Abstract
For an edge weighted undirected graph G and an integer k ≥ 2, a k-way cut is a set of edges whose removal leaves G with at least k components. We propose a simple approximation algorithm to the minimum k-way cut problem. It computes a nearly optimal k-way cut by using a set of minimum 3-way cuts.We show that the performance ratio of our algorithm is 2−3/k for an odd k and 2−(3k−4)/(k 2−k) for an even k. The running time is O(kmn 3 log(n 2/m)) where n and m are the numbers of vertices and edges respectively.
This research was partially supported by the Scientific Grant-in-Aid from Ministry of Education, Science, Sports and Culture of Japan. The first author was also supported by the IBM Asia Fellowship Program.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
E. Dalhaus, D. S. Johnson, C. H. Papadimitriou, P. Seymour and M. Yannakakis, The complexity of the multiway cuts, extended abstract 1983. The complexity of the multiterminal cuts, SIAM J. Comput. Vol. 23, No. 4, 1994, 864–894.
O. Goldschmidt and D. S. Hochbaum, Polynomial algorithm for the k-cut problem, In Proc. 29th IEEE FOCS, 1988, 444–451.
A. V. Goldberg and R. E. Tarjan, A new approach to the maximum flow problem, J. of ACM, Vol. 35, No. 4, 1988, 921–940.
S. Kapoor, On minimum 3-cuts and approximating k-cuts using cut trees, Lecture Notes in Comput. Sci., 1084, Springer-Verlag, Integer programming and combinatorial optimization, 1996, 132–146.
D. R. Karger and C. Stein, A new approach to the minimum cut problems, J. of ACM, Vol. 43, No. 4, 1996, 601–640.
Y. Kamidoi, S. Wakabayasi and N. Yoshida, A new approach to the minimum k-way partition problem for weighted graphs, Technical Report of IEICE. COMP97-25, 1997, 25–32.
C. H. Lee, M. Kim and C. I. Park, An efficient k-way graph partitioning algorithm for task allocation in parallel computing systems, In Proc. IEEE Int. Conf. on Computer-Aided Design, 1990, 748–751.
T. Lengaur, Combinatorial Algorithms for Integrated Circuit Layout, Wiley 1990.
H. Nagamochi and T. Ibaraki, A fast algorithm for computing minimum 3-way and 4-way cuts, Lecture Notes in Comput. Sci., 1610, Springer-Verlag, 7th Conf. on Integer Programming and Combinatorial Optimization, 1999, 377–390.
H. Nagamochi, S. Katayama and T. Ibaraki, A faster algorithm for computing minimum 5-way and 6-way cuts in graphs, Lecture Notes in Computer Science 1627, Springer-Verlag, 5th Annual Int. Computing and Combinatorics Conf., 1999, 164–173.
H. S. Stone, Multiprocessor scheduling with the aid of network flow algorithms, IEEE Trans. on Software Engg., SE-3, 1977, 85–93.
H. Saran and V. V. Vazirani, Finding k-cuts within twice the optimal, In Proc. 32nd IEEE FOCS, 1991, 743–751.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhao, L., Nagamochi, H., Ibaraki, T. (1999). Approximating the Minimum k-way Cut in a Graph via Minimum 3-way Cuts. In: Algorithms and Computation. ISAAC 1999. Lecture Notes in Computer Science, vol 1741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46632-0_38
Download citation
DOI: https://doi.org/10.1007/3-540-46632-0_38
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66916-6
Online ISBN: 978-3-540-46632-1
eBook Packages: Springer Book Archive