Total Ordering Problem

We show that it is NP-complete to determine the chromatic index of an arbitrary graph. The problem remains NP-complete even for cubic graphs.

Classes of machines using very limited amounts of nondeterminism are studied. The P=? NP question is related to questions about classes lying within P. Complete sets for these classes are given.

It is shown that the pathwidth of a cograph equals its treewidth, and a linear time algorithm to determine the pathwidth of a cograph and build a corresponding path-decomposition is given.

Based on a new version of the Hopcroft and Tarjan planarity testing algorithm, this paper develops an $O(m\log n)$-time algorithm to find a maximal planar subgraph.

We show that computing the volume of a polyhedron given either as a list of facets or as a list of vertices is as hard as computing the permanent of a matrix.

The number of essential multiplications required to multiply matrices of size $N \times N$ and $N \times N^{0.172} $ is bounded by $CN^2 \log ^2 N$.

Condition Estimates

Bounds on Multiprocessing Timing Anomalies

A Graph-Theoretic Approach to a Communications Problem

The Numerical Solution of Parabolic and Elliptic Differential Equations

An Algorithm for Least-Squares Estimation of Nonlinear Parameters

A method is described for producing monotone piecewise cubic interpolants to monotone data which is completely local and which is extremely simple to implement.

Ranks of graphs: The size of acyclic orientation cover for deadlock-free packet routing

possesses properties (1.1), (1.2), and (1.3). In order to find the joint probability density function of (yo, yi , , yn), or of any n + 1 successive variates, it is necessary to invert the matrix Tn . In this paper, we derive an exact recursive procedure for the numerical inversion of an arbitrary positive definite Toeplitz matrix of finite order, which takes full advantage of the strong restrictions placed on its elements by (1.1), (1.2), and (1.3). The number of multiplications required for the inversion of an nth order Toeplitz matrix, using this procedure, is proportional to n2, rather than to n', as in the case of methods which are suitable for arbitrary Hermitian matrices. To the author's knowledge, this inversion algorithm is the first to be specifically designed to take advantage of the peculiar simplicity of the general Toeplitz matrix. In addition, the closing section of the paper is devoted to a statement of an algorithm for the inversion of lnon-Hernmitian matrices of the form (1.1).

Induced Matchings in Subcubic Planar Graphs