 
Summary: A General Approach to Online Network Optimization Problems
Noga Alon Baruch Awerbuch y Yossi Azar z Niv Buchbinder x
Joseph (SeĈ) Naor {
Abstract
We study a wide range of online graph and network optimization problems, focusing on problems that
arise in the study of connectivity and cuts in graphs. In a general online network design problem, we have a
communication network known to the algorithm in advance. What is not known in advance are the bandwidth
or cut demands between nodes in the network. Our results include an O(log m log n) competitive randomized
algorithm for the online nonmetric facility location and for a generalization of the problem called the multicast
problem. In the nonmetric facility location m is the number of facilities and n is the number of clients. The
competitive ratio is nearly tight. We also present an O(log 2 n log k) competitive randomized algorithm for the
online group Steiner problem in trees and an O(log 3
n log k) competitive randomized algorithm for the problem
in general graphs, where n is the number of vertices in the graph and k is the number of groups. Finally,
we design a deterministic O(log 3 n log log n) competitive algorithm for the online multicut problem. Our
algorithms are based on a unied framework for designing online algorithms for problems involving connectivity
and cuts. We rst present a general O(log m)deterministic algorithm for generating fractional solution that
satises the online connectivity or cut demands, where m is the number of edges in the graph. This may be
of independent interest for solving fractional online bandwidth allocation problems, and is applicable to the
node version as well. The integral solutions are obtained by an online rounding of the fractional solution. This
