Maximum weight archipelago subgraph problem

Abstract

This paper is devoted to a new problem of combinatorial optimization. The problem is called Maximum Weight Archipelago Subgraph Problem (MWASP). Archipelago is a signed graph such that the negative edges connect the components of the graph of the positive edges. The new problem is to find a subset of edges in a weighted signed graph such that (i) if the edges of the subset are deleted from the graph then the remaining graph is an archipelago; and (ii) the subset has minimal total weight among the subsets having property (i). The problem is NP-complete, however a polynomial algorithm is provided to obtain the maximal weight of an edge what is still necessary to delete. The problem MWAP is used to analyze the relation of the blue chips of the Dow Jones Index.