Oblivious Buy-at-Bulk in Planar Graphs
Srivathsan Srinivasagopalan, Costas Busch, S.S. Iyengar

TL;DR
This paper presents a deterministic polynomial-time algorithm for the oblivious buy-at-bulk network design problem in planar graphs, achieving an optimal $O(\log n)$ approximation ratio for all demands and fusion functions.
Contribution
It introduces the first tight analysis for planar graphs, improving the approximation ratio by a factor of $\log n$ over previous results, and handles demand and fusion function obliviousness.
Findings
Achieves $O(\log n)$ approximation ratio for planar graphs.
Algorithm is deterministic and runs in polynomial time.
First tight analysis for this problem in planar graphs.
Abstract
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 . 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 . The algorithm is deterministic and computes the fixed set of paths in polynomial time, and guarantees a approximation ratio for any set of demands and any canonical fusion function , where is the number of nodes. The algorithm is asymptotically optimal, since it is known that this problem cannot be approximated with better than ratio. To our…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsComplexity and Algorithms in Graphs · Optimization and Search Problems · Advanced Graph Theory Research
