A Preemptive Algorithm for Maximizing Disjoint Paths on Trees

We consider the on-line 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 on-line fashion, where every request is a path in the tree. The on-line algorithm may accept a request only if it does not share a...

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Bibliographic Details
Published in:Algorithmica Vol. 57; no. 3; pp. 517 - 537
Main Authors: Azar, Yossi, Feige, Uriel, Glasner, Daniel
Format: Journal Article Conference Proceeding
Language:English
Published: New York Springer-Verlag 01.07.2010
Springer
Subjects:
Algorithm Analysis and Problem Complexity
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Computer Science
Computer science; control theory; systems
Computer systems and distributed systems. User interface
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Exact sciences and technology
Mathematics of Computing
Software
Theoretical computing
Theory of Computation
Online algorithms
Admission control
Disjoint paths
Disjoint paths on trees
Call control
Access control
Preemption
Lower bound
On line
Logarithmic function
Competitiveness
Routing
Approximation algorithm
Randomized algorithm
Combinatorial optimization
Randomization
Network protocol
Capacity constraint
Deterministic algorithms
ISSN:0178-4617, 1432-0541
Online Access:Get full text
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Summary:We consider the on-line 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 on-line fashion, where every request is a path in the tree. The on-line 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 on-line algorithm can have a competitive ratio better than Ω(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 (Proc. of the 10th ACM-SIAM Symposium on Discrete Algorithm, pp. 1–10, 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 on-line algorithm that achieves constant competitive ratio on the line. In the current work we present a randomized on-line algorithm with preemption that has constant competitive ratio on any tree. Our results carry over to the related problem of maximizing the number of accepted paths subject to a capacity constraint on vertices (in the disjoint path problem this capacity is 1). Moreover, if the available capacity is at least 4, randomization is not needed and our on-line algorithm becomes deterministic.
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-009-9305-4