{"type":"ScholarlyArticle","title":"Parameterized Algorithms for Kidney Exchange","authors":[{"name":"Arnab Maiti","slug":"arnab-maiti","given":"Arnab","family":"Maiti","affiliation":"Indian Institute of Technology Kharagpur"},{"name":"Palash Dey","slug":"palash-dey","given":"Palash","family":"Dey","affiliation":"Indian Institute of Technology Kharagpur"}],"abstract":"In kidney exchange programs, multiple patient-donor pairs each of whom are otherwise incompatible, exchange their donors to receive compatible kidneys. The Kidney Exchange problem is typically modelled as a directed graph where every vertex is either an altruistic donor or a pair of patient and donor; directed edges are added from a donor to its compatible patients. The computational task is to find if there exists a collection of disjoint cycles and paths starting from altruistic donor vertices of length at most l_c and l_p respectively that covers at least some specific number t of non-altruistic vertices (patients). We study parameterized algorithms for the kidney exchange problem in this paper. Specifically, we design FPT algorithms parameterized by each of the following parameters: (1) the number of patients who receive kidney, (2) treewidth of the input graph + max{l_p, l_c}, and (3) the number of vertex types in the input graph when l_p <= l_c. We also present interesting algorithmic and hardness results on the kernelization complexity of the problem. Finally, we present an approximation algorithm for an important special case of Kidney Exchange.","doi":"10.24963/ijcai.2022/58","url":"https://ijcai.org/proceedings/2022/58","pdf":"https://ijcai.org/proceedings/2022/0058.pdf","markdown":"https://ijcai.org/proceedings/2022/58.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/58","volume":{"slug":"2022","title":"Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2022","url":"https://ijcai.org/proceedings/2022/","year":2022,"location":"Vienna","dates":"23-29 July 2022","editors":"Luc De Raedt","isbn":"978-1-956792-00-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2022"},"section":"Agent-based and Multi-agent Systems","track":"Main Track","number":58,"pages":{"first":405,"last":411},"keywords":["Agent-based and Multi-agent Systems: Algorithmic Game Theory","Agent-based and Multi-agent Systems: Computational Social Choice","Agent-based and Multi-agent Systems: Cooperative Games"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38986564","length_sec":86,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38984707","length_sec":325,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Abraham et al., 2007] David J. 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