Random generation of combinatorial structures from a uniform
Theoretical Computer Science
The complexity of counting stable marriages
SIAM Journal on Computing
Three fast algorithms for four problems in stable marriage
SIAM Journal on Computing
The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
Communications of the ACM
The Complexity of Ferromagnetic Ising with Local Fields
Combinatorics, Probability and Computing
Sampling stable marriages: why spouse-swapping won't work
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating the partition function of the ferromagnetic Potts model
Journal of the ACM (JACM)
Approximating the partition function of the ferromagnetic Potts model
Journal of the ACM (JACM)
The expressibility of functions on the boolean domain, with applications to counting CSPs
Journal of the ACM (JACM)
| Hi-index | 5.23 |
We investigate the complexity of approximately counting stable matchings in the k-attribute model, where the preference lists are determined by dot products of ''preference vectors'' with ''attribute vectors'', or by Euclidean distances between ''preference points ''and ''attribute points''. Irving and Leather (1986) [14] proved that counting the number of stable matchings in the general case is #P-complete. Counting the number of stable matchings is reducible to counting the number of downsets in a (related) partial order [14] and is interreducible, in an approximation-preserving sense, to a class of problems that includes counting the number of independent sets in a bipartite graph (#BIS) (Dyer et al. (2004) [6]). It is conjectured that no FPRAS exists for this class of problems. We show this approximation-preserving interreducibility remains even in the restricted k-attribute setting when k=3 (dot products) or k=2 (Euclidean distances). Finally, we show it is easy to count the number of stable matchings in the 1-attribute dot-product setting.