In this paper we study approximation algorithms for multiroute cut problems in undirected graphs. In these problems the goal is to find a minimum cost set of edges to be removed from a given graph such that the edge-connectivity (or node-connectivity) between certain pairs of nodes is reduced below a given threshold K. In the usual cut problems the edge connectivity is required to be reduced be...

We show that Karger’s randomized contraction method [7] can be adapted to multiobjective global minimum cut problems with a constant number of edge or node budget constraints to give efficient algorithms. For global minimum cuts with a single edge-budget constraint, our extension of the randomized contraction method has running time Õ(n3) in an n-node graph improving upon the best-known randomi...

To tackle the problem with inexact, uncertainty and vague knowl- edge, constructive method is utilized to formulate lower and upper approx- imation sets. Rough set model over dual-universes in fuzzy approximation space is constructed. In this paper, we introduce the concept of rough set over dual-universes in fuzzy approximation space by means of cut set. Then, we discuss properties of rough se...

We introduce a graph clustering problem motivated by a stream processing application. Input to our problem is an undirected graph with vertex and edge weights. A cluster is a subset of the vertices. The size of a cluster is defined as the total vertex weight in the subset plus the total edge weight at the boundary of the cluster. The bounded size graph clustering problem (BSGC) is to partition ...

called the triangle inequalities. The paper deals with the problem of finding efficient algorithms to optimize a linear function over such a polytope. We briefly mention two reasons to seek for an efficient way to optimize a linear function over M(G). 1. The polytope M(G), for |V | > 4, properly contains the cut polytope associated with G (see, e.g., [5] for the details). Thus, if an edge cost ...

We consider a capacitated max k-cut problem in which a set of vertices is partitioned into k subsets. Each edge has a non-negative weight, and each subset has a possibly different capacity that imposes an upper bound on its size. The objective is to find a partition that maximizes the sum of edge weights across all pairs of vertices that lie in different subsets. We describe a local-search algo...

Several authors have studied the graphs for which every edge is a chord of a cycle; among 2-connected graphs, one characterization is that the deletion of one vertex never creates a cut-edge. Two new results: among 3-connected graphs with minimum degree at least 4, every two adjacent edges are chords of a common cycle if and only if deleting two vertices never creates two adjacent cut-edges; am...

2 Cut Sparsifier Before we state the main theorem, we remind the reader of the definition of connectivity: Definition 1 (Connectivity). The connectivity λe of edge e is the size of the smallest cut containing e. The main theorem gives a construction for a graph sparsifier which preserves cuts. Theorem 1 (Fung and Harvey [FH10], Hariharan and Panigrahi [HP10]). Consider graph G = (V,E) simple an...

We investigate using the Mondriaan matrix partitioner for unweighted graph partitioning in the communication volume and edge-cut metrics. By converting the unweighted graphs to appropriate matrices, we measure Mondriaan’s performance as a graph partitioner for the 10th DIMACS challenge on graph partitioning and clustering. We find that Mondriaan can effectively be used as a graph partitioner: w...

To investigate the effect of coupling edges, we compare cooperative cut (CoopCut) to the standard graph cut (GraphCut), and, for shrinking bias, also to curvature regularization. To ensure equivalent conditions, all methods used the same weights on the terminal edges (i.e., the same unary potentials), the same 8-neighbor graph structure, and the same inter-pixel edge weights. The unary potentia...