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research article

Stable Routing And Unique-Max Coloring On Trees

Haehnle, Nicolai  
•
Sanita, Laura  
•
Zenklusen, Rico
2013
Siam Journal On Discrete Mathematics

Some of the routing protocols used in telecommunication networks route traffic on a shortest path tree according to configurable integral link weights. One crucial issue for network operators is finding a weight function that ensures a stable routing: when some link fails, traffic whose path does not use that link should not be rerouted. In this paper we improve on several previously best results for finding small stable weights. As a conceptual contribution, we draw a connection between the stable weights problem and the seemingly unrelated unique-max coloring problem. In unique-max coloring, one is given a set of points and a family of subsets of those points called regions. The task is to assign to each region a color represented as an integer such that, for every point, one region containing it has a color strictly larger than the color of any other region containing this point. In our setting, points and regions become edges and paths of the shortest path tree, respectively, and based on this connection, we provide stable weight functions with a maximum weight of O(n log n) in the case of single link failure, where n is the number of vertices in the network. Furthermore, if the root of the shortest path tree is known, we present an algorithm for determining stable weights bounded by 4n, which is optimal up to constant factors. For the case of an arbitrary number of failures, we show how stable weights bounded by 3(n)n can be obtained. All the results improve on the previously best known bounds.

  • Details
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Type
research article
DOI
10.1137/100817565
Web of Science ID

WOS:000316868600007

Author(s)
Haehnle, Nicolai  
Sanita, Laura  
Zenklusen, Rico
Date Issued

2013

Publisher

Siam Publications

Published in
Siam Journal On Discrete Mathematics
Volume

27

Issue

1

Start page

109

End page

125

Subjects

routing protocols

•

unique-max coloring

Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
DISOPT  
Available on Infoscience
May 13, 2013
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/92088
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