Improved Bounds for Bipartite Matching on Surfaces

Samir Datta (1) , Arjun Gopalan , Raghav Kulkarni (2) , Raghunath Tewari (3)

1 Chennai Mathematical Institute [Inde]
2 Department of Computer Science
3 Department of Computer Science and Engineering

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 the NC bound for O(log n) genus graphs from Mahajan and Varadarajan, and Kulkarni, Mahajan, and Varadarajan. For Part (1) we combine the flow technique of Miller and Naor with the double counting technique of Reinhardt and Allender . For Part (2) and (3) we extend Miller and Naor's result to higher genus surfaces in the spirit of Chambers, Erickson and Nayyeri.

Mots clés: Perfect Matching; Graphs on Surfaces; Space Complexity; NC; UL

Domaines: Complexité [cs.CC]; Algorithme et structure de données [cs.DS]

Samir Datta, Arjun Gopalan, Raghav Kulkarni, Raghunath Tewari. Improved Bounds for Bipartite Matching on Surfaces. STACS'12 (29th Symposium on Theoretical Aspects of Computer Science), Feb 2012, Paris, France. pp.254-265. ⟨hal-00678185⟩