Improved Bounds for Bipartite Matching on Surfaces

Samir Datta, Arjun Gopalan, Raghav Kulkarni & Raghunath Tewari
We exhibit the following new upper bounds on the space complexity and the parallel complexity of the Bipartite Perfect Matching (BPM) problem for graphs of small genus: (1) BPM in planar graphs is in UL (improves upon the SPL bound from Datta, Kulkarni, and Roy; (2) BPM in constant genus graphs is in NL (orthogonal to the SPL bound from Datta, Kulkarni, Tewari, and Vinodchandran.; (3) BPM in poly-logarithmic genus graphs is in NC; (extends...