Geometrical k-cut problem and an optimal solution for hypercubes

Authors:
Sang-Young Cho
Affiliations:
Hankuk University of Foreign Studies, Computer Science and Engineering Department, Wangsan Mohyeon, Yongin Kyeonggi, Korea
Venue:
MATH'07 Proceedings of the 12th WSEAS International Conference on Applied Mathematics
Year:
2007

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Abstract

We introduce a generalization of the (s, t)-cut problem, called the Geometrical k-cut problem, with the concept of geometrical partitioning. A topology graph is employed to represent the geometrical structure of the partitioned nodes of a given k-terminal graph. This problem is NP-hard in general. We propose an optimal algorithm to solve the problem for hypercube topology graphs in polynomial time. The time complexity of the algorithm is O(qn3), where q is the dimension of a hypercube graph and n is the number of nodes in a k-terminal graph, with the Goldberg-Tarjan's network flow algorithm.