We recently proposed a coarse-grained parallel multilevel algorithm for the k-way hypergraph partitioning problem. This paper presents a formal analysis of the algorithm’s scalability in terms of its isoefficiency function, describes its implementation in the Parkway 2.0 tool and provides a run-time and partition quality comparison with stateof-the-art serial hypergraph partitioners. The isoeff...

When closure operators are deened over gures in the plane, they are normally deened with respect to convex closure in the Euclidean plane. This report concentrates on discrete closure operators deened over the discrete, rectilinear plane. Basic to geometric convexity is the concept of a geodesic, or shortest path. Such geodesics can be regarded as the closure of two points. But, given the usual...

The gvuph partitioning problem is to divide the vertices of a graph into disjoint clusters to minimize the total cost of the edges cut by the clusters. A spectral partitioning heuristic uses the graph’s eigenvectors to construct a geometric representation of the graph (e.g., linear orderings) which are subsequently partitioned. Our main result shows that when all the eigenvectors are used, grap...

In optimizing the area of Very Large Scale Integrated (VLSI) layouts, circuit interconnections should generally be realized with minimum total interconnect. This chapter addresses several variations of the corresponding fundamental Steiner minimal tree (SMT) problem, where a given set of pins is to be connected using minimum total wirelength. Steiner trees are important in global routing and wi...

VLSI layout applications yield instances of the Steiner tree problem over grid graphs with holes, which are considered hard to be solved by current methods. In particular, preprocessing techniques developed for Steiner problems over general graphs are not likely to reduce signiicantly such VLSI instances. We propose a new preprocessing procedure, combining earlier ideas from the literature to m...

We present two approaches for the Euclidean TSP which compute high quality tours for large instances. Both approaches are based on pseudo backbones consisting of all common edges of good tours. The first approach starts with some pre-computed good tours. Using this approach we found record tours for seven VLSI instances. The second approach is window based and constructs from scratch very good ...

To prevent an exploit, the security analyst must implement a suitable countermeasure. In this paper, we consider cost-sensitive attack graphs (CAGs) for network vulnerability analysis. In these attack graphs, a weight is assigned to each countermeasure to represent the cost of its implementation. There may be multiple countermeasures with different weights for preventing a single exploit. Also,...