Generalization of min-cut partitioning to tree structures and its applications

A generalization of the min-cut partitioning problem, called min-cost tree partitioning, is introduced. In the generalized problem. the nodes of a hypergraph G are to be mapped onto the vertices of a tree structure T, and the cost function to be minimized is the cost of routing the hyperedges of G on the edges of T . The standard min-cut problem is the simple case in which the tree T is a single edge connecting two vertices. Several VLSI design applications for this problem are discussed. An iterative improvement heuristic for this problem in which nodes of the hypergraph are moved between the vertices of the tree is described. The running time of a single pass of the heuristic for the unweighted version of the problem is Q(P×D×t³), where P is the total number of pins in the hypergraph G, D is the maximum number of nodes in a hyperedge of G, and t is the number of vertices in the tree T . Several test results are discussed