A Novel Multithreaded Algorithm For Extracting Maximal Chordal Subgraphs

Conference · Thu Oct 25 04:00:00 EDT 2012

DOI:https://doi.org/10.1109/ICPP.2012.10· OSTI ID:1054479

Halappanavar, Mahantesh; Feo, John T; Dempsey, Kathryn; Ali, Hesham; Bhowmick, Sanjukta

Chordal graphs are triangulated graphs where any cycle larger than three is bisected by a chord. Many combinatorial optimization problems such as computing the minimum fill-in, 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 subgraph from a general graph. Our algorithm is based on an iterative approach where each thread can asynchronously update a subset of edges that are dynamically assigned to it. We 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 testset of carefully generated synthetical graphs with up to half-a-billion edges and real world networks from gene correlation studies. We demonstrate that our algorithm achieves high scalability for all inputs on both types of architectures.

• Research Organization: Pacific Northwest National Laboratory (PNNL), Richland, WA (US)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC05-76RL01830
• OSTI ID: 1054479
• Report Number(s): PNNL-SA-85602; 400470000
• Country of Publication: United States
• Language: English