Toward an Efficient Column Minimum Degree Code for Symmetric Multiprocessors

Ordering the columns of a nonsymmetric sparse matrix can reduce the fill created in its factorization. Minimum-degree is a popular heuristic for ordering symmetric matrices; a variant that can be used to order nonsymmetric matrices is called column minimum degree. In this paper we describe the design of a multithreaded approximate column minimum degree code. We present a framework for the algorithm, study potential sources of parallel inefficiency, and describe our attempts to circumvent the obstacles. We present experimental results that support our analysis.