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Greedy distributed optimization of unsplittable multicommodity flows

Published: 18 August 2008 Publication History

Abstract

We consider solutions for distributed unsplittable multicommodity flow problems, which are solved by multiple agents operating in a cooperative but uncoordinated manner. A requirement here is that each commodity routes its entire demand along a single path at any point in time. Assuming that the minimum capacity of any edge is at least polylogarithmic factor larger than the maximum demand of any commodity, we present a greedy distributed randomized algorithm, which with high probability, achieves 1+ε approximation, in O(H · logO(1)) m · (1/ε)0(1)) iterations where Hn is an upper bound on the number edges allowed on any flow-path. No prior results exist for our distributed model.
Our algorithm is based on simulating the splittable multicommodity flow solution of [1] and picking a path for routing the entire flow according to the probability distribution given by the splittable flow. We use Chernoff bounds to show that the real edge-congestions are sufficiently close to the edge-congestions in the simulation for the analysis of [1] to hold.

Reference

[1]
B. Awerbuch and R. Khandekar. Greedy Distributed Optimization of Multicommodity Flows. PODC, 2007.

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  • (2023)Maximum Length-Constrained Flows and Disjoint Paths: Distributed, Deterministic, and FastProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585202(1371-1383)Online publication date: 2-Jun-2023

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  1. Greedy distributed optimization of unsplittable multicommodity flows

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    cover image ACM Conferences
    PODC '08: Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
    August 2008
    474 pages
    ISBN:9781595939890
    DOI:10.1145/1400751
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    Publication History

    Published: 18 August 2008

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    Author Tags

    1. distributed
    2. multicommodity flows
    3. unsplittable

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    Overall Acceptance Rate 740 of 2,477 submissions, 30%

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    • (2023)Maximum Length-Constrained Flows and Disjoint Paths: Distributed, Deterministic, and FastProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585202(1371-1383)Online publication date: 2-Jun-2023

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