Stable Routing and Unique-Max Coloring on Trees
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 no...
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| Format: | Article |
| Language: | en_US |
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Society for Industrial and Applied Mathematics
2013
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| Online Access: | http://hdl.handle.net/1721.1/79613 |
| _version_ | 1826210046580621312 |
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| author | Hähnle, Nicolai Sanità, Laura Zenklusen, Rico |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Hähnle, Nicolai Sanità, Laura Zenklusen, Rico |
| author_sort | Hähnle, Nicolai |
| collection | MIT |
| description | 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[superscript n] n can be obtained. All the results improve on the previously best known bounds. |
| first_indexed | 2024-09-23T14:40:44Z |
| format | Article |
| id | mit-1721.1/79613 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:40:44Z |
| publishDate | 2013 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | mit-1721.1/796132022-10-01T22:00:58Z Stable Routing and Unique-Max Coloring on Trees Hähnle, Nicolai Sanità, Laura Zenklusen, Rico Massachusetts Institute of Technology. Department of Mathematics Zenklusen, Rico 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[superscript n] n can be obtained. All the results improve on the previously best known bounds. National Science Foundation (U.S.) (Grant CCF-1115849) National Science Foundation (U.S.) (Grant CCF-0829878) United States. Office of Naval Research (Grant N00014-12-1-0033) United States. Office of Naval Research (Grant N00014-11-1-0053) United States. Office of Naval Research (Grant N00014-09-1-0326) 2013-07-18T14:57:15Z 2013-07-18T14:57:15Z 2013-01 2012-08 Article http://purl.org/eprint/type/JournalArticle 0895-4801 1095-7146 http://hdl.handle.net/1721.1/79613 Hähnle, Nicolai, Laura Sanità, and Rico Zenklusen. “Stable Routing and Unique-Max Coloring on Trees.” SIAM Journal on Discrete Mathematics 27, no. 1 (January 10, 2013): 109-125. © 2013, Society for Industrial and Applied Mathematics en_US http://dx.doi.org/10.1137/100817565 SIAM Journal on Discrete Mathematics Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Society for Industrial and Applied Mathematics APS |
| spellingShingle | Hähnle, Nicolai Sanità, Laura Zenklusen, Rico Stable Routing and Unique-Max Coloring on Trees |
| title | Stable Routing and Unique-Max Coloring on Trees |
| title_full | Stable Routing and Unique-Max Coloring on Trees |
| title_fullStr | Stable Routing and Unique-Max Coloring on Trees |
| title_full_unstemmed | Stable Routing and Unique-Max Coloring on Trees |
| title_short | Stable Routing and Unique-Max Coloring on Trees |
| title_sort | stable routing and unique max coloring on trees |
| url | http://hdl.handle.net/1721.1/79613 |
| work_keys_str_mv | AT hahnlenicolai stableroutinganduniquemaxcoloringontrees AT sanitalaura stableroutinganduniquemaxcoloringontrees AT zenklusenrico stableroutinganduniquemaxcoloringontrees |