A branch and bound algorithm for the matrix bandwidth minimization

Abstract

-In this article we first review previous exact approaches as well as theoretical contributions for the problem of reducing the bandwidth of a matrix. This problem consists of finding a permutation of the rows and columns of a given matrix which keeps the non-zero elements in a band that is as close as possible to the main diagonal. This NP-complete problem can also be formulated as a labeling of vertices on a graph, where edges are the non-zero elements of the corresponding symmetrical matrix. We propose a new branch and bound algorithm and new expressions for known lower bounds for this problem.Empirical results with a collection of previously reported instances indicate that the proposed algorithm compares favourably to previous methods.

Parallel Low-Storage Runge—Kutta Solvers for ODE Systems with Limited Access Distance

“…Usually, one can choose between different orderings of the equations which may influence the bandwidth/access distance. Several heuristic and exact optimization algorithms exist, e.g., [34,46], which aim at a minimization of the bandwidth of sparse symmetric matrices and thus can be used for many ODE systems to find an ordering of the equations which provides a limited access distance.…”

Manipulating MDD Relaxations for Combinatorial Optimization

“…Near W = 35 we see the fastest solution times, and hence for the remainder of the experimental testing we fix W at 35. We note here that during our preliminary computational tests, the range of widths that seemed to perform best was W ∈ [20,40].…”

Branch and bound for the cutwidth minimization problem

“…The first one, Small, was reported in Martí et al (2008), the second one, Grids, was described in Rolim et al (1995) and the third one, Harwell-Boeing, is a subset of the public-domain Matrix Market library (available at http://math.nist.gov/MatrixMarket/data/Harwell-Boeing/). All these instances are available at http://heur.uv.es/optsicom/cutwidth.…”