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Documents authored by Rothe, Jörg

Document
DOI: 10.4230/DagRep.11.7.1
Coalition Formation Games (Dagstuhl Seminar 21331)

Authors: Edith Elkind, Judy Goldsmith, Anja Rey, and Jörg Rothe

Published in: Dagstuhl Reports, Volume 11, Issue 7 (2021)

Abstract
There are many situations in which individuals will choose to act as a group, or coalition. Examples include social clubs, political parties, partnership formation, and legislative voting. Coalition formation games are a class of cooperative games where the aim is to partition a set of agents into coalitions, according to some criteria, such as coalitional stability or maximization of social welfare. In our seminar we discussed applications, results, and new directions of research in the field of coalition formation games.
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Edith Elkind, Judy Goldsmith, Anja Rey, and Jörg Rothe. Coalition Formation Games (Dagstuhl Seminar 21331). In Dagstuhl Reports, Volume 11, Issue 7, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@Article{elkind_et_al:DagRep.11.7.1,
  author =	{Elkind, Edith and Goldsmith, Judy and Rey, Anja and Rothe, J\"{o}rg},
  title =	{{Coalition Formation Games (Dagstuhl Seminar 21331)}},
  pages =	{1--15},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2021},
  volume =	{11},
  number =	{7},
  editor =	{Elkind, Edith and Goldsmith, Judy and Rey, Anja and Rothe, J\"{o}rg},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.11.7.1},
  URN =		{urn:nbn:de:0030-drops-155885},
  doi =		{10.4230/DagRep.11.7.1},
  annote =	{Keywords: Coalition Formation, Cooperative Games}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2020.14
Bi-Criteria Approximation Algorithms for Load Balancing on Unrelated Machines with Costs

Authors: Trung Thanh Nguyen and Jörg Rothe

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

Abstract
We study a generalized version of the load balancing problem on unrelated machines with cost constraints: Given a set of m machines (of certain types) and a set of n jobs, each job j processed on machine i requires p_{i,j} time units and incurs a cost c_{i,j}, and the goal is to find a schedule of jobs to machines, which is defined as an ordered partition of n jobs into m disjoint subsets, in such a way that some objective function of the vector of the completion times of the machines is optimized, subject to the constraint that the total costs by the schedule must be within a given budget B. Motivated by recent results from the literature, our focus is on the case when the number of machine types is a fixed constant and we develop a bi-criteria approximation scheme for the studied problem. Our result generalizes several known results for certain special cases, such as the case with identical machines, or the case with a constant number of machines with cost constraints. Building on the elegant technique recently proposed by Jansen and Maack [K. Jansen and M. Maack, 2019], we construct a more general approach that can be used to derive approximation schemes to a wider class of load balancing problems with constraints.
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Trung Thanh Nguyen and Jörg Rothe. Bi-Criteria Approximation Algorithms for Load Balancing on Unrelated Machines with Costs. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 14:1-14:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{nguyen_et_al:LIPIcs.ISAAC.2020.14,
  author =	{Nguyen, Trung Thanh and Rothe, J\"{o}rg},
  title =	{{Bi-Criteria Approximation Algorithms for Load Balancing on Unrelated Machines with Costs}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{14:1--14:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.14},
  URN =		{urn:nbn:de:0030-drops-133582},
  doi =		{10.4230/LIPIcs.ISAAC.2020.14},
  annote =	{Keywords: bi-criteria approximation algorithm, polynomial-time approximation algorithm, load balancing, machine scheduling}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2020.19
Complexity of Stability

Authors: Fabian Frei, Edith Hemaspaandra, and Jörg Rothe

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

Abstract
Graph parameters such as the clique number, the chromatic number, and the independence number are central in many areas, ranging from computer networks to linguistics to computational neuroscience to social networks. In particular, the chromatic number of a graph (i.e., the smallest number of colors needed to color all vertices such that no two adjacent vertices are of the same color) can be applied in solving practical tasks as diverse as pattern matching, scheduling jobs to machines, allocating registers in compiler optimization, and even solving Sudoku puzzles. Typically, however, the underlying graphs are subject to (often minor) changes. To make these applications of graph parameters robust, it is important to know which graphs are stable for them in the sense that adding or deleting single edges or vertices does not change them. We initiate the study of stability of graphs for such parameters in terms of their computational complexity. We show that, for various central graph parameters, the problem of determining whether or not a given graph is stable is complete for Θ₂ᵖ, a well-known complexity class in the second level of the polynomial hierarchy, which is also known as "parallel access to NP."
Cite as

Fabian Frei, Edith Hemaspaandra, and Jörg Rothe. Complexity of Stability. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 19:1-19:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{frei_et_al:LIPIcs.ISAAC.2020.19,
  author =	{Frei, Fabian and Hemaspaandra, Edith and Rothe, J\"{o}rg},
  title =	{{Complexity of Stability}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{19:1--19:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.19},
  URN =		{urn:nbn:de:0030-drops-133631},
  doi =		{10.4230/LIPIcs.ISAAC.2020.19},
  annote =	{Keywords: Stability, Robustness, Complexity, Local Modifications, Colorability, Vertex Cover, Clique, Independent Set, Satisfiability, Unfrozenness, Criticality, DP, coDP, Parallel Access to NP}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2016.80
Structural Control in Weighted Voting Games

Authors: Anja Rey and Jörg Rothe

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

Abstract
Inspired by the study of control scenarios in elections and complementing manipulation and bribery settings in cooperative games with transferable utility, we introduce the notion of structural control in weighted voting games. We model two types of influence, adding players to and deleting players from a game, with goals such as increasing a given player's Shapley-Shubik or probabilistic Penrose-Banzhaf index in relation to the original game. We study the computational complexity of the problems of whether such structural changes can achieve the desired effect.
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Anja Rey and Jörg Rothe. Structural Control in Weighted Voting Games. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 80:1-80:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{rey_et_al:LIPIcs.MFCS.2016.80,
  author =	{Rey, Anja and Rothe, J\"{o}rg},
  title =	{{Structural Control in Weighted Voting Games}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{80:1--80:15},
  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.2016.80},
  URN =		{urn:nbn:de:0030-drops-64883},
  doi =		{10.4230/LIPIcs.MFCS.2016.80},
  annote =	{Keywords: algorithmic games theory, weighted voting games, structural control, power indices, computational complexity}
}
Document
DOI: 10.4230/DagSemProc.04421.2
Exact-Four-Colorability, Exact Domatic Number Problems, and the Boolean Hierarchy

Authors: Jörg Rothe

Published in: Dagstuhl Seminar Proceedings, Volume 4421, Algebraic Methods in Computational Complexity (2005)

Abstract
This talk surveys some of the work that was inspired by Wagner's general technique to prove completeness in the levels of the boolean hierarchy over NP. In particular, we show that it is DP-complete to decide whether or not a given graph can be colored with exactly four colors. DP is the second level of the boolean hierarchy. This result solves a question raised by Wagner in his 1987 TCS paper; its proof uses a clever reduction by Guruswami and Khanna. Similar results on various versions of the exact domatic number problem are also discussed. The result on Exact-Four-Colorability appeared in IPL, 2003. The results on exact domatic number problems, obtained jointly with Tobias Riege, are to appear in TOCS.
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Jörg Rothe. Exact-Four-Colorability, Exact Domatic Number Problems, and the Boolean Hierarchy. In Algebraic Methods in Computational Complexity. Dagstuhl Seminar Proceedings, Volume 4421, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{rothe:DagSemProc.04421.2,
  author =	{Rothe, J\"{o}rg},
  title =	{{Exact-Four-Colorability, Exact Domatic Number Problems, and the Boolean Hierarchy}},
  booktitle =	{Algebraic Methods in Computational Complexity},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4421},
  editor =	{Harry Buhrman and Lance Fortnow and Thomas Thierauf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.04421.2},
  URN =		{urn:nbn:de:0030-drops-1059},
  doi =		{10.4230/DagSemProc.04421.2},
  annote =	{Keywords: Exact Colorability , exact domatic number , boolean hierarchy completeness}
}
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