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이산수학 그룹
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Set systems related to a house allocation problem

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Title
Set systems related to a house allocation problem
Author(s)
D´aniel Gerbner; Bal´azs Keszegh; Abhishek Methuku; D´aniel T. Nagy; Bal´azs Patk´os; Casey Tompkins; Chuanqi Xiao.
Publication Date
2020-07
Journal
DISCRETE MATHEMATICS, v.343, no.7, pp.111886
Publisher
ELSEVIER SCIENCE BV
Abstract
© 2020 Elsevier B.V. We are given a set A of buyers, a set B of houses, and for each buyer a preference list, i.e., an ordering of the houses. A house allocation is an injective mapping τ from A to B, and τ is strictly better than another house allocation τ′≠τ if for every buyer i, τ′(i) does not come before τ(i) in the preference list of i. A house allocation is Pareto optimal if there is no strictly better house allocation. Let s(τ) be the image of τ i.e., the set of houses sold in the house allocation τ. We are interested in the largest possible cardinality f(m) of the family of sets s(τ) for Pareto optimal mappings τ taken over all sets of preference lists of m buyers and all sets of houses. This maximum exists since in a Pareto optimal mapping with m buyers, each buyer will always be assigned one of their top m choices. We improve the earlier upper bound on f(m) given by Asinowski et al. (2016), by making a connection between this problem and some problems in extremal set theory
URI
https://pr.ibs.re.kr/handle/8788114/7793
DOI
10.1016/j.disc.2020.111886
ISSN
0012-365X
Appears in Collections:
Pioneer Research Center for Mathematical and Computational Sciences(수리 및 계산과학 연구단) > Discrete Mathematics Group(이산 수학 그룹) > 1. Journal Papers (저널논문)
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