research-article

Improved distributed steiner forest construction

Authors:

Christoph Lenzen,

Boaz Patt-ShamirAuthors Info & Claims

PODC '14: Proceedings of the 2014 ACM symposium on Principles of distributed computing

Pages 262 - 271

https://doi.org/10.1145/2611462.2611464

Published: 15 July 2014 Publication History

Abstract

We present new distributed algorithms for constructing a Steiner Forest in the CONGEST model. Our deterministic algorithm finds, for any given constant ε>0, a (2+ε)-approximation in ~O(sk+√{min(st,n)}) rounds, where s is the shortest path diameter, t is the number of terminals, k is the number of terminal components in the input, and n is the number of nodes. Our randomized algorithm finds, with high probability, an O(log n)-approximation in time ~O(k+min(s,√ n)+D), where D is the unweighted diameter of the network. We also prove a matching lower bound of ~Ω(k+min(s,√n)+D) on the running time of any distributed approximation algorithm for the Steiner Forest problem. Previous algorithms were randomized, and obtained either an O(log n)-approximation in ~O(sk) time, or an O(1/ε)-approximation in O((√n+t)^1+ε+D) time.

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References

[1]

A. Agrawal, P. Klein, and R. Ravi. When trees collide: An approximation algorithm for the generalized Steiner tree problem on networks. SIAM J. Computing, 24:440--456, 1995.

Digital Library

[2]

S. Baswana and S. Sen. A simple and linear time randomized algorithm for computing sparse spanners in weighted graphs. Random Structures and Algorithms, 30(4):532--563, 2007.

Digital Library

[3]

M. Brazil, R. Graham, D. Thomas, and M. Zachariasen. On the history of the Euclidean Steiner tree problem. Archive for History of Exact Sciences, pages 1--28, 2013.

[4]

J. Byrka, F. Grandoni, T. Rothvoß, and L. Sanità. An improved LP-based Approximation for Steiner Tree. In Proc. 42nd ACM Symp. on Theory of Computing, pages 583--592, 2010.

Digital Library

[5]

P. Chalermsook and J. Fakcharoenphol. Simple Distributed Algorithms for Approximating Minimum Steiner Trees. In Proc.\ 11th Conf.\ on Computing and Combinatorics, pages 380--389, 2005.

Digital Library

[6]

M. Chlebík and J. Chlebíková. The Steiner tree problem on graphs: Inapproximability results. Theoretical Computer Science, 406(3):207--214, 2008.

Digital Library

[7]

R. Cole and U. Vishkin. Deterministic Coin Tossing and Accelerating Cascades: Micro and Macro Techniques for Designing Parallel Algorithms. In Proc. 18th ACM Symp. on Theory of Computing, pages 206--219, 1986.

Digital Library

[8]

R. Courant and H. Robbins. What is Mathematics? An Elementary Approach to Ideas and Methods. London. Oxford University Press, 1941.

[9]

A. Das Sarma, S. Holzer, L. Kor, A. Korman, D. Nanongkai, G. Pandurangan, D. Peleg, and R. Wattenhofer. Distributed Verification and Hardness of Distributed Approximation. In Proc.\ 43th ACM Symp.\ on Theory of Computing, pages 363--372, 2011.

Digital Library

[10]

M. Elkin. An Unconditional Lower Bound on the Time-Approximation Tradeoff for the Minimum Spanning Tree Problem. SIAM J. Computing, 36(2):463--501, 2006.

Digital Library

[11]

J. Fakcharoenphol, S. Rao, and K. Talwar. A Tight Bound on Approximating Arbitrary Metrics by Tree Metrics. Journal of Computer and System Sciences, 69(3):485--497, 2004.

Digital Library

[12]

R. G. Gallager, P. A. Humblet, and P. M. Spira. A Distributed Algorithm for Minimum-Weight Spanning Trees. ACM Trans. on Comp. Syst., 5(1):66--77, 1983.

Digital Library

[13]

J. Garay, S. Kutten, and D. Peleg. A sub-linear time distributed algorithm for minimum-weight spanning trees. SIAM J. Computing, 27:302--316, 1998.

Digital Library

[14]

M. Hauptmann and M. Karpinski. A Compendium on Steiner Tree Problems. http://theory.cs.uni-bonn.de/info5/steinerkompendium/netcompendium.html. Retreived January 2014.

[15]

R. M. Karp. Reducibility among combinatorial problems. In Complexity of Computer Computations, pages 85--103. Plenum, New York, 1972.

[16]

M. Khan, F. Kuhn, D. Malkhi, G. Pandurangan, and K. Talwar. Efficient Distributed Approximation Algorithms via Probabilistic Tree Embeddings. Distributed Computing, 25:189--205, 2012.

[17]

E. Kushilevitz and N. Nisan. Communication Complexity. Cambridge University Press, 1997.

Digital Library

[18]

S. Kutten and D. Peleg. Fast Distributed Construction of Small k-Dominating Sets and Applications. J. Algorithms, 28(1):40--66, 1998.

Digital Library

[19]

C. Lenzen and B. Patt-Shamir. Fast Routing Table Construction Using Small Messages: Extended Abstract. In Proc. 45th Ann. ACM Symp. on Theory of Computing, pages 381--390, 2013.

Digital Library

[20]

C. Lenzen and B. Patt-Shamir. Improved Distributed Steiner Forest Construction. CoRR, abs/1405.2011, 2014.

[21]

Z. Lotker, B. Patt-Shamir, and D. Peleg. Distributed MST for constant diameter graphs. Distributed Computing, 18(6):453--460, 2006.

Digital Library

[22]

D. Peleg. Distributed Computing: A Locality-Sensitive Approach. SIAM, Philadelphia, PA, 2000.

[23]

D. Peleg and V. Rubinovich. Near-tight Lower Bound on the Time Complexity of Distributed MST Construction. SIAM J. Computing, 30:1427--1442, 2000.

Digital Library

[24]

H. Takahashi and A. Matsuyama. An Approximate Solution for the Steiner Problem in Graphs. Mathematica Japonica, 6:573--577, 1980.

[25]

R. E. Tarjan. Data Structures and network Algorithms, chapter 6. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 1983.

Cited By

Abboud ACensor-Hillel KKhoury SLenzen C(2020)Fooling views: a new lower bound technique for distributed computations under congestionDistributed Computing10.1007/s00446-020-00373-433:6(545-559)Online publication date: 1-Dec-2020
https://dl.acm.org/doi/10.1007/s00446-020-00373-4
Saikia PKarmakar S(2020)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-Jan-2020
https://dl.acm.org/doi/10.1007/978-3-030-36987-3_7
Pandurangan GRobinson PScquizzato M(2019)A Time- and Message-Optimal Distributed Algorithm for Minimum Spanning TreesACM Transactions on Algorithms10.1145/336500516:1(1-27)Online publication date: 15-Nov-2019
https://dl.acm.org/doi/10.1145/3365005
Show More Cited By

Index Terms

Improved distributed steiner forest construction
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis
      1. Routing and network design problems
  2. Randomness, geometry and discrete structures

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Highlights
- Improved distributed approximation for Steiner tree.
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Abstract
In this paper we present two deterministic distributed algorithms for the Steiner tree (ST) problem in the CONGEST model. The first algorithm computes a 2 ( 1 − 1 / ℓ )-approximate ST using O ( S + n log ⁎ ⁡ n ) rounds and O ( m S + n ...

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cover image ACM Conferences

PODC '14: Proceedings of the 2014 ACM symposium on Principles of distributed computing

July 2014

444 pages

ISBN:9781450329446

DOI:10.1145/2611462

General Chair:
Magnús Halldórsson
Reykjavik Universite, Iceland
,
Program Chair:
Shlomi Dolev
Ben-Gurion University, Israel

Copyright © 2014 ACM.

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: 15 July 2014

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PODC '14: ACM Symposium on Principles of Distributed Computing

July 15 - 18, 2014

Paris, France

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PODC '14 Paper Acceptance Rate 39 of 141 submissions, 28%;

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

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Cited By

Abboud ACensor-Hillel KKhoury SLenzen C(2020)Fooling views: a new lower bound technique for distributed computations under congestionDistributed Computing10.1007/s00446-020-00373-433:6(545-559)Online publication date: 1-Dec-2020
https://dl.acm.org/doi/10.1007/s00446-020-00373-4
Saikia PKarmakar S(2020)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-Jan-2020
https://dl.acm.org/doi/10.1007/978-3-030-36987-3_7
Pandurangan GRobinson PScquizzato M(2019)A Time- and Message-Optimal Distributed Algorithm for Minimum Spanning TreesACM Transactions on Algorithms10.1145/336500516:1(1-27)Online publication date: 15-Nov-2019
https://dl.acm.org/doi/10.1145/3365005
Saikia PKarmakar SHansdah RKrishnaswamy DVaidya N(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
https://dl.acm.org/doi/10.1145/3288599.3288629
Censor-Hillel KDory M(2019)Fast distributed approximation for TAP and 2-edge-connectivityDistributed Computing10.1007/s00446-019-00353-333:2(145-168)Online publication date: 16-May-2019
https://doi.org/10.1007/s00446-019-00353-3
Lenzen CPatt-Shamir BPeleg D(2019)Distributed distance computation and routing with small messagesDistributed Computing10.1007/s00446-018-0326-632:2(133-157)Online publication date: 1-Apr-2019
https://dl.acm.org/doi/10.1007/s00446-018-0326-6
Friedrichs SLenzen C(2018)Parallel Metric Tree Embedding Based on an Algebraic View on Moore-Bellman-FordJournal of the ACM10.1145/323159165:6(1-55)Online publication date: 22-Nov-2018
https://dl.acm.org/doi/10.1145/3231591
Ghaffari MHaeupler B(2016)Distributed algorithms for planar networks IIProceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms10.5555/2884435.2884451(202-219)Online publication date: 10-Jan-2016
https://dl.acm.org/doi/10.5555/2884435.2884451
Friedrichs SLenzen CScheideler CGilbert S(2016)Parallel Metric Tree Embedding based on an Algebraic View on Moore-Bellman-FordProceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/2935764.2935777(455-466)Online publication date: 11-Jul-2016
https://dl.acm.org/doi/10.1145/2935764.2935777
Ghaffari MHaeupler BGiakkoupis G(2016)Distributed Algorithms for Planar Networks IProceedings of the 2016 ACM Symposium on Principles of Distributed Computing10.1145/2933057.2933109(29-38)Online publication date: 25-Jul-2016
https://dl.acm.org/doi/10.1145/2933057.2933109
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