article

Improving graph partitions using submodular functions

Authors:

Sachin B. Patkar,

H. NarayananAuthors Info & Claims

Discrete Applied Mathematics, Volume 131, Issue 2

Pages 535 - 553

https://doi.org/10.1016/S0166-218X(02)00472-9

Published: 12 September 2003 Publication History

Abstract

We investigate into the role of submodular functions in designing new heuristics and approximate algorithms to some NP-hard problems arising in the field of VLSI Design Automation. In particular, we design and implement efficient heuristic for improving a bipartition of a graph in the sense of ratioCut (Discrete Appl. Math. 90 (1999) 3; 29th Annual Symposium on Foundations of Computer Science, 1988, p. 422). We also design an approximate algorithm for another NP-hard problem which is a dual of the well-known NP-hard problem of finding a densest k-subgraph of a graph (see J. Algorithms 34 (2000) 203; Proceedings of the 34th Annual Symposium on Foundations of Computer Science, 1993, p. 692). Our algorithms are based on submodular function and are implementable in polynomial time using efficient network flow based subroutines. To the best of our knowledge our algorithms are the first ones to use submodular functions based approach for the problems considered here. We also describe the experimental results which provide the evidence of our heuristic for improving the ratioCut.

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Cited By

Hein MSetzer S(2011)Beyond spectral clustering - tight relaxations of balanced graph cutsProceedings of the 25th International Conference on Neural Information Processing Systems10.5555/2986459.2986723(2366-2374)Online publication date: 12-Dec-2011
https://dl.acm.org/doi/10.5555/2986459.2986723
Andersen RLang KTeng S(2008)An algorithm for improving graph partitionsProceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms10.5555/1347082.1347154(651-660)Online publication date: 20-Jan-2008
https://dl.acm.org/doi/10.5555/1347082.1347154
Narasimhan MBilmes J(2007)Local search for balanced submodular clusteringsProceedings of the 20th international joint conference on Artifical intelligence10.5555/1625275.1625434(981-986)Online publication date: 6-Jan-2007
https://dl.acm.org/doi/10.5555/1625275.1625434
Show More Cited By

Index Terms

Improving graph partitions using submodular functions
1. Computing methodologies
  1. Artificial intelligence
    1. Computer vision
      1. Computer vision problems
        Interest point and salient region detections
    2. Search methodologies
      1. Discrete space search
      2. Game tree search
2. Software and its engineering
  1. Software notations and tools
    1. General programming languages
      1. Language features
        Procedures, functions and subroutines

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cover image Discrete Applied Mathematics

Discrete Applied Mathematics Volume 131, Issue 2

Submodularity

12 September 2003

299 pages

ISSN:0166-218X

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Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 12 September 2003

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Cited By

Hein MSetzer S(2011)Beyond spectral clustering - tight relaxations of balanced graph cutsProceedings of the 25th International Conference on Neural Information Processing Systems10.5555/2986459.2986723(2366-2374)Online publication date: 12-Dec-2011
https://dl.acm.org/doi/10.5555/2986459.2986723
Andersen RLang KTeng S(2008)An algorithm for improving graph partitionsProceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms10.5555/1347082.1347154(651-660)Online publication date: 20-Jan-2008
https://dl.acm.org/doi/10.5555/1347082.1347154
Narasimhan MBilmes J(2007)Local search for balanced submodular clusteringsProceedings of the 20th international joint conference on Artifical intelligence10.5555/1625275.1625434(981-986)Online publication date: 6-Jan-2007
https://dl.acm.org/doi/10.5555/1625275.1625434
Lang KAndersen RLaender AFalcão AOlsen ØSilva MBaeza-Yates RMcGuinness DOlstad B(2007)Finding dense and isolated submarkets in a sponsored search spending graphProceedings of the sixteenth ACM conference on Conference on information and knowledge management10.1145/1321440.1321526(613-622)Online publication date: 6-Nov-2007
https://dl.acm.org/doi/10.1145/1321440.1321526
Patkar SNarayanan H(2003)An Efficient Practical Heuristic For Good Ratio-Cut PartitioningProceedings of the 16th International Conference on VLSI Design10.5555/832285.835620Online publication date: 4-Jan-2003
https://dl.acm.org/doi/10.5555/832285.835620

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