A Novel Multithreaded Algorithm for Extracting Maximal Chordal Subgraphs

Chordal graphs are triangulated graphs where any cycle larger than three is bisected by a chord. Many combinatorial optimization problems such as computing the size of the maximum clique and the chromatic number are NP-hard on general graphs but have polynomial time solutions on chordal graphs. In this paper, we present a novel multithreaded algorithm to extract a maximal chordal sub graph from a general graph. We develop an iterative approach where each thread can asynchronously update a subset of edges that are dynamically assigned to it per iteration and implement our algorithm on two different multithreaded architectures - Cray XMT, a massively multithreaded platform, and AMD Magny-Cours, a shared memory multicore platform. In addition to the proof of correctness, we present the performance of our algorithm using a test set of synthetical graphs with up to half-a-billion edges and real world networks from gene correlation studies and demonstrate that our algorithm achieves high scalability for all inputs on both types of architectures.