Martin Volf

A graphical characterization of the largest chain graphs

The paper presents a graphical characterization of the largest chain graphs which serve as unique representatives of classes of Markov equivalent chain graphs. The characterization is a basis for an algorithm constructing, for a given chain graph, the largest chain graph equivalent to it. The algorithm was used to generate a catalog of the largest chain graphs with at most five vertices. Every item of the catalog contains the largest chain graph of a class of Markov equivalent chain graphs and an economical record of the induced independency model.

Parallel Graph-Partitioning Using the Mob Heuristic

In this paper we study graph partitioning which is an important NP-complete problem. We have implemented two mob heuristics and analysed their performance. Our main result is that for randomly generated graphs the mob heuristics with an exponential schedule is more efficient than that with the linear schedule, proposed earlier. With the other parameters of the heuristic being identical the exponential schedule doubles the speedup.