Given a directed graph G, a set of k terminals and an integer p, the Directed Vertex Multiway Cut problem asks if there is a set S of at most p (nonterminal) vertices whose removal disconnects each terminal from all other terminals. Directed Edge Multiway Cut is the analogous problem where S is a set of at most p edges. These two problems indeed are known to be equivalent. A natural generalizat...

Motivated by applications from computer network security and software engineering, we study the problem of reducing reachability on a graph with unknown edge costs. When the costs are known, reachability reduction can be solved using a linear relaxation of sparsest cut. Problems arise, however, when edge costs are unknown. In this case, blindly applying sparsest cut with incorrect edge costs ca...

We propose a fixed-parameter tractable algorithm for the Max-Cut problem on embedded 1-planar graphs parametrized by the crossing number k of the given embedding. A graph is called 1-planar if it can be drawn in the plane with at most one crossing per edge. Our algorithm recursively reduces a 1-planar graph to at most 3 planar graphs, using edge removal and node contraction. The Max-Cut problem...

An edge cut W of a connected graph G is a k-restricted edge cut if G−W is disconnected, and every component of G −W has at least k vertices. The k-restricted edge connectivity is defined as the minimum cardinality over all k-restricted edge cuts. A permutation graph is obtained by taking two disjoint copies of a graph and adding a perfect matching between the two copies. The k-restricted edge c...

For a large class of irregular mesh applications, the structure of the mesh changes from one phase of the computation to the next. Eventually, as the mesh evolves, the adapted mesh has to be repartitioned to ensure good load balance. If this new graph is partitioned from scratch, it may lead to an excessive migration of data among processors. In this paper, we present schemes for computing repa...

Let K be an abelian group and G be a connected graph, both finite. Using basic properties of circulations, we show that it is easy to generate uniformly random K-circulations on G. This leads to efficient algorithms for computing the cut edges, cut edge-pairs, and cut vertices of a graph; for example, the cut edges are “usually” the edges where a random circulation vanishes. In the distributed ...

The safety of people and the security of the vital functions of society are among the core tasks of governments. Various networks, especially transportation networks, are important for human life. Much research has been done to analyse the vulnerability of road networks and most of the methods were based on analysing the topological structure of the network using graph theory. For instance, Dem...

The ultra-precision diamond cutting process exhibits strong size effects due to the ultra-small depth of cut that is comparable with the cutting edge radius. In the present work, we elucidate the underlying machining mechanisms of single crystal cerium under diamond cutting by means of molecular dynamics simulations, with an emphasis on the evaluation of the effect of depth of cut on the cuttin...

OF THE DISSERTATION On Generation of Cut Conjunctions, Minimal k-Connected Spanning Subgraphs, Minimal Connected and Spanning Subsets and Vertices by Konrad Borys Dissertation Director: Professor Endre Boros We consider the following problems: • Cut conjunctions in graphs: given an undirected graphG = (V,E) and a collection of vertex pairs B ⊆ V × V generate all minimal edge sets X ⊆ E such tha...

In order to obtain basic information on the improving the surface integrity of machined surfaces, the relationship between the residual stress of cut surfaces and the cutting edge shapes of cutting tools was examined. Dry facing on a lathe was performed with cutting tools that had various nose radiuses and cutting edge roundnesses. The residual stresses of the cut surfaces were measured by X-ra...