Paul K. Stockmeyer

An Algorithm for Reducing the Bandwidth and Profile of a Sparse Matrix

A new algorithm for reducing the bandwidth and profile of a sparse matrix is described. Extensive testing on finite element matrices indicates that the algorithm typically produces bandwidth and profile which are comparable to those of the commonly-used reverse Cuthill–McKee algorithm, yet requires significantly less computation time.

A Comparison of Several Bandwidth and Profile Reduction Algorithms

Abstract : This paper compares and analyzes six algorithms which have been suggested recently for use in reducing, by permutations, the bandwidth and profile of sparse matrices. This problem arises in many different areas of scientific computation such as in the finite element method for approximating solutions of partial differential equations and in analyzing large-scale power transmission systems.

The falsity of the reconstruction conjecture for tournaments

The conjecture that for all sufficiently large p any tournament of order p is uniquely reconstructable from its point-deleted subtournaments is shown to be false. Counterexamples are presented for all orders of the form 2n + 1 and 2n + 2. The largest previously known counterexamples were of order 8.

Algorithm 508: Matrix Bandwidth and Profile Reduction [F1]

This program, REDUCE, reduces the bandwidth and profile of sparse symmetric matrices, using row and corresponding column permutations. I t is a realization of the algorithm described by the authors in [4]. I t was extensively tested and compared with several other programs [5] and was found to be considerably faster than the others, generally superior for bandwidth reduction and as satisfactory as any other for profile reduction.

Reconstruction of sequences

Abstract Every sequence of length n determines ( n k ) subsequences of length k . We investigate the relationship between such subsequences and the original sequence. In particular, we show that for n >;7 and k ⩾[ n /2] the subsequences uniquely determine the original sequence, and for k 2 n they do not.

On the Optimality of Linear Merge

Let

Pseudosimilar vertices in a graph

M(m,n)

Exchanging disks in the tower of hanoi

be the minimum number of pairwise comparisons which will always suffice to merge two linearly ordered lists of lengths m and n. We prove that

What Did Lincoln Really Mean

M(m,m + d) = 2m + d - 1

More Mathematics in the Bedroom: A Paradoxical Probability.

whenever