TY - JOUR
T1 - Transformation from arbitrary matchings to stable matchings
AU - Tamura, Akihisa
N1 - Funding Information:
* Supported by Grant-in-Aids for Co-operative Research (63490010) of the Ministry of Education, Science and Culture.
PY - 1993/3
Y1 - 1993/3
N2 - D. E. Knuth (1976, "Mariages stables," Presses Univ. Montréal, Montreal) conjectured that any matching can be transformed to some stable matching by a sequence of b-interchanges. Given a matching M and a blocking pair (m, w) for M, a b-interchange for M by (m, w) is defined as a transformation from M to a matching obtained by replacing two pairs (m, pM (m)) and (pM (w), w) in M with (m, w) and (pM (w), pM (m)). In this paper, we give a counter-example in which some matching cannot be transformed to any stable matching by b-interchanges. However, any matching can be transformed to some stable matching by using b-interchanges and identifying special cycling. We also give an algorithm to find either such cycling or a stable matching.
AB - D. E. Knuth (1976, "Mariages stables," Presses Univ. Montréal, Montreal) conjectured that any matching can be transformed to some stable matching by a sequence of b-interchanges. Given a matching M and a blocking pair (m, w) for M, a b-interchange for M by (m, w) is defined as a transformation from M to a matching obtained by replacing two pairs (m, pM (m)) and (pM (w), w) in M with (m, w) and (pM (w), pM (m)). In this paper, we give a counter-example in which some matching cannot be transformed to any stable matching by b-interchanges. However, any matching can be transformed to some stable matching by using b-interchanges and identifying special cycling. We also give an algorithm to find either such cycling or a stable matching.
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U2 - 10.1016/0097-3165(93)90051-9
DO - 10.1016/0097-3165(93)90051-9
M3 - Article
AN - SCOPUS:38249005148
VL - 62
SP - 310
EP - 323
JO - Journal of Combinatorial Theory - Series A
JF - Journal of Combinatorial Theory - Series A
SN - 0097-3165
IS - 2
ER -