TY - GEN

T1 - Distributed algorithms for network diameter and girth

AU - Peleg, David

AU - Roditty, Liam

AU - Tal, Elad

PY - 2012

Y1 - 2012

N2 - This paper considers the problem of computing the diameter D and the girth g of an n-node network in the CONGEST distributed model. In this model, in each synchronous round, each vertex can transmit a different short (say, O(logn) bits) message to each of its neighbors. We present a distributed algorithm that computes the diameter of the network in O(n) rounds. We also present two distributed approximation algorithms. The first computes a 2/3 multiplicative approximation of the diameter in rounds. The second computes a 2∈-∈1/g multiplicative approximation of the girth in rounds. Recently, Frischknecht, Holzer and Wattenhofer [11] considered these problems in the CONGEST model but from the perspective of lower bounds. They showed an rounds lower bound for exact diameter computation. For diameter approximation, they showed a lower bound of rounds for getting a multiplicative approximation of. Both lower bounds hold for networks with constant diameter. For girth approximation, they showed a lower bound of rounds for getting a multiplicative approximation of on a network with constant girth. Our exact algorithm for computing the diameter matches their lower bound. Our diameter and girth approximation algorithms almost match their lower bounds for constant diameter and for constant girth.

AB - This paper considers the problem of computing the diameter D and the girth g of an n-node network in the CONGEST distributed model. In this model, in each synchronous round, each vertex can transmit a different short (say, O(logn) bits) message to each of its neighbors. We present a distributed algorithm that computes the diameter of the network in O(n) rounds. We also present two distributed approximation algorithms. The first computes a 2/3 multiplicative approximation of the diameter in rounds. The second computes a 2∈-∈1/g multiplicative approximation of the girth in rounds. Recently, Frischknecht, Holzer and Wattenhofer [11] considered these problems in the CONGEST model but from the perspective of lower bounds. They showed an rounds lower bound for exact diameter computation. For diameter approximation, they showed a lower bound of rounds for getting a multiplicative approximation of. Both lower bounds hold for networks with constant diameter. For girth approximation, they showed a lower bound of rounds for getting a multiplicative approximation of on a network with constant girth. Our exact algorithm for computing the diameter matches their lower bound. Our diameter and girth approximation algorithms almost match their lower bounds for constant diameter and for constant girth.

UR - http://www.scopus.com/inward/record.url?scp=84884186295&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-31585-5_58

DO - 10.1007/978-3-642-31585-5_58

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AN - SCOPUS:84884186295

SN - 9783642315848

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 660

EP - 672

BT - Automata, Languages, and Programming - 39th International Colloquium, ICALP 2012, Proceedings

PB - Springer Verlag

T2 - 39th International Colloquium on Automata, Languages, and Programming, ICALP 2012

Y2 - 9 July 2012 through 13 July 2012

ER -