Oblivious Buy-at-Bulk in Planar Graphs
| Autor: | Srinivasagopalan, Srivathsan, Busch, Costas, Iyengar, S. S. |
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| Rok vydání: | 2010 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In the oblivious buy-at-bulk network design problem in a graph, the task is to compute a fixed set of paths for every pair of source-destinations in the graph, such that any set of demands can be routed along these paths. The demands could be aggregated at intermediate edges where the fusion-cost is specified by a canonical (non-negative concave) function $f$. We give a novel algorithm for planar graphs which is oblivious with respect to the demands, and is also oblivious with respect to the fusion function $f$. The algorithm is deterministic and computes the fixed set of paths in polynomial time, and guarantees a $O(\log n)$ approximation ratio for any set of demands and any canonical fusion function $f$, where $n$ is the number of nodes. The algorithm is asymptotically optimal, since it is known that this problem cannot be approximated with better than $\Omega(\log n)$ ratio. To our knowledge, this is the first tight analysis for planar graphs, and improves the approximation ratio by a factor of $\log n$ with respect to previously known results. Comment: 13 Pages (includes 1 page of appendix). Submitted to WALCOM-2011 - Workshop on Algorithms and Computation |
| Databáze: | arXiv |
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