Guy Kortsarz

The dense k-subgraph problem

Abstract. This paper considers the problem of computing the dense k -vertex subgraph of a given graph, namely, the subgraph with the most edges. An approximation algorithm is developed for the problem, with approximation ratio O(nδ) , for some δ < 1/3 .

How to Allocate Network Centers

This paper deals with the issue of allocating and utilizing centers in a distributed network, in its various forms. The paper discusses the significant parameters of center allocation, defines the resulting optimization problems, and proposes several approximation algorithms for selecting centers and for distributing the users among them. We concentrate mainly on balanced versions of the problem, i.e., in which it is required that the assignment of clients to centers be as balanced as possible. The main results are constant ratio approximation algorithms for the balanced ?-centers and balanced ?-weighted centers problems, and logarithmic ratio approximation algorithms for the ?-dominating set and the k-tolerant set problems.

On choosing a dense subgraph

This paper concerns the problem of computing the densest k-vertex subgraph of a given graph, namely, the subgraph with the most edges, or with the highest edges-to-vertices ratio. A sequence of approximation algorithms is developed for the problem, with each step yielding a better ratio at the cost of a more complicated solution. The approximation ratio of our final algorithm is O/spl tilde/(n/sup 0.3885/). We also present a method for converting an approximation algorithm for an unweighted graph problem (from a specific class of maximization problems) into one for the corresponding weighted problem, and apply it to the densest subgraph problem.<<ETX>>

Hardness of Approximation for Vertex-Connectivity Network Design Problems

In the survivable network design problem (SNDP), the goal is to find a minimum-cost spanning subgraph satisfying certain connectivity requirements. We study the vertex-connectivity variant of SNDP in which the input specifies, for each pair of vertices, a required number of vertex-disjoint paths connecting them. We give the first strong lower bound on the approximability of SNDP, showing that the problem admits no efficient

Generating Sparse 2-Spanners

2^{\log^{1-\epsilon} n}

Approximating Node Connectivity Problems via Set Covers

ratio approximation for any fixed

Approximation Algorithms for Minimum-Time Broadcast

\epsilon\! >\! 0

Approximating the weight of shallow Steiner trees

, unless

Generalized submodular cover problems and applications

\NP\subseteq \DTIME(n^{\polylog(n)})

Minimum Color Sum of Bipartite Graphs

. We show hardness of approximation results for some important special cases of SNDP, and we exhibit the first lower bound on the approximability of the related classical NP-hard problem of augmenting the connectivity of a graph using edges from a given set.