# On efficient distributed construction of near optimal routing schemes

On efficient distributed construction of near optimal routing schemes Given a distributed network represented by a weighted undirected graph $$G=(V,E)$$ G = ( V , E ) on n vertices, and a parameter k, we devise a randomized distributed algorithm that whp computes a routing scheme in $$O(n^{1/2+1/k}+D)\cdot n^{o(1)}$$ O ( n 1 / 2 + 1 / k + D ) · n o ( 1 ) rounds, where D is the hop-diameter of the network. Moreover, for odd k, the running time of our algorithm is $$O(n^{1/2 + 1/(2k)} + D) \cdot n^{o(1)}$$ O ( n 1 / 2 + 1 / ( 2 k ) + D ) · n o ( 1 ) . Our running time nearly matches the lower bound of $$\tilde{\Omega }(n^{1/2}+D)$$ Ω ~ ( n 1 / 2 + D ) rounds (which holds for any scheme with polynomial stretch). The routing tables are of size $$\tilde{O}(n^{1/k})$$ O ~ ( n 1 / k ) , the labels are of size $$O(k\log ^2n)$$ O ( k log 2 n ) , and every packet is routed on a path suffering stretch at most $$4k-5+o(1)$$ 4 k - 5 + o ( 1 ) . Our construction nearly matches the state-of-the-art for routing schemes built in a centralized sequential manner. The previous best algorithms for building routing tables in a distributed small messages model were by Lenzen and Patt-Shamir (In: Symposium on theory of computing conference, STOC’13, Palo Alto, CA, USA, 2013) and Lenzen and Patt-Shamir (In: Proceedings of the 2015 ACM symposium on principles of distributed computing, PODC 2015, Donostia-San Sebastián, Spain, 2015). The former has similar properties but suffers from substantially larger routing tables of size $$O(n^{1/2+1/k})$$ O ( n 1 / 2 + 1 / k ) , while the latter has sub-optimal running time of $$\tilde{O}(\min \{(nD)^{1/2}\cdot n^{1/k},n^{2/3+2/(3k)}+D\})$$ O ~ ( min { ( n D ) 1 / 2 · n 1 / k , n 2 / 3 + 2 / ( 3 k ) + D } ) . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Distributed Computing Springer Journals

# On efficient distributed construction of near optimal routing schemes

, Volume 31 (2) – Jun 1, 2017
19 pages

/lp/springer_journal/on-efficient-distributed-construction-of-near-optimal-routing-schemes-iyhgEqOIRz
Publisher
Springer Journals
Copyright © 2017 by Springer-Verlag Berlin Heidelberg
Subject
Computer Science; Computer Communication Networks; Computer Hardware; Computer Systems Organization and Communication Networks; Software Engineering/Programming and Operating Systems; Theory of Computation
ISSN
0178-2770
eISSN
1432-0452
D.O.I.
10.1007/s00446-017-0304-4
Publisher site
See Article on Publisher Site

### Abstract

Given a distributed network represented by a weighted undirected graph $$G=(V,E)$$ G = ( V , E ) on n vertices, and a parameter k, we devise a randomized distributed algorithm that whp computes a routing scheme in $$O(n^{1/2+1/k}+D)\cdot n^{o(1)}$$ O ( n 1 / 2 + 1 / k + D ) · n o ( 1 ) rounds, where D is the hop-diameter of the network. Moreover, for odd k, the running time of our algorithm is $$O(n^{1/2 + 1/(2k)} + D) \cdot n^{o(1)}$$ O ( n 1 / 2 + 1 / ( 2 k ) + D ) · n o ( 1 ) . Our running time nearly matches the lower bound of $$\tilde{\Omega }(n^{1/2}+D)$$ Ω ~ ( n 1 / 2 + D ) rounds (which holds for any scheme with polynomial stretch). The routing tables are of size $$\tilde{O}(n^{1/k})$$ O ~ ( n 1 / k ) , the labels are of size $$O(k\log ^2n)$$ O ( k log 2 n ) , and every packet is routed on a path suffering stretch at most $$4k-5+o(1)$$ 4 k - 5 + o ( 1 ) . Our construction nearly matches the state-of-the-art for routing schemes built in a centralized sequential manner. The previous best algorithms for building routing tables in a distributed small messages model were by Lenzen and Patt-Shamir (In: Symposium on theory of computing conference, STOC’13, Palo Alto, CA, USA, 2013) and Lenzen and Patt-Shamir (In: Proceedings of the 2015 ACM symposium on principles of distributed computing, PODC 2015, Donostia-San Sebastián, Spain, 2015). The former has similar properties but suffers from substantially larger routing tables of size $$O(n^{1/2+1/k})$$ O ( n 1 / 2 + 1 / k ) , while the latter has sub-optimal running time of $$\tilde{O}(\min \{(nD)^{1/2}\cdot n^{1/k},n^{2/3+2/(3k)}+D\})$$ O ~ ( min { ( n D ) 1 / 2 · n 1 / k , n 2 / 3 + 2 / ( 3 k ) + D } ) .

### Journal

Distributed ComputingSpringer Journals

Published: Jun 1, 2017

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