Graphillion: software library for very large sets of labeled graphs

Abstract

Several graph libraries have been developed in the past few decades, and they were basically designed to work with a few graphs. However, there are many problems in which we have to consider all subgraphs satisfying certain constraints on a given graph. Since the number of subgraphs can increase exponentially with the graph size, explicitly representing these is infeasible. Hence, libraries concerned with efficiently representing a single graph instance are not suitable for such problems. In this paper, we develop Graphillion, a software library for very large of (vertex-)labeled graphs, based on zero-suppressed binary decision diagrams. Graphillion is not based on a traditional representation of graphs. Instead, a graph is simply regarded as a set of edge sets ignoring vertices, which allows us to employ powerful tools of a of sets (a of sets) and permits large graph to be handled efficiently. We also utilize advanced graph enumeration algorithms, which enable the simple family tools to understand the graph structure. Graphillion is implemented as a Python library to encourage easy development of its applications, without introducing significant performance overheads. In experiments, we consider two case studies, a puzzle solver and a power network optimizer, in which several operations and heavy optimization have to be performed over very large of constrained graphs (i.e., cycles or forests with complicated conditions). The results show that Graphillion allows us to manage a huge number of graphs with very low development effort.