On reachable assignments under dichotomous preferences

We consider the problem of determining whether a target item assignment can be reached from an initial item assignment by a sequence of pairwise exchanges of items between agents. In particular, we consider the situation where each agent has a dichotomous preference over the items, that is, each age...

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Bibliographic Details
Published inTheoretical computer science Vol. 979; p. 114196
Main Authors Ito, Takehiro, Kakimura, Naonori, Kamiyama, Naoyuki, Kobayashi, Yusuke, Nozaki, Yuta, Okamoto, Yoshio, Ozeki, Kenta
Format Journal Article
LanguageEnglish
Published Elsevier B.V 10.11.2023
Subjects
Combinatorial reconfiguration
Dichotomous preference
Item assignment
Item exchange
Combinatorial reconfiguration
Item exchange
Dichotomous preference
Item assignment
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Summary:We consider the problem of determining whether a target item assignment can be reached from an initial item assignment by a sequence of pairwise exchanges of items between agents. In particular, we consider the situation where each agent has a dichotomous preference over the items, that is, each agent evaluates each item as acceptable or unacceptable. Furthermore, we assume that communication between agents is limited, and the relationship is represented by an undirected graph. Then, a pair of agents can exchange their items only if they are connected by an edge and the involved items are acceptable. We prove that this problem is PSPACE-complete even when the communication graph is complete (that is, every pair of agents can exchange their items), and this problem can be solved in polynomial time if an input graph is a tree.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2023.114196