Title: On Selecting Nodes for Monitoring A Network Speaker: Howard Karloff, AT&T Labs--Research I will start by discussing a recently proposed scheme for monitoring an ISP's customer's end-to-end performance in a network. To efficiently implement the scheme, one needs to solve the following Monitor Placement problem: We are given a graph with weights on its edges, a subset B of ``branch nodes'' b, and a subset M of ``potential monitoring nodes'' m. The goal is to choose a smallest subset M' of M such that for each specified branch node b, there are two distinct monitoring nodes m1, m2 in M' such that all shortest paths from b to m1 are vertex disjoint (except for b) from all shortest paths from b to m2. While the problem is provably hard to solve, even approximately (unless P=NP), we give a fast algorithm called Double Hitting Set which, on our testbed, often finds the exact integral optimum. What's more, it shows how to find a good lower bound on the optimum, proving that Double Hitting Set's output is (usually) very close to the optimum. I will also discuss other algorithms our group developed for Monitor Placement. This is joint work with many people.