Group Activity Selection with Few Agent Types

GANIAN, Robert, Sebastian ORDYNIAK a C. S. RAHUL. Group Activity Selection with Few Agent Types. Online. In Michael A. Bender and Ola Svensson and Grzegorz Herman. 27th Annual European Symposium on Algorithms (ESA 2019). Nemecko: Dagstuhl, 2019, s. 1-16. ISBN 978-3-95977-124-5. Dostupné z: https://dx.doi.org/10.4230/LIPIcs.ESA.2019.48.

Základní údaje

• Originální název: Group Activity Selection with Few Agent Types
• Autoři: GANIAN, Robert (203 Česká republika, garant, domácí), Sebastian ORDYNIAK (276 Německo) a C. S. RAHUL (356 Indie).
• Vydání: Nemecko, 27th Annual European Symposium on Algorithms (ESA 2019), od s. 1-16, 16 s. 2019.
• Nakladatel: Dagstuhl

Další údaje

• Originální jazyk: angličtina
• Typ výsledku: Stať ve sborníku
• Obor: 10201 Computer sciences, information science, bioinformatics
• Stát vydavatele: Německo
• Utajení: není předmětem státního či obchodního tajemství
• Forma vydání: elektronická verze "online"
• WWW: URL
• Kód RIV: RIV/00216224:14330/19:00113722
• Organizační jednotka: Fakulta informatiky
• ISBN: 978-3-95977-124-5
• ISSN: 1868-8969
• Doi: http://dx.doi.org/10.4230/LIPIcs.ESA.2019.48
• UT WoS: 000570729400048
• Klíčová slova anglicky: Parameterized Complexity
• Štítky: core_A, firank_A

Anotace

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.