Author

# Johannes Uhlmann

Other affiliations: University of Tübingen

Bio: Johannes Uhlmann is an academic researcher from Technical University of Berlin. The author has contributed to research in topics: Minimax & Parameterized complexity. The author has an hindex of 6, co-authored 8 publications receiving 328 citations. Previous affiliations of Johannes Uhlmann include University of Tübingen.

##### Papers

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TL;DR: This work investigates two systems of fully proportional representation suggested by Chamberlin & Courant and Monroe and investigates the parameterized complexity of winner determination of the two classical and two new rules with respect to several parameters.

Abstract: We investigate two systems of fully proportional representation suggested by Chamberlin & Courant and Monroe. Both systems assign a representative to each voter so that the "sum of misrepresentations" is minimized. The winner determination problem for both systems is known to be NP-hard, hence this work aims at investigating whether there are variants of the proposed rules and/or specific electorates for which these problems can be solved efficiently. As a variation of these rules, instead of minimizing the sum of misrepresentations, we considered minimizing the maximal misrepresentation introducing effectively two new rules. In the general case these "minimax" versions of classical rules appeared to be still NP-hard.
We investigated the parameterized complexity of winner determination of the two classical and two new rules with respect to several parameters. Here we have a mixture of positive and negative results: e.g., we proved fixed-parameter tractability for the parameter the number of candidates but fixed-parameter intractability for the number of winners.
For single-peaked electorates our results are overwhelmingly positive: we provide polynomial-time algorithms for most of the considered problems. The only rule that remains NP-hard for single-peaked electorates is the classical Monroe rule.

215 citations

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TL;DR: A provably effective preprocessing based on data reduction, a forbidden subgraph characterization of $s-plex cluster graphs, and a depth-bounded search tree which is used to find optimal edge modification sets are developed.

Abstract: We introduce the $s$-Plex Cluster Editing problem as a generalization of the well-studied Cluster Editing problem; both are NP-hard and both are motivated by graph-based data clustering. Instead of transforming a given graph by a minimum number of edge modifications into a disjoint union of cliques (this is Cluster Editing), the task in the case of $s$-Plex Cluster Editing is to transform a graph into a cluster graph consisting of a disjoint union of so-called $s$-plexes. Herein, an $s$-plex is a vertex set $S$ inducing a subgraph in which every vertex has degree at least $|S|-s$. Cliques are 1-plexes. The advantage of $s$-plexes for $s\geq2$ is that they allow us to model a more relaxed cluster notion ($s$-plexes instead of cliques), better reflecting inaccuracies of the input data. We develop a provably effective preprocessing based on data reduction (yielding a so-called problem kernel), a forbidden subgraph characterization of $s$-plex cluster graphs, and a depth-bounded search tree which is used to find optimal edge modification sets. Altogether, this yields efficient algorithms in case of moderate numbers of edge modifications; this is often a reasonable assumption under a maximum parsimony model for data clustering.

50 citations

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TL;DR: Several NP-completeness and (fixed-parameter) tractability results for restricted classes of graphs such as trees, interval graphs, and graphs of bounded treewidth are provided.

Abstract: The MULTICUT problem is defined as: given an undirected graph and a collection of pairs of terminal vertices, find a minimum set of edges or vertices whose removal disconnects each pair. We mainly focus on the case of removing vertices, where we distinguish between allowing or disallowing the removal of terminal vertices. Complementing and refining previous results from the literature, we provide several NP-completeness and (fixed-parameter) tractability results for restricted classes of graphs such as trees, interval graphs, and graphs of bounded treewidth.

24 citations

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TL;DR: This paper proposes a simple and effective heuristic to save memory in dynamic programming on tree decompositions when solving graph optimization problems based on a tree-like set covering problem.

24 citations

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21 Jan 2006

TL;DR: In this paper, the authors provide several NP-completeness and (fixed-parameter) tractability results for restricted classes of graphs such as trees, interval graphs, and graphs of bounded treewidth.

Abstract: The Multicut problem is defined as: given an undirected graph and a collection of pairs of terminal vertices, find a minimum set of edges or vertices whose removal disconnects each pair. We mainly focus on the case of removing vertices, where we distinguish between allowing or disallowing the removal of terminal vertices. Complementing and refining previous results from the literature, we provide several NP-completeness and (fixed-parameter) tractability results for restricted classes of graphs such as trees, interval graphs, and graphs of bounded treewidth.

24 citations

##### Cited by

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TL;DR: This handbook, written by thirty-six prominent members of the computational social choice community, covers the field comprehensively and offers detailed introductions to each of the field's major themes.

Abstract: The rapidly growing field of computational social choice, at the intersection of computer science and economics, deals with the computational aspects of collective decision making. This handbook, written by thirty-six prominent members of the computational social choice community, covers the field comprehensively. Chapters devoted to each of the field's major themes offer detailed introductions. Topics include voting theory (such as the computational complexity of winner determination and manipulation in elections), fair allocation (such as algorithms for dividing divisible and indivisible goods), coalition formation (such as matching and hedonic games), and many more. Graduate students, researchers, and professionals in computer science, economics, mathematics, political science, and philosophy will benefit from this accessible and self-contained book.

396 citations

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TL;DR: In this article, a natural axiom for committee voting, called justified representation (JR), was proposed, which requires that if a large enough group of voters exhibits agreement by supporting the same candidate, then at least one voter in this group has an approved candidate in the winning committee.

Abstract: We consider approval-based committee voting, i.e. the setting where each voter approves a subset of candidates, and these votes are then used to select a fixed-size set of winners (committee). We propose a natural axiom for this setting, which we call justified representation (JR). This axiom requires that if a large enough group of voters exhibits agreement by supporting the same candidate, then at least one voter in this group has an approved candidate in the winning committee. We show that for every list of ballots it is possible to select a committee that provides JR. However, it turns out that several prominent approval-based voting rules may fail to output such a committee. In particular, while Proportional Approval Voting (PAV) always outputs a committee that provides JR, Reweighted Approval Voting (RAV), a tractable approximation to PAV, does not have this property. We then introduce a stronger version of the JR axiom, which we call extended justified representation (EJR), and show that PAV satisfies EJR, while other rules we consider do not; indeed, EJR can be used to characterize PAV within the class of weighted PAV rules. We also consider several other questions related to JR and EJR, including the relationship between JR/EJR and core stability, and the complexity of the associated algorithmic problems.

185 citations

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TL;DR: This paper considers committee selection rules that can be viewed as generalizations of single-winner scoring rules, including SNTV, Bloc, k-Borda, STV, as well as several variants of the Chamberlin–Courant rule and the Monroe rule and their approximations.

Abstract: The goal of this paper is to propose and study properties of multiwinner voting rules which can be consider as generalisations of single-winner scoring voting rules. We consider SNTV, Bloc, k-Borda, STV, and several variants of Chamberlin--Courant's and Monroe's rules and their approximations. We identify two broad natural classes of multiwinner score-based rules, and show that many of the existing rules can be captured by one or both of these approaches. We then formulate a number of desirable properties of multiwinner rules, and evaluate the rules we consider with respect to these properties.

181 citations

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25 Jan 2015

TL;DR: The problem is hard in general, but a number of tractability results for its natural special cases are shown.

Abstract: We consider the following problem: There is a set of items (e.g., movies) and a group of agents (e.g., passengers on a plane); each agent has some intrinsic utility for each of the items. Our goal is to pick a set of K items that maximize the total derived utility of all the agents (i.e., in our example we are to pick K movies that we put on the plane's entertainment system). However, the actual utility that an agent derives from a given item is only a fraction of its intrinsic one, and this fraction depends on how the agent ranks the item among the chosen, available, ones. We provide a formal specification of the model and provide concrete examples and settings where it is applicable. We show that the problem is hard in general, but we show a number of tractability results for its natural special cases.

171 citations