TY - JOUR

T1 - Tight Bounds for Distributed Minimum-Weight Spanning Tree Verification

AU - Kor, Liah

AU - Korman, Amos

AU - Peleg, David

N1 - United States-Israel Binational Science Foundation (BSF); ANR project DISPLEXITY; INRIA project GANGL.K. and D. P. are supported by a grant from the United States-Israel Binational Science Foundation (BSF).A.K. is supported by the ANR project DISPLEXITY, and by the INRIA project GANG.

PY - 2013/8

Y1 - 2013/8

N2 - This paper introduces the notion of distributed verification without preprocessing. It focuses on the Minimum-weight Spanning Tree (MST) verification problem and establishes tight upper and lower bounds for the time and message complexities of this problem. Specifically, we provide an MST verification algorithm that achieves simultaneously messages and time, where m is the number of edges in the given graph G, n is the number of nodes, and D is G's diameter. On the other hand, we show that any MST verification algorithm must send messages and incur time in worst case. Our upper bound result appears to indicate that the verification of an MST may be easier than its construction, since for MST construction, both lower bounds of messages and time hold, but at the moment there is no known distributed algorithm that constructs an MST and achieves simultaneously messages and time. Specifically, the best known time-optimal algorithm (using time) requires O(m+n (3/2)) messages, and the best known message-optimal algorithm (using messages) requires O(n) time. On the other hand, our lower bound results indicate that the verification of an MST is not significantly easier than its construction.

AB - This paper introduces the notion of distributed verification without preprocessing. It focuses on the Minimum-weight Spanning Tree (MST) verification problem and establishes tight upper and lower bounds for the time and message complexities of this problem. Specifically, we provide an MST verification algorithm that achieves simultaneously messages and time, where m is the number of edges in the given graph G, n is the number of nodes, and D is G's diameter. On the other hand, we show that any MST verification algorithm must send messages and incur time in worst case. Our upper bound result appears to indicate that the verification of an MST may be easier than its construction, since for MST construction, both lower bounds of messages and time hold, but at the moment there is no known distributed algorithm that constructs an MST and achieves simultaneously messages and time. Specifically, the best known time-optimal algorithm (using time) requires O(m+n (3/2)) messages, and the best known message-optimal algorithm (using messages) requires O(n) time. On the other hand, our lower bound results indicate that the verification of an MST is not significantly easier than its construction.

KW - Distributed algorithms

KW - Distributed verification

KW - Labeling schemes

KW - Minimum-weight spanning tree

UR - http://www.scopus.com/inward/record.url?scp=84878805675&partnerID=8YFLogxK

U2 - https://doi.org/10.1007/s00224-013-9479-7

DO - https://doi.org/10.1007/s00224-013-9479-7

M3 - مقالة

SN - 1432-4350

VL - 53

SP - 318

EP - 340

JO - Theory of Computing Systems

JF - Theory of Computing Systems

IS - 2

ER -