Article

Free access

Excluded minors, network decomposition, and multicommodity flow

Authors:

Philip Klein,

Serge A. Plotkin,

Satish RaoAuthors Info & Claims

STOC '93: Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing

Pages 682 - 690

https://doi.org/10.1145/167088.167261

Published: 01 June 1993 Publication History

PDF eReader

References

[1]

B. Awerbuch, B. Berger, L. Cowen, and D. Peleg. Fast constructions of sparse neighborhood covers. In Proc. l Oth Annual ACM Symposium on Principles of Distributed Computing, 1992.

Google Scholar

[2]

B. Awerbuch, A. V. Goldberg, M. Luby, and S. A. Plotkin. Network Decomposition and Locality in Distributed Computation, In Proc. 30th IEEE Annual Symposium on Foundations of Computer Science, pages 364-369, 1989.

Digital Library

Google Scholar

[3]

B. Awerbuch and D. Peleg. Routing with polynomial communication-space trade-off. SIAMJ. Disc. Math, 5(2): 151-162, 1992.

Digital Library

Google Scholar

[4]

Baruch Awerbuch, Amotz Bar-Noy, Nati Linial, and David Peleg. Improved routing strategies with succinct tables. J. Alg., 11:307-341, 1990.

Digital Library

Google Scholar

[5]

Baruch Awerbuch and David Peleg. Network synchronization with polylogarithmic overhead. In Proc. 31st IEEEAnnual Symposium on Foundations of Computer Science, pages 514-522, 1990.

Digital Library

Google Scholar

[6]

Sandeep N. Bhatt and Tom Leighton. A framework for solving VLSI layout problems, f Comp. and Syst. Sci., 28(2):300-343, April 1984.

Google Scholar

[7]

E Hias, A. Feinstein, and C.E. Shannon. A note on the maximum flow through a network. IRS Trans. Information Theory, 2:117-119, 1956.

Crossref

Google Scholar

[8]

L. R. Ford, Jr. and D. R. Fulkerson. Maximal Flow Through a Network. Canadian Journal af Math., 8:399-404, 1956.

Google Scholar

[9]

N. Garg, V. V. Vazirani, and M. Yannakakis. Approximate max-flow min-(multi)cut theorems and their applications. In Proc. 23th ACM Symposium on the Theory of Computing, May 1993.

Digital Library

Google Scholar

[10]

E N. Klein, S. Rao, A. Agrawal, and R. Ravi. An approximate max-flow min-cut relation for multicommodity flow, with applications. Submitted to Combinatorica (1992). Preliminary version appeared as "Approximation through multicommodity flow," In Proc. 31 th IEEEAnnual Symposium on Foundations of Computer Science, pages 726-727, 1990.

Google Scholar

[11]

T. Leighton and S. Rao. An approximate max-flow min-cut theorem for uniform multicommodity flow problems with applications to approximation algorithms. In Proc. 29th IEEE Annual Symposium on Faundatiam of Computer Science, pages 422-431, 1988.

Digital Library

Google Scholar

[12]

N. Linial and M. Saks. Decomposing graphs into regions of smaU diameter. In Proc. 2ndACM-SIAM Symposium on Discrete Algorithms, pages 320-330. ACM/SIAM, January 1991.

Digital Library

Google Scholar

[13]

H. Okamura and I.D. Seymour. Multicommodity flows in planar graphs, f Combinatorial Theory (B), 31:75-81, 1981.

Google Scholar

[14]

D. Peleg and E. Upfal. A tradeoff between size and efficiency for routing tables. J. ACM, 36:510-530, 1989.

Digital Library

Google Scholar

[15]

S. Plotkin and t#. Tardos. Improved bounds on the max-flow min-cut ratio for multicommodity flows. In Proc. 23th ACM Symposium on the Theory of Computing, May 1993.

Digital Library

Google Scholar

[16]

ED. Seymour. Matroids and multicommodity flows. EuropeanJournalofCombinatorics, 2:257-290, 1981.

Google Scholar

[17]

E Shahrokhi and D. Matula. The maximum concurrent flow problem, f Assoc. Comput. Mach., 37:318- 334, 1990.

Digital Library

Google Scholar

[18]

S. Tragoudas. VLSIpartitioning approximation algorithms based on multicommodity flow and other techniques. PhD thesis, University of Texas at Dallas, 1991.

Digital Library

Google Scholar

Cited By

View all

Filtser A(2024)Scattering and Sparse Partitions, and Their ApplicationsACM Transactions on Algorithms10.1145/367256220:4(1-42)Online publication date: 5-Aug-2024
https://dl.acm.org/doi/10.1145/3672562
Chang YOshman RNolin AHalldorsson MBalliu A(2023)Efficient Distributed Decomposition and Routing Algorithms in Minor-Free Networks and Their ApplicationsProceedings of the 2023 ACM Symposium on Principles of Distributed Computing10.1145/3583668.3594604(55-66)Online publication date: 19-Jun-2023
https://dl.acm.org/doi/10.1145/3583668.3594604
Friedrich TIssac DKumar NMallek NZeif ZSaha BServedio R(2023)Approximate Max-Flow Min-Multicut Theorem for Graphs of Bounded TreewidthProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585150(1325-1334)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585150
Show More Cited By

Index Terms

Excluded minors, network decomposition, and multicommodity flow
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Network flows
  2. Mathematical analysis
    1. Mathematical optimization
      1. Continuous optimization
        Linear programming
2. Theory of computation
  1. Design and analysis of algorithms
    1. Graph algorithms analysis
      1. Network flows
    2. Mathematical optimization
      1. Continuous optimization
        Linear programming
  2. Randomness, geometry and discrete structures

Recommendations

Computing excluded minors
SODA '08: Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms

By Robertson and Seymour's graph minor theorem, every minor ideal can be characterised by a finite family of excluded minors. (A minor ideal is a class of graphs closed under taking minors.) We study algorithms for computing excluded minor ...
On the relative importance of excluded minors

If E is a set of matroids, then EX(E) denotes the set of matroids that have no minor isomorphic to a member of E. If E^'@?E, we say that E^' is superfluous if EX(E-E^')-EX(E) contains only finitely many 3-connected matroids. We determine the superfluous ...
Excluded minors are almost fragile II: Essential elements
Abstract
Let M be an excluded minor for the class of P-representable matroids for some partial field P, let N be a 3-connected strong P-stabilizer that is non-binary, and suppose M has a pair of elements { a , b } such that M ﹨ a , b is 3-...

Comments

Information & Contributors

Information

Published In

STOC '93: Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing

June 1993

812 pages

ISBN:0897915917

DOI:10.1145/167088

Chairmen:
Rao Kosaraju
John Hopkins Univ., Baltimore, MD
,
David Johnson
AT&T Bell Lab.
,
Alok Aggarwal
IBM T. J. Watson Research Center,Yorktown Heights, NY

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]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 June 1993

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Qualifiers

Article

Conference

STOC93

Sponsor:

SIGACT

STOC93: 25th Annual ACM Symposium on the Theory of Computing

May 16 - 18, 1993

California, San Diego, USA

Acceptance Rates

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

157
Total Citations
View Citations
1,436
Total Downloads

Downloads (Last 12 months)175
Downloads (Last 6 weeks)30

Reflects downloads up to 04 Oct 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Filtser A(2024)Scattering and Sparse Partitions, and Their ApplicationsACM Transactions on Algorithms10.1145/367256220:4(1-42)Online publication date: 5-Aug-2024
https://dl.acm.org/doi/10.1145/3672562
Chang YOshman RNolin AHalldorsson MBalliu A(2023)Efficient Distributed Decomposition and Routing Algorithms in Minor-Free Networks and Their ApplicationsProceedings of the 2023 ACM Symposium on Principles of Distributed Computing10.1145/3583668.3594604(55-66)Online publication date: 19-Jun-2023
https://dl.acm.org/doi/10.1145/3583668.3594604
Friedrich TIssac DKumar NMallek NZeif ZSaha BServedio R(2023)Approximate Max-Flow Min-Multicut Theorem for Graphs of Bounded TreewidthProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585150(1325-1334)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585150
Reichman DLieder FBourgin DTalmon NGriffiths T(2023)The Computational Challenges of Means Selection Problems: Network Structure of Goal Systems Predicts Human PerformanceCognitive Science10.1111/cogs.1333047:8Online publication date: 28-Aug-2023
https://doi.org/10.1111/cogs.13330
Chang HConroy JLe HMilenkovic LSolomon SThan C(2023)Covering Planar Metrics (and Beyond): O(1) Trees Suffice2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00139(2231-2261)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00139
Busch CChen DFiltser AHathcock DHershkowitz DRajaraman R(2023)One Tree to Rule Them All: Poly-Logarithmic Universal Steiner Tree2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00012(60-76)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00012
Huang CMari MMathieu CVygen J(2023)Approximating Maximum Integral Multiflows on Bounded Genus GraphsDiscrete & Computational Geometry10.1007/s00454-023-00552-770:4(1266-1291)Online publication date: 9-Oct-2023
https://doi.org/10.1007/s00454-023-00552-7
Dvořák ZLahiri A(2023)Maximum Edge Colouring Problem On Graphs That Exclude a Fixed MinorGraph-Theoretic Concepts in Computer Science10.1007/978-3-031-43380-1_21(291-304)Online publication date: 23-Sep-2023
https://doi.org/10.1007/978-3-031-43380-1_21
Cohen-Addad VLeonardi SGupta A(2022)Bypassing the surface embedding: approximation schemes for network design in minor-free graphsProceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3519935.3520049(343-356)Online publication date: 9-Jun-2022
https://dl.acm.org/doi/10.1145/3519935.3520049
Filtser ALe HLeonardi SGupta A(2022)Locality-sensitive orderings and applications to reliable spannersProceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3519935.3520042(1066-1079)Online publication date: 9-Jun-2022
https://dl.acm.org/doi/10.1145/3519935.3520042
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Get Access

Login options

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

Cited By

Index Terms

Recommendations

Computing excluded minors

On the relative importance of excluded minors

Excluded minors are almost fragile II: Essential elements