TY - GEN

T1 - Fast partial distance estimation and applications

AU - Lenzen, Christoph

AU - Patt-Shamir, Boaz

N1 - Publisher Copyright:
© Copyright 2015 ACM.

PY - 2015/7/21

Y1 - 2015/7/21

N2 - We study approximate distributed solutions to the weighted all-pairs-shortest-paths (APSP) problem in the CONGEST model. We obtain the following results. A deterministic (1 + ε)-approximation to APSP with running time O(ε-2nlogn) rounds. The best previously known algorithm was randomized and slower by a (log n) factor. In many cases, routing schemes involve relabeling, i.e., assigning new names to nodes and that are used in distance and routing queries. It is known that relabeling is necessary to achieve running times of o(n/ log n). In the relabeling model, we obtain the following results. A randomized O(k)-approximation to APSP, for any inateger k > 1, running in O(n1/2+1/k + D) rounds, where D is the hop diameter of the network. This algorithm simplifies the best previously known result and reduces its approximaation ratio from O(k log k) to O(k). Also, the new algorithm uses O(logn)-bit labels, which is asymptotically optimal. A randomized O(k)-approximation to APSP, for any integer k > 1, running in time O((nD)1/2 • n1/k + D) and producing compact routing tables of size labels consist of O(k log n) bits. This improves on the apaproximation ratio of (k2) for tables of that size achieved by the best previously known algorithm, which terminates faster, in O(n1/2+1/k + D) rounds. In addition, we improve on the time complexity of the best known deterministic algorithm for distributed approximate Steiner forest.

AB - We study approximate distributed solutions to the weighted all-pairs-shortest-paths (APSP) problem in the CONGEST model. We obtain the following results. A deterministic (1 + ε)-approximation to APSP with running time O(ε-2nlogn) rounds. The best previously known algorithm was randomized and slower by a (log n) factor. In many cases, routing schemes involve relabeling, i.e., assigning new names to nodes and that are used in distance and routing queries. It is known that relabeling is necessary to achieve running times of o(n/ log n). In the relabeling model, we obtain the following results. A randomized O(k)-approximation to APSP, for any inateger k > 1, running in O(n1/2+1/k + D) rounds, where D is the hop diameter of the network. This algorithm simplifies the best previously known result and reduces its approximaation ratio from O(k log k) to O(k). Also, the new algorithm uses O(logn)-bit labels, which is asymptotically optimal. A randomized O(k)-approximation to APSP, for any integer k > 1, running in time O((nD)1/2 • n1/k + D) and producing compact routing tables of size labels consist of O(k log n) bits. This improves on the apaproximation ratio of (k2) for tables of that size achieved by the best previously known algorithm, which terminates faster, in O(n1/2+1/k + D) rounds. In addition, we improve on the time complexity of the best known deterministic algorithm for distributed approximate Steiner forest.

KW - Congest model

KW - Routing table construction

KW - Source detection

KW - Steiner forests

KW - Weighted all-pairs shortest paths

UR - http://www.scopus.com/inward/record.url?scp=84957666208&partnerID=8YFLogxK

U2 - 10.1145/2767386.2767398

DO - 10.1145/2767386.2767398

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:84957666208

T3 - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

SP - 153

EP - 162

BT - PODC 2015 - Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing

PB - Association for Computing Machinery

Y2 - 21 July 2015 through 23 July 2015

ER -