10 Search Results for "Rothe, Jörg"

Document
DOI: 10.4230/LIPIcs.IPEC.2025.14
A Simple Algorithm for Combinatorial n-Fold ILPs Using the Steinitz Lemma

Authors: Sushmita Gupta, Pallavi Jain, Sanjay Seetharaman, and Meirav Zehavi

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
We present an algorithm for a class of n-fold ILPs whose existing algorithms in literature are often either (1) based on the augmentation framework where one starts with an arbitrary solution and then iteratively moves towards an optimal solution by solving appropriate programs; or (2) require solving a linear relaxation of the program; or (3) are based on decomposition/proximity based arguments. Combinatorial n-fold ILPs is a class of n-fold ILPs introduced and studied by Knop et al. [MP2020] that captures several other problems in a variety of domains. We present a simple and direct algorithm that solves combinatorial n-fold ILPs with unbounded non-negative variables via an application of the Steinitz lemma. Depending on the structure of the input ILP, we also improve upon the existing algorithms in the literature in terms of the running time, thereby showing an improvement that mirrors the one shown by Rohwedder [ICALP2025] contemporaneously and independently.
Cite as

Sushmita Gupta, Pallavi Jain, Sanjay Seetharaman, and Meirav Zehavi. A Simple Algorithm for Combinatorial n-Fold ILPs Using the Steinitz Lemma. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 14:1-14:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gupta_et_al:LIPIcs.IPEC.2025.14,
  author =	{Gupta, Sushmita and Jain, Pallavi and Seetharaman, Sanjay and Zehavi, Meirav},
  title =	{{A Simple Algorithm for Combinatorial n-Fold ILPs Using the Steinitz Lemma}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{14:1--14:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.14},
  URN =		{urn:nbn:de:0030-drops-251467},
  doi =		{10.4230/LIPIcs.IPEC.2025.14},
  annote =	{Keywords: n-fold integer linear program, parameterized algorithms}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.29
Beyond Exact Fairness: Envy-Free Incomplete Connected Fair Division

Authors: Ajaykrishnan E S and Daniel Lokshtanov

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
We study the problem of Envy-Free Incomplete Connected Fair Division, where exactly p vertices of an undirected graph must be allocated to agents such that each agent receives a connected share and does not envy another agent’s share. Focusing on agents with additive valuations, we show that the problem remains computationally hard when parameterized by p and the number of agents. This result holds even for star graphs and with the input numbers given in unary representation, thereby resolving an open problem posed by Gahlawat and Zehavi (FSTTCS 2023). In stark contrast, we show that if one is willing to tolerate even the slightest amount of envy, then the problem becomes efficient with respect to the natural parameters. Specifically, we design an Efficient Parameterized Approximation Scheme parameterized by p and the number of agent types. Our algorithm works on general graphs and remains efficient even when the input numbers are provided in binary representation.
Cite as

Ajaykrishnan E S and Daniel Lokshtanov. Beyond Exact Fairness: Envy-Free Incomplete Connected Fair Division. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 29:1-29:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{es_et_al:LIPIcs.FSTTCS.2025.29,
  author =	{E S, Ajaykrishnan and Lokshtanov, Daniel},
  title =	{{Beyond Exact Fairness: Envy-Free Incomplete Connected Fair Division}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{29:1--29:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.29},
  URN =		{urn:nbn:de:0030-drops-251101},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.29},
  annote =	{Keywords: Envy-Free Incomplete Connected Fair Division, Efficient Parameterized Approximation Scheme, W\lbrack1\rbrack-hardness}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.54
Reforming an Unfair Allocation by Exchanging Goods

Authors: Sheung Man Yuen, Ayumi Igarashi, Naoyuki Kamiyama, and Warut Suksompong

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
Fairly allocating indivisible goods is a frequently occurring task in everyday life. Given an initial allocation of the goods, we consider the problem of reforming it via a sequence of exchanges to attain fairness in the form of envy-freeness up to one good (EF1). We present a vast array of results on the complexity of determining whether it is possible to reach an EF1 allocation from the initial allocation and, if so, the minimum number of exchanges required. In particular, we uncover several distinctions based on the number of agents involved and their utility functions. Furthermore, we derive essentially tight bounds on the worst-case number of exchanges needed to achieve EF1.
Cite as

Sheung Man Yuen, Ayumi Igarashi, Naoyuki Kamiyama, and Warut Suksompong. Reforming an Unfair Allocation by Exchanging Goods. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 54:1-54:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{yuen_et_al:LIPIcs.ISAAC.2025.54,
  author =	{Yuen, Sheung Man and Igarashi, Ayumi and Kamiyama, Naoyuki and Suksompong, Warut},
  title =	{{Reforming an Unfair Allocation by Exchanging Goods}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{54:1--54:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.54},
  URN =		{urn:nbn:de:0030-drops-249626},
  doi =		{10.4230/LIPIcs.ISAAC.2025.54},
  annote =	{Keywords: fair division, indivisible goods, envy-freeness, exchanges}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.44
Approximation Schemes for k-Subset Sum Ratio and k-Way Number Partitioning Ratio

Authors: Sotiris Kanellopoulos, Giorgos Mitropoulos, Antonis Antonopoulos, Nikos Leonardos, Aris Pagourtzis, Christos Pergaminelis, Stavros Petsalakis, and Kanellos Tsitouras

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
The Subset Sum Ratio problem (SSR) asks, given a multiset A of positive integers, to find two disjoint subsets of A such that the largest-to-smallest ratio of their sums is minimized. In this paper we study the k-version of SSR, namely k-Subset Sum Ratio (k-SSR), which asks to minimize the largest-to-smallest ratio of sums of k disjoint subsets of A. We develop an approximation scheme for k-SSR running in O(n^{2k}/ε^{k-1}) time, where n = |A| and ε is the error parameter. To the best of our knowledge, this is the first FPTAS for k-SSR for fixed k > 2. We also study the k-way Number Partitioning Ratio (k-PART) problem, which differs from k-SSR in that the k subsets must constitute a partition of A; this problem in fact corresponds to the objective of minimizing the largest-to-smallest sum ratio in the family of Multiway Number Partitioning problems. We present a more involved FPTAS for k-PART, also achieving O(n^{2k}/ε^{k-1}) time complexity. Notably, k-PART is also equivalent to the Minimum Envy-Ratio problem with identical valuation functions, which has been studied in the context of fair division of indivisible goods. Thus, for the case of identical valuations, our FPTAS represents a significant improvement over the O(n^{4k²+1}/ε^{2k²}) bound obtained by Nguyen and Rothe’s FPTAS [Trung Thanh Nguyen and Jörg Rothe, 2014] for Minimum Envy-Ratio with general additive valuations. Lastly, we propose a second FPTAS for k-SSR, which employs carefully designed calls to the first one; the new scheme has a time complexity of Õ(n/ε^{3k-1}), thus being much faster when n≫ 1/ ε.
Cite as

Sotiris Kanellopoulos, Giorgos Mitropoulos, Antonis Antonopoulos, Nikos Leonardos, Aris Pagourtzis, Christos Pergaminelis, Stavros Petsalakis, and Kanellos Tsitouras. Approximation Schemes for k-Subset Sum Ratio and k-Way Number Partitioning Ratio. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 44:1-44:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kanellopoulos_et_al:LIPIcs.ISAAC.2025.44,
  author =	{Kanellopoulos, Sotiris and Mitropoulos, Giorgos and Antonopoulos, Antonis and Leonardos, Nikos and Pagourtzis, Aris and Pergaminelis, Christos and Petsalakis, Stavros and Tsitouras, Kanellos},
  title =	{{Approximation Schemes for k-Subset Sum Ratio and k-Way Number Partitioning Ratio}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{44:1--44:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.44},
  URN =		{urn:nbn:de:0030-drops-249521},
  doi =		{10.4230/LIPIcs.ISAAC.2025.44},
  annote =	{Keywords: Fully polynomial-time approximation schemes, Subset Sum Ratio, Number Partitioning, Fair division, Envy minimization, Pseudo-polynomial time algorithms}
}
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.
Cite as

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.
Cite as

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/OASIcs.Gabbrielli.9
A Concurrent Language for Argumentation: Preliminary Notes

Authors: Stefano Bistarelli and Carlo Taticchi

Published in: OASIcs, Volume 86, Recent Developments in the Design and Implementation of Programming Languages (2020)

Abstract
While agent-based modelling languages naturally implement concurrency, the currently available languages for argumentation do not allow to explicitly model this type of interaction. In this paper we introduce a concurrent language for handling process arguing and communicating using a shared argumentation framework (reminding shared constraint store as in concurrent constraint). We introduce also basic expansions, contraction and revision procedures as main bricks for enforcement, debate, negotiation and persuasion.
Cite as

Stefano Bistarelli and Carlo Taticchi. A Concurrent Language for Argumentation: Preliminary Notes. In Recent Developments in the Design and Implementation of Programming Languages. Open Access Series in Informatics (OASIcs), Volume 86, pp. 9:1-9:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bistarelli_et_al:OASIcs.Gabbrielli.9,
  author =	{Bistarelli, Stefano and Taticchi, Carlo},
  title =	{{A Concurrent Language for Argumentation: Preliminary Notes}},
  booktitle =	{Recent Developments in the Design and Implementation of Programming Languages},
  pages =	{9:1--9:22},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-171-9},
  ISSN =	{2190-6807},
  year =	{2020},
  volume =	{86},
  editor =	{de Boer, Frank S. and Mauro, Jacopo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Gabbrielli.9},
  URN =		{urn:nbn:de:0030-drops-132311},
  doi =		{10.4230/OASIcs.Gabbrielli.9},
  annote =	{Keywords: Argumentation, Concurrent Language, Debating, Negotiation, Belief Revision}
}
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.
Cite as

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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