This paper shows that the situation changes substantially if the problem not only becomes NP-hard, but also the optimal cost version has no approximation algorithm achieving the approximation ratio of N1-Ɛ, where N is the instance size, unless P=NP.Expand

Partial MAXSAT is introduced and how to solve it using local search algorithms is investigated, giving weight to clauses for their own purpose, which will hide the initial weight as the algorithms proceed.Expand

The first nontrivial result for approximation of factor less than two for stable marriage problem is given, which achieves an approximation ratio of 2/(1 + L−2) for instances in which only men have ties of length at most L.Expand

The problem of finding a largest stable matching where preference lists may include ties and unacceptable partners (MAX SMTI) is known to be NP-hard, and the current best approximation algorithm achieves the ratio of 1.5.Expand

A 1.875-approximation algorithm is given, which is the first result on the approximation ratio better than two on the problem of finding a stable matching of maximum size when both ties and unacceptable partners are allowed in preference lists.Expand

This paper considers an extension of the Hospitals/Residents problem in which each hospital specifies not only an upper bound but also a lower bound on its number of positions, and gives an exponential-time exact algorithm for this problem.Expand

The Hospitals/Residents problem is a many-to-one extension of the stable marriage problem in which each hospital specifies not only an upper bound but also a lower bound on its number of positions, and an exponential-time exact algorithm is given for a special case where all the upper bound quotas are one.Expand