Ganian, R, Ordyniak, S orcid.org/0000-0003-1935-651X and Rahul, CS (2019) Group Activity Selection with Few Agent Types. In: LIPIcs : Leibniz International Proceedings in Informatics. 27th Annual European Symposium on Algorithms (ESA 2019), 09-11 Sep 2019, Munich/Garching, Germany. Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik , 48:1-48:16.
Abstract
The Group Activity Selection Problem (GASP) models situations where a group of agents needs to be distributed to a set of activities while taking into account preferences of the agents w.r.t. individual activities and activity sizes. The problem, along with its well-known variants sGASP and gGASP, has previously been studied in the parameterized complexity setting with various parameterizations, such as number of agents, number of activities and solution size. However, the complexity of the problem parameterized by the number of types of agents, a natural parameter proposed already in the first paper that introduced GASP, has so far remained unexplored. In this paper we establish the complexity map for GASP, sGASP and gGASP when the number of types of agents is the parameter. Our positive results, consisting of one fixed-parameter algorithm and one XP algorithm, rely on a combination of novel Subset Sum machinery (which may be of general interest) and identifying certain compression steps which allow us to focus on solutions which are "acyclic". These algorithms are complemented by matching lower bounds, which among others close a gap to a recently obtained tractability result of Gupta, Roy, Saurabh and Zehavi (2017). In this direction, the techniques used to establish W[1]-hardness of sGASP are of particular interest: as an intermediate step, we use Sidon sequences to show the W[1]-hardness of a highly restricted variant of multi-dimensional Subset Sum, which may find applications in other settings as well.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Robert Ganian, Sebastian Ordyniak, and C. S. Rahul. This is an open access article under the terms of the Creative Commons Attribution 3.0 Unported (CC BY 3.0) (https://creativecommons.org/licenses/by/3.0/deed.en_US) |
Keywords: | group activity selection problem; parameterized complexity analysis; multi-agent systems |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 17 Nov 2020 14:00 |
Last Modified: | 25 Jun 2023 22:30 |
Status: | Published |
Publisher: | Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik |
Identification Number: | 10.4230/LIPIcs.ESA.2019.48 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:168088 |