2011 | OriginalPaper | Buchkapitel
Oblivious Buy-at-Bulk in Planar Graphs
verfasst von : Srivathsan Srinivasagopalan, Costas Busch, S. Sitharama Iyengar
Erschienen in: WALCOM: Algorithms and Computation
Verlag: Springer Berlin Heidelberg
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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-destination 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 Ω(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.