## Departmental Papers (CIS)

#### Date of this Version

January 2001

#### Document Type

Conference Paper

#### Recommended Citation

Chandra Chekuri, Sanjeev Khanna, and Joseph Naor, "A Deterministic Algorithm for the COST-DISTANCE Problem", . January 2001.

#### Abstract

The COST-DISTANCE network design problem is the following. We are given an undirected graph *G* = (*V*,*E*), a designated *root* vertex *r* ∈ *V*, and a set of terminals *S* ⊂ of *V*. We are also given two non-negative real valued functions defined on *E*, namely, a cost function *c* and a length function *l*, and a non-negative weight function *w* on the set *S*. The goal is to find a tree *T* that connects the terminals in *S* to the root *r* and minimizes σ _{e ∈ T}*c*(*e*) + σ _{t ∈ S}*w*(*t*)*l _{T}*(

*r*,

*t*), where

*l*(

_{T}*r*,

*t*) is the length of the path in

*T*from

*t*to

*r*.

We give a *deterministic O*(log *k*) approximation algorithm for the COST-DISTANCE network design problem, in a sense derandomizing the algorithm given in [4]. Our algorithm is based on a natural linear programming relaxation of the problem and in the process we show that its integrality gap is *O*(log *k*).

**Date Posted:** 11 March 2005

## Comments

Copyright SIAM, 2001. Published in

Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2001), pages 232-233.