Article

Local MST computation with short advice

Authors:

Pierre Fraigniaud,

Emmanuelle LebharAuthors Info & Claims

SPAA '07: Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures

Pages 154 - 160

https://doi.org/10.1145/1248377.1248402

Published: 09 June 2007 Publication History

Abstract

We use the recently introduced advising scheme framework for measuring the difficulty of locally distributively computing a Minimum Spanning Tree (MST). An (m,t)-advising scheme for a distributed problem P is a way, for every possible input I of P, to provide an "advice" (i.e., a bit string) about I to each node so that: (1) the maximum size of the advices is at most m bits, and (2) the problem P can be solved distributively in at most t rounds using the advices as inputs. In case of MST, the output returned by each node of a weighted graph G is the edge leading to its parent in some rooted MST T of G. Clearly, there is a trivial (log n,0)-advising scheme for MST (each node is given the local port number of the edge leading to the root of some MST T), and it is known that any (0,t)-advising scheme satisfies t ≥ Ω (√n). Our main result is the construction of an (O(1),O(log n))-advising scheme for MST. That is, by only giving a constant number of bits of advice to each node, one can decrease exponentially the distributed computation time of MST in arbitrary graph, compared to algorithms dealing with the problem in absence of any a priori information. We also consider the average size of the advices. On the one hand, we show that any (m,0)-advising scheme for MST gives advices of average size Ω(log n). On the other hand we design an (m,1)-advising scheme for MST with advices of constant average size, that is one round is enough to decrease the average size of the advices from log(n) to constant.

References

[1]

B. Awerbuch. Optimal distributed algorithms for minimum weight spanning tre, counting, leader election and related problems. In Proc. Annual ACM Symp. on Theory of Computing (STOC), pp. 230--240, 1987.

Digital Library

[2]

Y. Afek, S. Kuten, and M. Yung. Local detection for global self stabilization. In Proc. 4th Workshop on Distributed Algorithms, pp. 15--28, 1991.

Digital Library

[3]

R. Cohen, P. Fraigniaud, D. Ilcinkas, A. Korman, and D. Peleg. Labeling schemes for tree representation. In Proc. 7th International Workshop on Distributed Computing (IWDC), pp. 13--24, 2005.

Digital Library

[4]

R. Cohen, P. Fraigniaud, D. Ilcinkas, A. Korman, and D. Peleg. Label-Guided Graph Exploration by a Finite Automaton. In 32nd Int. Colloquium on Automata, Languages and Programming (ICALP), LNCS 3580, Springer, pp. 335--346, 2005.

Digital Library

[5]

F. Chin and H. F. Ting. An almost linear time and O(n log n+e) messages distributed algorithm for minimum-weight spanning trees. In Proc 26th IEEE Symp. on Foundations of Computer Science (FOCS), pp. 257--266, 1985.

Digital Library

[6]

T.H. Cormen, T. Leiserson, and R.L. Rivest. Introduction to Algorithms. MIT Press/McGraw-Hill, 1990.

Digital Library

[7]

M. Elkin. A Faster Distributed Protocol for Constructing a Minimum Spanning Tree. In Proc. ACM-SIAM on Discrete Algorithms (SODA), pp. 352--361, 2004.

Digital Library

[8]

M. Elkin. An Unconditional Lower Bound on the Hardness of Approximation of Distributed Minimum Spanning Tree Problem. In Proc. 36th Annual ACM Symp. on Theory of Computing (STOC), pp. 331--340, 2004.

Digital Library

[9]

P. Fraigniaud, D. Ilcinkas, and A. Pelc. Oracle size: a new measure of difficulty for communication tasks. Proc. 25th Annual ACM Symposium on Principles of Distributed Computing (PODC), pp. 179--187, 2006.

Digital Library

[10]

P. Fraigniaud, D. Ilcinkas, and A. Pelc. Tree Exploration with an Oracle. 31st Int. Symp. on Mathematical Foundations of Computer Science (MFCS), LNCS 4162, Springer, pp. 24--37, 2006.

Digital Library

[11]

E. Gafni. Improvements in the time complexity of two message-optimal election algorithms. In Proc 4th ACM Symp. on Principles of Distributed Computing (PODC), pp. 175--185, 1985.

Digital Library

[12]

R. G. Gallager, P. A. Humblet, and P. M. Spira. A distributed algorithm for minimum-weight spanning trees. ACM Trans. on Programming Lang. and Syst., 5:66--67, 1983.

Digital Library

[13]

A. Korman and S. Kutten. Distributed Verification of Minimum Spanning Trees Proc. 25th Annual Symposium on Principles of Distributed Computing (PODC)., pp. 26--34, 2006.

Digital Library

[14]

A. Korman, S. Kutten, and D. Peleg. Proof Labeling Schemes. Proc. 24th Annual Symposium on Principles of Distributed Computing (PODC)., pp. 9--18, 2005.

Digital Library

[15]

F. Kuhn, T. Moscibroda, and R. Wattenhofer. What cannot be compute Locally! In Proc. 23th ACM Symp. on Principles of Distributed Computing, (PODC), pp. 300--309, 2004.

Digital Library

[16]

N. Linial. Locality in distributed graph algorithms. SIAM J. on Computing 21(1):193--201, 1992.

Digital Library

[17]

Z. Lotker, B. Patt-Shamir and D. Peleg. Distributed MST for Constant Diameter Graphs In Proc. 20th ACM Symp. on Principles of Distributed Computing, (PODC), pp. 63--72, 2001.

Digital Library

[18]

M. Naor and L. Stockmeyer. What can be computed locally? In 25th ACM Symposium on Theory of Computing (STOC), pp. 184--193, 1993.

Digital Library

[19]

D. Peleg. Distributed Computing: A Locality-Sensitive Approach. SIAM Monographs on Discrete Mathematics, 2000.

Digital Library

[20]

D. Peleg and R. Rubinovich. A near-tight lower bound on the time complexity of distributed MST construction. In 40th IEEE SYmp. on Foundations of Computer Science (FOCS), pp. 253--261, 1999.

Digital Library

Cited By

Balliu ABrandt SKuhn FNowicki KOlivetti DRotenberg ESuomela JKuznetsov PGelles ROlivetti D(2024)Brief Announcement: Local Advice and Local DecompressionProceedings of the 43rd ACM Symposium on Principles of Distributed Computing10.1145/3662158.3662805(117-120)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3662158.3662805
Bhattacharya AGorain BMandal P(2023)Pebble Guided Treasure Hunt in PlaneNetworked Systems10.1007/978-3-031-37765-5_11(141-156)Online publication date: 7-Jul-2023
https://doi.org/10.1007/978-3-031-37765-5_11
Rabie M(2017)Global Versus Local Computations: Fast Computing with IdentifiersStructural Information and Communication Complexity10.1007/978-3-319-72050-0_6(90-105)Online publication date: 30-Dec-2017
https://doi.org/10.1007/978-3-319-72050-0_6
Show More Cited By

Index Terms

Local MST computation with short advice
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph enumeration
      2. Trees
2. Software and its engineering
  1. Software organization and properties
    1. Software system structures
      1. Distributed systems organizing principles
        Organizing principles for web applications

Recommendations

Local MST Computation with Short Advice
Special Title: Parallelism on Algorithms and Architectures (SPAA); Guest Editors: Cyril Gavoille, Boaz Patt-Shamir and Christian Scheideler

We use the recently introduced advising scheme framework for measuring the difficulty of locally distributively computing a Minimum Spanning Tree (MST). An (m,t)-advising scheme for a distributed problem ℘ is a way, for every possible input I of ℘, to ...
Distributed MST for constant diameter graphs

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 ...
A Simple Deterministic Distributed MST Algorithm with Near-Optimal Time and Message Complexities

The distributed minimum spanning tree (MST) problem is one of the most central and fundamental problems in distributed graph algorithms. Kutten and Peleg devised an algorithm with running time O(D + √n ⋅ log^* n), where D is the hop diameter of the input ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

SPAA '07: Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures

June 2007

376 pages

ISBN:9781595936677

DOI:10.1145/1248377

General Chair:
Phillip B. Gibbons
Intel Research, USA
,
Program Chair:
Christian Scheideler
Technische Universität München, Germany

Copyright © 2007 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]

Sponsors

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 09 June 2007

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Article

Conference

SPAA07

Sponsor:

SPAA07: 19th ACM Symposium on Parallelism in Algorithms and Architectures

June 9 - 11, 2007

California, San Diego, USA

Acceptance Rates

Overall Acceptance Rate 447 of 1,461 submissions, 31%

Upcoming Conference

SPAA '25

Sponsor:
sigact
sigact

37th ACM Symposium on Parallelism in Algorithms and Architectures

July 28 - August 1, 2025

Portland , OR , USA

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

38
Total Citations
View Citations
303
Total Downloads

Downloads (Last 12 months)8
Downloads (Last 6 weeks)0

Reflects downloads up to 26 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Balliu ABrandt SKuhn FNowicki KOlivetti DRotenberg ESuomela JKuznetsov PGelles ROlivetti D(2024)Brief Announcement: Local Advice and Local DecompressionProceedings of the 43rd ACM Symposium on Principles of Distributed Computing10.1145/3662158.3662805(117-120)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3662158.3662805
Bhattacharya AGorain BMandal P(2023)Pebble Guided Treasure Hunt in PlaneNetworked Systems10.1007/978-3-031-37765-5_11(141-156)Online publication date: 7-Jul-2023
https://doi.org/10.1007/978-3-031-37765-5_11
Rabie M(2017)Global Versus Local Computations: Fast Computing with IdentifiersStructural Information and Communication Complexity10.1007/978-3-319-72050-0_6(90-105)Online publication date: 30-Dec-2017
https://doi.org/10.1007/978-3-319-72050-0_6
Fu LJarabek J(2016)Optimizations for Multiple Collective Sources in Delivery Systems2016 IEEE/WIC/ACM International Conference on Web Intelligence (WI)10.1109/WI.2016.0075(461-464)Online publication date: Oct-2016
https://doi.org/10.1109/WI.2016.0075
Blin LFraigniaud P(2015)Space-Optimal Time-Efficient Silent Self-Stabilizing Constructions of Constrained Spanning Trees2015 IEEE 35th International Conference on Distributed Computing Systems10.1109/ICDCS.2015.66(589-598)Online publication date: Jun-2015
https://doi.org/10.1109/ICDCS.2015.66
Arfaoui HFraigniaud PPelc A(2013)Local Decision and Verification with Bounded-Size Outputs15th International Symposium on Stabilization, Safety, and Security of Distributed Systems - Volume 825510.5555/2718693.2718703(133-147)Online publication date: 13-Nov-2013
https://dl.acm.org/doi/10.5555/2718693.2718703
Fraigniaud PKorman APeleg D(2013)Towards a complexity theory for local distributed computingJournal of the ACM10.1145/249922860:5(1-26)Online publication date: 28-Oct-2013
https://dl.acm.org/doi/10.1145/2499228
Korman ASereni JViennot L(2013)Toward more localized local algorithmsDistributed Computing10.1007/s00446-012-0174-826:5-6(289-308)Online publication date: 1-Oct-2013
https://dl.acm.org/doi/10.1007/s00446-012-0174-8
Arfaoui HFraigniaud PPelc A(2013)Local Decision and Verification with Bounded-Size OutputsStabilization, Safety, and Security of Distributed Systems10.1007/978-3-319-03089-0_10(133-147)Online publication date: 2013
https://doi.org/10.1007/978-3-319-03089-0_10
Fraigniaud PHalldórsson MKorman A(2012)On the Impact of Identifiers on Local DecisionPrinciples of Distributed Systems10.1007/978-3-642-35476-2_16(224-238)Online publication date: 2012
https://doi.org/10.1007/978-3-642-35476-2_16
Show More Cited By

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Figures

Tables

Media

View Table of Conten