Hardness of Low Congestion Routing in Directed Graphs

نویسندگان

  • Venkatesan Guruswami
  • Kunal Talwar
چکیده

We prove a strong inapproximability result for routing on directed graphs with low congestion. Given as input a directed graph on N vertices and a set of source-destination pairs that can be connected via edge-disjoint paths, we prove that it is hard, assuming NP doesn’t have n log n) time randomized algorithms, to route even a 1/N fraction of the pairs, even if we are allowed to use each edge on c(N) paths. Here the congestion c(N) can be any function in the range 1 6 c(N) 6 α logN/ log logN for some absolute constant α > 0. The hardness result is in the right ballpark since a factorN approximation algorithm is known for this problem. An important feature of our result is that it holds with perfect completeness, and shows hardness of low-congestion routing of instances where all the input source-destination pairs can be routed on edge-disjoint paths. Consequently, our result also implies that it is hard to find a routing of all the source-destination pairs that incurs congestion at most α logN/ log logN , even if there exists an edge-disjoint (i.e., congestion 1) routing of all the pairs. This shows the optimality, up to constant factors, of the approximation guarantee of the classic Raghavan-Thompson algorithm based on randomized rounding of the fractional multicommodity flow solution.

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عنوان ژورنال:
  • Electronic Colloquium on Computational Complexity (ECCC)

دوره 13  شماره 

صفحات  -

تاریخ انتشار 2006