Progress in complexity of counting problems

Authors:
Jin-Yi Cai
Affiliations:
University of Wisconsin-Madison
Venue:
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
Year:
2011

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Abstract

There has been remarkable progress in the classification program of the complexity of counting problems. This program is carried out in at least three interrelated formulations: Graph Homomorphisms, Counting CSP, and Holant Problems. In each formulation, complexity dichotomy theorems have been achieved which classify every problem in a given class to be either solvable in polynomial time or #P-hard.