Test Algorithm

Table 1: Comparison of sum of cluster densities for MDS Peeling+DPRP and for the best of 10 Density-FM runs. Results for avq.small benchmark using Density-FM would require many days of SPARC-10 time. Bounded Size Maximum Density Subhyper-graph (BMDS) problem : Given a hypergraph H(V; E) and an integer B, nd the subhypergraph of H with maximum density and size B. While MDS was polynomial time solvable, BMDS is shown NP-complete by reduction from Maximum Clique. Max-Density Subhypergraph with Prescribed Node problem : Given a hypergraph H(V; E) and a prescribed node p, nd the maximum density subhypergraph which contains node p. This can be solved using the 0 ? 1 fractional programming technique in 11] by assigning the variable corresponding to p to 1, and transforming the resulting fractional expression to a series of ow computations. Max-Density Subhypergraph with Excluded Node problem : Given a hypergraph H(V; E) and a prescribed node p, nd the maximum density subhypergraph which does not contain node p. This problem can be solved in the same time complexity as the MDS problem. We can remove node p and all edges incident from p, and solve the MDS problem in the remaining hypergraph. 6 Acknowledgments We are grateful to Dr. Lars Hagen for his valuable comments, and to Professor Laura Sanchis for providing k-way FM code 13]. Also, thanks to Dr. L. T. Liu for valuable discussion.