Group Activity Selection with Few Agent Types

D 2019

Group Activity Selection with Few Agent Types

GANIAN, Robert, Sebastian ORDYNIAK and C. S. RAHUL

Basic information

Original name

Group Activity Selection with Few Agent Types

Authors

GANIAN, Robert (203 Czech Republic, guarantor, belonging to the institution), Sebastian ORDYNIAK (276 Germany) and C. S. RAHUL (356 India)

Edition

Nemecko, 27th Annual European Symposium on Algorithms (ESA 2019), p. 1-16, 16 pp. 2019

Publisher

Dagstuhl

Other information

Language

English

Type of outcome

Stať ve sborníku

Field of Study

10201 Computer sciences, information science, bioinformatics

Country of publisher

Germany

Confidentiality degree

není předmětem státního či obchodního tajemství

Publication form

electronic version available online

References:

URL

RIV identification code

RIV/00216224:14330/19:00113722

Organization unit

Faculty of Informatics

ISBN

978-3-95977-124-5

ISSN

DOI

http://dx.doi.org/10.4230/LIPIcs.ESA.2019.48

UT WoS

000570729400048

Keywords in English

Parameterized Complexity

Abstract

V originále

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.

Citovat

GANIAN, Robert, Sebastian ORDYNIAK and 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, p. 1-16. ISBN 978-3-95977-124-5. Available from: https://dx.doi.org/10.4230/LIPIcs.ESA.2019.48.

@inproceedings{1648258,
   author = {Ganian, Robert and Ordyniak, Sebastian and Rahul, C. S.},
   address = {Nemecko},
   booktitle = {27th Annual European Symposium on Algorithms (ESA 2019)},
   doi = {http://dx.doi.org/10.4230/LIPIcs.ESA.2019.48},
   editor = {Michael A. Bender and Ola Svensson and Grzegorz Herman},
   keywords = {Parameterized Complexity},
   howpublished = {elektronická verze "online"},
   language = {eng},
   location = {Nemecko},
   isbn = {978-3-95977-124-5},
   pages = {1-16},
   publisher = {Dagstuhl},
   title = {Group Activity Selection with Few Agent Types},
   url = {https://drops.dagstuhl.de/opus/volltexte/2019/11169/},
   year = {2019}
}

TY  - JOUR
ID  - 1648258
AU  - Ganian, Robert - Ordyniak, Sebastian - Rahul, C. S.
PY  - 2019
TI  - Group Activity Selection with Few Agent Types
PB  - Dagstuhl
CY  - Nemecko
SN  - 9783959771245
KW  - Parameterized Complexity
UR  - https://drops.dagstuhl.de/opus/volltexte/2019/11169/
L2  - https://drops.dagstuhl.de/opus/volltexte/2019/11169/
N2  - 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.
ER  -

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

Detailed Information on Publication Record