Some observations on holographic algorithms

Authors:
Leslie G. Valiant
Affiliations:
School of Engineering and Applied Sciences, Harvard University
Venue:
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Year:
2010

Citing 16
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Abstract

We define the notion of diversity for families of finite functions, and express the limitations of a simple class of holographic algorithms in terms of limitations on diversity. We go on to describe polynomial time holographic algorithms for computing the parity of the following quantities for degree three planar undirected graphs: the number of 3-colorings up to permutation of colors, the number of connected vertex covers, and the number of induced forests or feedback vertex sets. In each case the parity can be computed for any slice of the problem, in particular for colorings where the first color is used a certain number of times, or where the connected vertex cover, feedback set or induced forest has a certain number of nodes. These holographic algorithms use bases of three components, rather than two.