Paper Info
Title
Group Activity Selection with Few Agent Types.
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.
Year
DOI
Venue
2018
10.4230/LIPIcs.ESA.2019.48
Leibniz International Proceedings in Informatics
Keywords
Field
DocType
group activity selection problem,parameterized complexity analysis,multi-agent systems
Discrete mathematics,Combinatorics,Subset sum problem,Parameterized complexity,Autonomous system (Internet),Group activity,Mathematics
Journal
Volume
ISSN
Citations 
144
1868-8969
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Robert Ganian120840.19
Sebastian Ordyniak217630.27
C. S. Rahul322.43