MIT, Cambridge, MA, USA;Lab. for Comput. Sci., MIT, Cambridge, MA, USA;Lab. for Comput. Sci., MIT, Cambridge, MA, USA;-
Venue:
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Year:
1993

Citing 0
Cited 9

Estimating All Pairs Shortest Paths in Restricted Graph Families: A Unified Approach

WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
Fast deterministic distributed algorithms for sparse spanners

Theoretical Computer Science
Fault-tolerant spanners for general graphs

Proceedings of the forty-first annual ACM symposium on Theory of computing
Estimating all pairs shortest paths in restricted graph families: a unified approach

Journal of Algorithms
Fault Tolerant Spanners for General Graphs

SIAM Journal on Computing
Navigating in a Graph by Aid of Its Spanning Tree Metric

SIAM Journal on Discrete Mathematics
Fast deterministic distributed algorithms for sparse spanners

SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Deterministic distributed construction of linear stretch spanners in polylogarithmic time

DISC'07 Proceedings of the 21st international conference on Distributed Computing
Multipath spanners via fault-tolerant spanners

MedAlg'12 Proceedings of the First Mediterranean conference on Design and Analysis of Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper introduces the first near-linear (specifically, O(Elog n+nlog/sup 2/ n)) time algorithm for constructing a sparse neighborhood cover in sequential and distributed environments. This automatically implies analogous improvements (from quadratic to near-linear) to all the results in the literature that rely on network decompositions, both in sequential and distributed domains, including adaptive routing schemes with O/spl tilde/(1) stretch and memory, small edge cuts in planar graphs, sequential algorithms for dynamic approximate shortest paths with O/spl tilde/(E) cost for edge insertion/deletion and O/spl tilde/(1) time to answer shortest-path queries, weight and distance-preserving graph spanners with O/spl tilde/(E) running time and space, and distributed asynchronous "from-scratch" breadth-first-search and network synchronizer constructions with O/spl tilde/(1) message and space overhead (down from O(n)).