Integer Programming over a Finite Additive Group

An Algorithm for Solving the Linear Integer Programming Problem over a Finite Additive Group, with Extensions to Solving General Linear and Certain Nonlinear Integer Problems

Ralph Gomory has recently aroused interest in a special type of knapsack problem in which the constraint coefficients and constant term are elements of a finite additive group. The significance of this problem lies in the fact that it is closely related to the general integer linear programming problem, resulting by removing the nonnegativity restrictions on those variables in the general probl...

Topics in group methods for integer programming

Integer Sequences and Matrices Over Finite Fields

In this expository article we collect the integer sequences that count several different types of matrices over finite fields and provide references to the Online Encyclopedia of Integer Sequences (OEIS). Section 1 contains the sequences, their generating functions, and examples. Section 2 contains the proofs of the formulas for the coefficients and the generating functions of those sequences i...

Programming Research Group A NOTE ON PROBABILISTIC INTEGER SORTING

We present a new probabilistic sequential algorithm for stable sorting n uniformly distributed keys in an arbitrary range. The algorithm runs in linear time with very-high probability 1 ? 2 ?(n) (the best previously known probability bound has been 1 ? 2 ?(n=(lg n lg lg n))). We also describe an EREW PRAM version of the algorithm that sorts in O((n=p + lg p) lg n= lg (n=p + lg n)) time using p ...

Computational experience with a group theoretic integer programming algorithm