Group Activity Selection with Few Agent Types

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F19%3A00113722" target="_blank" >RIV/00216224:14330/19:00113722 - isvavai.cz</a>

Result on the web

<a href="https://drops.dagstuhl.de/opus/volltexte/2019/11169/" target="_blank" >https://drops.dagstuhl.de/opus/volltexte/2019/11169/</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.ESA.2019.48" target="_blank" >10.4230/LIPIcs.ESA.2019.48</a>

Result language

angličtina

Original language name

Group Activity Selection with Few Agent Types

Original language description

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.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

—

OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2019

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

27th Annual European Symposium on Algorithms (ESA 2019)

ISBN

9783959771245

ISSN

1868-8969

e-ISSN

—

Number of pages

16

Pages from-to

1-16

Publisher name

Dagstuhl

Place of publication

Nemecko

Event location

Nemecko

Event date

Jan 1, 2019

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

000570729400048