A Preemptive Algorithm for Maximizing Disjoint Paths on Trees

We consider the online version of the maximum vertex disjoint path problem when the underlying network is a tree. In this problem, a sequence of requests arrives in an online fashion, where every request is a path in the tree. The online algorithm may accept a request only if it does not share a vertex with a previously accepted request. The goal is to maximize the number of accepted requests. It is known that no online algorithm can have a competitive ratio better than (log n) for this problem, even if the algorithm is randomized and the tree is simply a line. Obviously, it is desirable to beat the logarithmic lower bound. Adler and Azar [SODA 1999] showed that if preemption is allowed (namely, previously accepted requests may be discarded, but once a request is discarded it can no longer be accepted), then there is a randomized online algorithm that achieves constant competitive ratio on the line. In the current work we present a randomized online algorithm with preemption that has ...

• Type: Journal
• Year: 2010
• Where: ALGORITHMICA
• Authors: Yossi Azar, Uriel Feige, Daniel Glasner
• Keywords: Accepted Requests, ALGORITHMICA 2010, Online, Online Algorithm