In the stable marriage problem, any instance admits the so-called man-optimal stable matching, in which every man is assigned the best possible partner. However, there are instances for which all men receive low-ranke...
详细信息
In the stable marriage problem, any instance admits the so-called man-optimal stable matching, in which every man is assigned the best possible partner. However, there are instances for which all men receive low-ranked partners even in the man-optimal stable matching. In this paper we consider the problem of improving the man-optimal stable matching by changing only one mans preference list. We show that the optimization variant and the decision variant of this problem can be solved in time O(n(3)) and O(n(2)), respectively, where n is the number of men (women) in an input. We further extend the problem so that we are allowed to change k mens preference lists. We show that the problem is W[1]-hard with respect to the parameter k and give O(n(2k+1))-time and O(n(k+1))-time exact algorithms for the optimization and decision variants, respectively. Finally, we show that the problems become easy when k = n;we give O(n(2.5) log n)-time and O(n(2))-timealgorithms for the optimization and decision variants, respectively
Given a digraph D = (V, A) and a positive integer k, an arc set F C A is called a k-arborescence if it is the disjoint union of k spanning arborescences. The problem of finding a minimum cost k-arborescence is known t...
详细信息
ISBN:
(纸本)9781510819672
Given a digraph D = (V, A) and a positive integer k, an arc set F C A is called a k-arborescence if it is the disjoint union of k spanning arborescences. The problem of finding a minimum cost k-arborescence is known to be polynomial-time solvable using matroid intersection. In this paper we study the following problem: find a minimum cardinality subset of arcs that contains at least one arc from every minimum cost k-arborescence. For k = 1. the problem was solved in [A. Bernath, G. Pap, Blocking optimal arborescences, IPCO 2013]. In this paper we give an algorithm for general k that has polynomial running time if k is fixed.
暂无评论