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DOI: 10.4230/LIPIcs.ESA.2019.48

Group Activity Selection with Few Agent Types

Authors: Robert Ganian, Sebastian Ordyniak, and C. S. Rahul

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

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.

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Robert Ganian, Sebastian Ordyniak, and C. S. Rahul. Group Activity Selection with Few Agent Types. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 48:1-48:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{ganian_et_al:LIPIcs.ESA.2019.48,
  author =	{Ganian, Robert and Ordyniak, Sebastian and Rahul, C. S.},
  title =	{{Group Activity Selection with Few Agent Types}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{48:1--48:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.48},
  URN =		{urn:nbn:de:0030-drops-111693},
  doi =		{10.4230/LIPIcs.ESA.2019.48},
  annote =	{Keywords: group activity selection problem, parameterized complexity analysis, multi-agent systems}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2016.41

On the Complexity Landscape of Connected f-Factor Problems

Authors: Robert Ganian, N. S. Narayanaswamy, Sebastian Ordyniak, C. S. Rahul, and M. S. Ramanujan

Published in: LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)

Abstract

Given an n-vertex graph G and a function f:V(G) -> {0, ..., n-1}, an f-factor is a subgraph H of G such that deg_H(v)=f(v) for every vertex v in V(G); we say that H is a connected f-factor if, in addition, the subgraph H is connected. A classical result of Tutte (1954) is the polynomial time algorithm to check whether a given graph has a specified f-factor. However, checking for the presence of a connected f-factor is easily seen to generalize Hamiltonian Cycle and hence is NP-complete. In fact, the Connected f-Factor problem remains NP-complete even when f(v) is at least n^epsilon for each vertex v and epsilon<1; on the other side of the spectrum, the problem was known to be polynomial-time solvable when f(v) is at least n/3 for every vertex v. In this paper, we extend this line of work and obtain new complexity results based on restricting the function f. In particular, we show that when f(v) is required to be at least n/(log n)^c, the problem can be solved in quasi-polynomial time in general and in randomized polynomial time if c <= 1. We also show that when c>1, the problem is NP-intermediate.

Cite as

Robert Ganian, N. S. Narayanaswamy, Sebastian Ordyniak, C. S. Rahul, and M. S. Ramanujan. On the Complexity Landscape of Connected f-Factor Problems. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 41:1-41:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{ganian_et_al:LIPIcs.MFCS.2016.41,
  author =	{Ganian, Robert and Narayanaswamy, N. S. and Ordyniak, Sebastian and Rahul, C. S. and Ramanujan, M. S.},
  title =	{{On the Complexity Landscape of  Connected f-Factor Problems}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{41:1--41:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.41},
  URN =		{urn:nbn:de:0030-drops-65013},
  doi =		{10.4230/LIPIcs.MFCS.2016.41},
  annote =	{Keywords: f-factors, connected f-factors, quasi-polynomial time algorithms, randomized algorithms}
}

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Documents authored by Rahul, C. S.

Group Activity Selection with Few Agent Types

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On the Complexity Landscape of Connected f-Factor Problems

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