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Efficient distributed approximation algorithms via probabilistic tree embeddings

Published: 18 August 2008 Publication History

Abstract

We present a uniform approach to design efficient distributed approximation algorithms for various network optimization problems. Our approach is randomized and based on a probabilistic tree embedding due to Fakcharoenphol, Rao, and Talwar (FRT embedding). We show how to efficiently compute an (implicit) FRT embedding in a decentralized manner and how to use the embedding to obtain expected O(log n)-approximate distributed algorithms for the generalized Steiner forest problem, the minimum routing cost spanning tree problem, and the $k$-source shortest paths problem in arbitrary networks. The time complexities of our algorithms are within a polylogarithmic factor of the optimum.
The distributed construction of the FRT embedding is based on the computation of least elements (LE) lists, a distributed data structure that might be of independent interest. Assuming a global order on the nodes of a network, the LE list of a node stores the smallest node (w.r.t. the given order) within every distance $d$. Assuming a random order on the nodes, we give an almost-optimal distributed algorithm for computing LE lists on weighted graphs. For unweighted graphs, our LE lists computation has asymptotically optimal time complexity O(D), where D is the diameter of the network. As a byproduct, we get an improved synchronous leader election algorithm for general networks.

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  • (2020)Distributed Approximation Algorithms for Steiner Tree in the CONGESTED CLIQUEInternational Journal of Foundations of Computer Science10.1142/S012905412050036731:07(941-968)Online publication date: 10-Nov-2020
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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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Published: 18 August 2008

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Author Tags

  1. distributed approximation
  2. generalized steiner forests
  3. least element lists
  4. metric spaces
  5. network optimization
  6. probabilistic tree embeddings

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

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Cited By

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  • (2021)Dynamic maintenance of low-stretch probabilistic tree embeddings with applicationsProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458139(1226-1245)Online publication date: 10-Jan-2021
  • (2021)Improved distributed approximation for Steiner tree in the CONGEST modelJournal of Parallel and Distributed Computing10.1016/j.jpdc.2021.08.004158:C(196-212)Online publication date: 1-Dec-2021
  • (2020)Distributed Approximation Algorithms for Steiner Tree in the CONGESTED CLIQUEInternational Journal of Foundations of Computer Science10.1142/S012905412050036731:07(941-968)Online publication date: 10-Nov-2020
  • (2019)A simple 2(1-1/l) factor distributed approximation algorithm for steiner tree in the CONGEST modelProceedings of the 20th International Conference on Distributed Computing and Networking10.1145/3288599.3288629(41-50)Online publication date: 4-Jan-2019
  • (2019)2(1 – 1/ℓ)-Factor Steiner Tree Approximation in Õ(n^1/3) Rounds in the CONGESTED CLIQUE2019 Seventh International Symposium on Computing and Networking (CANDAR)10.1109/CANDAR.2019.00018(82-91)Online publication date: Nov-2019
  • (2019)Round-Message Trade-Off in Distributed Steiner Tree Construction in the CONGEST ModelDistributed Computing and Internet Technology10.1007/978-3-030-36987-3_7(111-126)Online publication date: 9-Dec-2019
  • (2018)The Complexity of Leader ElectionProceedings of the 19th International Conference on Distributed Computing and Networking10.1145/3154273.3154308(1-10)Online publication date: 4-Jan-2018
  • (2015)Sublinear bounds for randomized leader electionTheoretical Computer Science10.1016/j.tcs.2014.02.009561:PB(134-143)Online publication date: 4-Jan-2015
  • (2015)Cooperative network designComputer Networks: The International Journal of Computer and Telecommunications Networking10.1016/j.comnet.2015.03.01783:C(265-279)Online publication date: 4-Jun-2015
  • (2014)Can quantum communication speed up distributed computation?Proceedings of the 2014 ACM symposium on Principles of distributed computing10.1145/2611462.2611488(166-175)Online publication date: 15-Jul-2014
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