MAXIMUM K-COVERING OF WEIGHTED TRANSITIVE GRAPHS WITH APPLICATIONS

Consider a weighted transitive graph, where each vertex is assigned a positive weight. Given a positive integer k, the maximum k-covering problem is to find k disjoint cliques covering a set or vertices with maximum total weight. An O(kn2)-time algorithm to solve the problem in a transitive graph is proposed, where n is the number or vertices. Based on the proposed algorithm the weighted version of a number of problems in VLSI layout (e.g., k-layer topological via minimization), computational geometry (e.g., maximum multidimensional k-chain), graph theory (e.g., maximum k-independent set in interval graphs), and sequence manipulation (eg., maximum increasing k-subsequence) can be solved in O(kn2), where n is the input size.