Takuro Fukunaga

Approximability of the capacitated b -edge dominating set problem

In this paper, we discuss the approximability of the capacitated b-edge dominating set problem, which generalizes the edge dominating set problem by introducing capacities and demands on the edges. We present an approximation algorithm for this problem and show that it achieves a factor of 8/3 for general graphs and a factor of 2 for bipartite graphs. Moreover, we discuss the relationships of the edge dominating set problem and the vertex cover problem. The results show that improving the approximation factor beyond 8/3 using our approach of adding valid inequalities to a natural linear programming relaxation is as hard as improving the approximation factor for vertex cover beyond 2.

Computing minimum multiway cuts in hypergraphs from hypertree packings

Hypergraph k-cut problem is a problem of finding a minimum capacity set of hyperedges whose removal divides a given hypergraph into k connected components. We present an algorithm for this problem which runs in strongly polynomial-time if both k and the rank of the hypergraph are constants. Our algorithm extends the algorithm due to Thorup (2008) for computing minimum k-cuts of graphs from greedy packings of spanning trees.

The Set Connector Problem in Graphs

Given a graph G= (V,E) with an edge cost and families

Divide-and-Conquer Algorithms for Partitioning Hypergraphs and Submodular Systems

\mathcal{V}_i\subseteq 2^V

Approximating a Generalization of Metric TSP

, i= 1,2,...,mof disjoint subsets, an edge subset Fi¾? Eis called a set connector if, for each

Iterative Rounding Approximation Algorithms for Degree-Bounded Node-Connectivity Network Design

\mathcal{V}_i

Graph Orientations with Set Connectivity Requirements

, the graph

Covering problems in edge- and node-weighted graphs

(V,F)/\mathcal{V}_i

Covering Problems in Edge- and Node-Weighted Graphs

obtained from (V,F) by contracting each

Computing minimum multiway cuts in hypergraphs

X\in \mathcal{V}_i