Diffusion Methods for Classification with Pairwise Relationships

We define two algorithms for propagating information in classification problems with pairwise relationships. The algorithms involve contraction maps and are related to non-linear diffusion and random walks on graphs. The approach is also related to message passing and mean field methods. The algorithms we describe are guaranteed to converge on graphs with arbitrary topology. Moreover … Read more

Minimum weight t-composition of an integer

If $p \geq t$ are positive integers, a t-composition of p is an ordered t-tuple of positive integers summing p. If $T=(s_1, s_2, \dots, s_t)$ is a t-composition of p and W is a $p-(t-1) \times t$ matrix, call $W(T)= \sum_{k=1}^t w_{s_k k}$ the weight of the t-composition T. We show that finding a minimum … Read more

On cost matrices with two and three distinct values of Hamiltonian paths and cycles

Polynomially testable characterization of cost matrices associated with a complete digraph on $n$ nodes such that all the Hamiltonian cycles (tours) have the same cost is well known. Tarasov~\cite{TARA81} obtained a characterization of cost matrices where tour costs take two distinct values. We provide a simple alternative characterization of such cost matrices that can be … Read more

Speeding up dynamic shortest path algorithms

Dynamic shortest path algorithms update the shortest paths to take into account a change in an edge weight. This paper describes a new technique that allows the reduction of heap sizes used by several dynamic shortest path algorithms. For unit weight change, the updates can be done without heaps. These reductions almost always reduce the … Read more