Joseph Douglas Horton

A polynomial-time algorithm to find the shortest cycle basis of a graph

Define the length of a basis of the cycle space of a graph to be the sum of the lengths of all cycles in the basis. An algorithm is given that finds a cycle basis with the shortest possible length in

A Polynomial Time Algorithm to Find the Minimum Cycle Basis of a Regular Matroid

O(m^3 n)

Sub-latin squares and incomplete orthogonal arrays

operations, where m is the number of edges and n is the number of vertices. This is the first known polynomial-time algorithm for this problem. Edges may be weighted or unweighted. Also, the shortest cycle basis is shown to have at most

Resolvable path designs

{{3(n - 1)(n - 2)} / 2}

Merge Path Improvements for Minimal Model Hyper Tableaux

edges for the unweighted case.

Room designs and one-factorizations

O(mn^2 )

The Cascade Vulnerability Problem

algorithm to obtain a suboptimal cycle basis of length

Non-hamiltonian 3-connected cubic bipartite graphs

O(n^2 )

A recursive construction for Room designs

for unweighted graphs is also given.

Clause trees: a tool for understanding and implementing resolution in automated reasoning

An algorithm is given to solve the minimum cycle basis problem for regular matroids. The result is based upon Seymours decomposition theorem for regular matroids; the Gomory-Hu tree, which is essentially the solution for cographic matroids; and the corresponding result for graphs. The complexity of the algorithm is O((n + m)4), provided that a regular matroid is represented as a binary n×m matrix. The complexity decreases to O((n+m)3.376) using fast matrix multiplication.