A new approach to the maximum-flow problem
Journal of the ACM (JACM)
A fast parametric maximum flow algorithm and applications
SIAM Journal on Computing
Combinatorial algorithms for integrated circuit layout
Combinatorial algorithms for integrated circuit layout
Computing the strength of a graph
SIAM Journal on Computing
A faster algorithm for computing the strength of a network
Information Processing Letters
Spectral partitioning: the more eigenvectors, the better
DAC '95 Proceedings of the 32nd annual ACM/IEEE Design Automation Conference
Algorithms for graphic polymatroids and parametric &smacr;-sets
Journal of Algorithms
Spectral partitioning with multiple eigenvectors
Discrete Applied Mathematics - Special volume on VLSI
Greedily finding a dense subgraph
Journal of Algorithms
An Efficient Practical Heuristic For Good Ratio-Cut Partitioning
VLSID '03 Proceedings of the 16th International Conference on VLSI Design
Finding dense and isolated submarkets in a sponsored search spending graph
Proceedings of the sixteenth ACM conference on Conference on information and knowledge management
An algorithm for improving graph partitions
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Local search for balanced submodular clusterings
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Submodular fractional programming for balanced clustering
Pattern Recognition Letters
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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.