Approximating Holant problems by winding [article]

Colin McQuillan
2013 arXiv   pre-print
We give an FPRAS for Holant problems with parity constraints and not-all-equal constraints, a generalisation of the problem of counting sink-free-orientations. The approach combines a sampler for near-assignments of "windable" functions -- using the cycle-unwinding canonical paths technique of Jerrum and Sinclair -- with a bound on the weight of near-assignments. The proof generalises to a larger class of Holant problems; we characterise this class and show that it cannot be extended by
more » ... bility reductions. We then ask whether windability is equivalent to expressibility by matchings circuits (an analogue of matchgates), and give a positive answer for functions of arity three.
arXiv:1301.2880v1 fatcat:4xpvaztdcbdtzal4nz6orjjeo4