An Asymptotically Optimal Minimum Degree Ordering of Regular Grids

It has previously been shown that there exists a minimum degree ordering for regular grids that is considerably worse than nested dissection in terms of ll-in and operations for factorization 1]. This paper proves the existence of a minimum degree ordering for regular grids that has the same optimal asymptotic order complexity for ll-in and operation count as nested dissection. The analysis is veriied by showing exact match between analytical prediction and experimental measurement. The analysis motivates a peripheral preordering strategy for use with the popular multiple minimum degree (MMD) algorithm, and is shown to consistently reduce ll-in and operation count for regular grids.