Distributed MST for constant diameter graphs

Z. Lotker; B. Patt-Shamir; D. Peleg

doi:10.1145/383962.383984

Distributed MST for constant diameter graphs

Z. Lotker, B. Patt-Shamir, D. Peleg

Tel Aviv University

Research output: Contribution to conference › Paper › peer-review

20 Scopus citations

Abstract

This paper considers the problem of distributively constructing a minimum-weight spanning tree (MST) for graphs of constant diameter in the bounded-messages model, where each message can contain at most B bits for some parameter B. It is shown that the time required to compute an MST for graphs of diameter 4 or 3 can be as high as Ω(3√n/B) and Ω(4√n/2√B), respectively. The lower bound holds even if the algorithm is allowed to be randomized. On the other hand, it is shown that O(log n) time units suffice to compute an MST deterministically for graphs with diameter 2, when B = O(log n). These results complement a previously known lower bound of Ω(2√n/B) for graphs of diameter Ω(log n).

Original language	English
Pages	63-71
Number of pages	9
DOIs	https://doi.org/10.1145/383962.383984
State	Published - 2001
Externally published	Yes
Event	20th Annual ACM Symposium on Principles of Distributed Computing - Newport, Rhode Island, United States Duration: 26 Aug 2001 → 29 Aug 2001

Conference

Conference	20th Annual ACM Symposium on Principles of Distributed Computing
Country/Territory	United States
City	Newport, Rhode Island
Period	26/08/01 → 29/08/01

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10.1145/383962.383984

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abstract = "This paper considers the problem of distributively constructing a minimum-weight spanning tree (MST) for graphs of constant diameter in the bounded-messages model, where each message can contain at most B bits for some parameter B. It is shown that the time required to compute an MST for graphs of diameter 4 or 3 can be as high as Ω(3√n/B) and Ω(4√n/2√B), respectively. The lower bound holds even if the algorithm is allowed to be randomized. On the other hand, it is shown that O(log n) time units suffice to compute an MST deterministically for graphs with diameter 2, when B = O(log n). These results complement a previously known lower bound of Ω(2√n/B) for graphs of diameter Ω(log n).",

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AB - This paper considers the problem of distributively constructing a minimum-weight spanning tree (MST) for graphs of constant diameter in the bounded-messages model, where each message can contain at most B bits for some parameter B. It is shown that the time required to compute an MST for graphs of diameter 4 or 3 can be as high as Ω(3√n/B) and Ω(4√n/2√B), respectively. The lower bound holds even if the algorithm is allowed to be randomized. On the other hand, it is shown that O(log n) time units suffice to compute an MST deterministically for graphs with diameter 2, when B = O(log n). These results complement a previously known lower bound of Ω(2√n/B) for graphs of diameter Ω(log n).

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Distributed MST for constant diameter graphs

Abstract

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