@inproceedings{926cfa05a4764abe83b7e2599db0b324,
title = "Parameterized complexity of stable roommates with ties and incomplete lists through the lens of graph parameters",
abstract = "We continue and extend previous work on the parameterized complexity analysis of the NP-hard Stable Roommates with Ties and Incomplete Lists problem, thereby strengthening earlier results both on the side of parameterized hardness as well as on the side of fixed-parameter tractability. Other than for its famous sister problem Stable Marriage which focuses on a bipartite scenario, Stable Roommates with Incomplete Lists allows for arbitrary acceptability graphs whose edges specify the possible matchings of each two agents (agents are represented by graph vertices). Herein, incomplete lists and ties reflect the fact that in realistic application scenarios the agents cannot bring all other agents into a linear order. Among our main contributions is to show that it is W[1]-hard to compute a maximum-cardinality stable matching for acceptability graphs of bounded treedepth, bounded tree-cut width, and bounded feedback vertex number (these are each time the respective parameters). However, if we “only” ask for perfect stable matchings or the mere existence of a stable matching, then we obtain fixed-parameter tractability with respect to tree-cut width but not with respect to treedepth. On the positive side, we also provide fixed-parameter tractability results for the parameter feedback edge set number.",
keywords = "Acceptability graph, Feedback set numbers, Fixed-parameter tractability, Stable matching, Tree-cut width, Treedepth, Treewidth, W[1]hardness",
author = "Robert Bredereck and Klaus Heeger and Du{\v s}an Knop and Rolf Niedermeier",
note = "Publisher Copyright: {\textcopyright} Robert Bredereck, Klaus Heeger, Du{\v s}an Knop, and Rolf Niedermeier; licensed under Creative Commons License CC-BY; 30th International Symposium on Algorithms and Computation, ISAAC 2019 ; Conference date: 08-12-2019 Through 11-12-2019",
year = "2019",
month = dec,
day = "1",
doi = "10.4230/LIPIcs.ISAAC.2019.44",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Pinyan Lu and Guochuan Zhang",
booktitle = "30th International Symposium on Algorithms and Computation, ISAAC 2019",
address = "Germany",
}