TY - GEN

T1 - Deterministic distributed construction of linear stretch spanners in polylogarithmic time

AU - Derbel, Bilel

AU - Gavoille, Cyril

AU - Peleg, David

PY - 2007

Y1 - 2007

N2 - The paper presents a deterministic distributed algorithm that given an n node unweighted graph constructs an O(n3/2) edge 3-spanner for it in O(log n) time. This algorithm is then extended into a deterministic algorithm for computing an O(kn1+1/k) edge O(k)-spanner in 2O(k) logk-1 n time for every integer parameter k ≥ 1. This establishes that the problem of the deterministic construction of a linear (in k) stretch spanner with few edges can be solved in the distributed setting in polylogarithmic time. The paper also investigates the distributed construction of sparse spanners with almost pure additive stretch (1 + ε, β), i.e., such that the distance in the spanner is at most 1 + ε times the original distance plus β. It is shown, for every ε > 0, that in O(ε-1 log n) time one can deterministically construct a spanner with O(n3/2) edges that is both a 3-spanner and a (1 + ε, 8 log n)-spanner. Furthermore, it is shown that in nO(1/√log n) + O(1/ε) time one can deterministically construct a spanner with O(n 3/2) edges which is both a 3-spanner and a (1 + ε, 4)-spanner. This algorithm can be transformed into a Las Vegas randomized algorithm with guarantees on the stretch and time, running in O(ε-1 +log n) expected time.

AB - The paper presents a deterministic distributed algorithm that given an n node unweighted graph constructs an O(n3/2) edge 3-spanner for it in O(log n) time. This algorithm is then extended into a deterministic algorithm for computing an O(kn1+1/k) edge O(k)-spanner in 2O(k) logk-1 n time for every integer parameter k ≥ 1. This establishes that the problem of the deterministic construction of a linear (in k) stretch spanner with few edges can be solved in the distributed setting in polylogarithmic time. The paper also investigates the distributed construction of sparse spanners with almost pure additive stretch (1 + ε, β), i.e., such that the distance in the spanner is at most 1 + ε times the original distance plus β. It is shown, for every ε > 0, that in O(ε-1 log n) time one can deterministically construct a spanner with O(n3/2) edges that is both a 3-spanner and a (1 + ε, 8 log n)-spanner. Furthermore, it is shown that in nO(1/√log n) + O(1/ε) time one can deterministically construct a spanner with O(n 3/2) edges which is both a 3-spanner and a (1 + ε, 4)-spanner. This algorithm can be transformed into a Las Vegas randomized algorithm with guarantees on the stretch and time, running in O(ε-1 +log n) expected time.

KW - Distributed algorithms

KW - Graph spanners

KW - Time complexity

UR - http://www.scopus.com/inward/record.url?scp=38049086308&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-75142-7_16

DO - 10.1007/978-3-540-75142-7_16

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AN - SCOPUS:38049086308

SN - 9783540751410

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

SP - 179

EP - 192

BT - Distributed Computing - 21st International Symposium, DISC 2007, Proceedings

PB - Springer Verlag

T2 - 21st International Symposium on Distributed Computing, DISC 2007

Y2 - 24 September 2007 through 26 September 2007

ER -