eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-10-12
24:1
24:16
10.4230/LIPIcs.DISC.2017.24
article
Improved Deterministic Distributed Construction of Spanners
Grossman, Ofer
Parter, Merav
Graph spanners are fundamental graph structures with a wide range of applications in distributed networks. We consider a standard synchronous message passing model where in each round O(log n) bits can be transmitted over every edge (the CONGEST model).
The state of the art of deterministic distributed spanner constructions suffers from large messages. The only exception is the work of Derbel et al., which computes an optimal-sized (2k-1)-spanner but uses O(n^(1-1/k)) rounds.
In this paper, we significantly improve this bound. We present a deterministic distributed algorithm that given an unweighted n-vertex graph G = (V,E) and a parameter k > 2, constructs a (2k-1)-spanner with O(k n^(1+1/k)) edges within O(2^k n^(1/2 - 1/k)) rounds for every even k. For odd k, the number of rounds is O(2^k n^(1/2 - 1/(2k))). For the weighted case, we provide the first deterministic construction of a 3-spanner with O(n^(3/2)) edges that uses O(log n)-size messages and ~O(1) rounds. If the vertices have IDs in [1,Theta(n)], the spanner is computed in only 2 rounds!
https://drops.dagstuhl.de/storage/00lipics/lipics-vol091-disc2017/LIPIcs.DISC.2017.24/LIPIcs.DISC.2017.24.pdf
spanners
clustering
deterministic algorithms
congest model