Let us start with two examples. A company has a machine which drills holes into printed
circuit boards. Since it produces many of these boards it wants the machine to complete one …

Discrete optimization problems are everywhere, from traditional operations research
planning (scheduling, facility location and network design); to computer science databases; …

We present approximation algorithms for the metric uncapacitated facility location problem
and the metric k-median problem achieving guarantees of 3 and 6 respectively. The …

We present a general approximation technique for a large class of graph problems. Our
technique mostly applies to problems of covering, at minimum cost, the vertices of a graph …

We present a factor 2 approximation algorithm for finding a minimum-cost subgraph having
at least a specified number of edges in each cut. This class of problems includes, among …

We give the first approximation algorithm for the generalized network Steiner problem, a
problem in network design. An instance consists of a network with link-costs and} for each …

We explore random sampling as a tool for solving undirected graph problems. We show that
the sparse graph, or skeleton, which arises when we randomly sample a graph's edges will …

Consider a setting in which a group of nodes, situated in a large underlying network, wishes
to reserve bandwidth on which to support communication. Virtual private networks (VPNs) …

Network Design is an active research area in the intersection of Combinatorial Optimization
and Theoretical Computer Science that focuses on problems arising in the realm of modern …

The primal-dual method is a standard tool in the design of algorithms for combinatorial
optimization problems. This chapter shows how the primal-dual method can be modi ed to …