A nondifferentiable optimization approach to ratio-cut partitioning

Authors:
Kārlis Freivalds
Affiliations:
University of Latvia, Institute of Mathematics and Computer Science, Riga, Latvia
Venue:
WEA'03 Proceedings of the 2nd international conference on Experimental and efficient algorithms
Year:
2003

Citing 13
Cited 1

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Abstract

We propose a new method for finding the minimum ratio-cut of a graph. Ratio-cut is NP-hard problem for which the best previously known algorithm gives an O(log n)-factor approximation by solving its dually related maximum concurrent flow problem.We formulate the minimum ratio-cut as a certain nondifferentiable optimization problem, and show that the global minimum of the optimization problem is equal to the minimum ratio-cut. Moreover, we provide strong symbolic computation based evidence that any strict local minimum gives an approximation by a factor of 2. We also give an efficient heuristic algorithm for finding a local minimum of the proposed optimization problem based on standard nondifferentiable optimization methods and evaluate its performance on several families of graphs. We achieve O(n1.6) experimentally obtained running time on these graphs.