Talks
Spring 2016

FPTAS for #BIS with Degree Bounds on One Side

Wednesday, Feb. 24, 2016 9:30 am10:15 am

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Location: 

Calvin Lab

Counting the number of independent sets for a bipartite graph (#BIS) plays a crucial role in the study of approximate counting. It has been conjectured that there is no fully polynomial-time (randomized) approximation scheme (FPTAS/FPRAS) for #BIS, and it was proved that the problem for instances with a maximum degree of 6 is already as hard as the general problem. In this paper, we obtain a surprising tractability result for a family of #BIS instances. We design a very simple deterministic fully polynomial-time approximation scheme (FPTAS) for #BIS when the maximum degree for one side is no larger than 5 . There is no restriction for the degrees on the other side, which do not even have to be bounded by a constant. Previously, FPTAS was only known for instances with a maximum degree of 5 for both sides.