Improved approaches to solve the One-To-One SkewGraM problem

Abstract

Network comparison is an essential issue in the analysis of biological, social, and communication networks, and recent network comparisons have required the simultaneous mining of several networks on a similar vertex set. In this work, we study the case where the input consists of a directed acyclic graph D and an undirected graph G on the same vertex set. The goal is then to find the longest path P in D whose vertices induce a connected subgraph of G. This problem is known to be NP-hard and has immediate applications in the analysis of biological networks and foreseeable applications in the analysis of social, information, and communication networks. We propose hereinafter improvements to an existing branch-and-bound method and different resolution approaches based on Integer Linear Programming. We also experimentally evaluate both simulated and real data.