Peter Danziger

Covering arrays avoiding forbidden edges

Covering arrays (CAs) can be used to detect the existence of faulty pairwise interactions between parameters or components in a software system. The generalization considered here applies to the situation in which some input combinations are invalid, a requirement quite common in software testing. In this paper, we study covering arrays avoiding forbidden edges (CAFEs), where certain pairwise interactions are forbidden while all others must be covered, and we aim to minimize the number of tests. We establish a theoretical framework for this problem, by providing connections to the edge clique covering problem, lower and upper bounds, complexity results and a recursive construction. We also give an algorithm for the case of binary alphabets.

Class‐uniformly resolvable designs

We investigate Class-Uniformly Resolvable Designs, which are resolvable designs in which each of the resolution classes has the same number of blocks of each size. We derive the fully general necessary conditions including a number of extremal bounds. We present two general constructions. We primarily consider the case of block sizes 2 and 3, where we find two infinite extremal families and finish two other infinite families by difference constructions. We present tables showing the current state of knowledge in the case of block size 2 and 3 for all orders up to 200.

A Cyclic Solution for an Infinite Class of Hamilton---Waterloo Problems

The main result of this paper is the explicit construction, for any positive integer n, of a cyclic two-factorization of

Cover starters for covering arrays of strength two

K_{50n+5}

Covering Arrays Avoiding Forbidden Edges

K50n+5 with

On the Hamilton–Waterloo Problem with cycle lengths of distinct parities

20n+2