BDD-Based Algorithm for SCC Decomposition of Edge-Coloured Graphs

Abstract

Edge-coloured directed graphs provide an essential structure for modelling and computing complex problems arising in many scientific disciplines. The size of edge-coloured graphs appearing in practice can be enormous in the number of both vertices and colours. An important fundamental problem that needs to be solved over edge-coloured graphs is detecting strongly connected components. The problem becomes challenging for large graphs with a large number of colours.In this paper, we describe a novel symbolic algorithm that computes all the monochromatic strongly connected components of an edge-coloured graph. In the worst case, the algorithm performs O(p • n • log n) symbolic steps, where p is the number of colours and n is the number of vertices. We evaluate the algorithm using an experimental implementation based on Binary Decision Diagrams (BDDs) and large (up to 2 48 ) coloured graphs produced by models appearing in systems biology.