 
Summary: Beating the logarithmic lower bound: randomized preemptive
disjoint paths and call control algorithms
Ran Adler y Yossi Azar z
March 19, 2001
Abstract
We consider the maximum disjoint paths problem and its generalization, the call
control problem, in the online setting. In the maximum disjoint paths problem, we are
given a sequence of connection requests for some communication network. Each request
consists of a pair of nodes, that wish to communicate over a path in the network. The
request has to be immediately connected or rejected, and the goal is to maximize the
number of connected pairs, such that no two paths share an edge. In the call control
problem, each request has an additional bandwidth specication, and the goal is to
maximize the total bandwidth of the connected pairs (throughput), while satisfying
the bandwidth constraints (assuming each edge has unit capacity). These classical
problems are central in routing and admission control in high speed networks and in
optical networks.
We present the rst known constantcompetitive algorithms for both problems on
the line. This settles an open problem of Garay et al. and of Leonardi. Moreover,
to the best of our knowledge, all previous algorithms for any of these problems, are
