Robert Bredereck

A characterization of the single-crossing domain

We characterize single-crossing preference profiles in terms of two forbidden substructures, one of which contains three voters and six (not necessarily distinct) alternatives, and one of which contains four voters and four (not necessarily distinct) alternatives. We also provide an efficient way to decide whether a preference profile is single-crossing.

Parameterized Algorithmics for Computational Social Choice: Nine Research Challenges

Computational Social Choice is an interdisciplinary research area involving Economics, Political Science, and Social Science on the one side, and Mathematics and Computer Science (including Artificial Intelligence and Multiagent Systems) on the other side. Typical computational problems studied in this field include the vulnerability of voting procedures against attacks, or preference aggregation in multi-agent systems. Parameterized Algorithmics is a subfield of Theoretical Computer Science seeking to exploit meaningful problem-specific parameters in order to identify tractable special cases of in general computationally hard problems. In this paper, we propose nine of our favorite research challenges concerning the parameterized complexity of problems appearing in this context. This work is dedicated to Jianer Chen, one of the strongest problem solvers in the history of parameterized algorithmics, on the occasion of his 60th birthday.

On Bounded-Degree Vertex Deletion parameterized by treewidth

Given an undirected graph G and an integer d>=0, the NP-hard Bounded-Degree Vertex Deletion problem asks to delete as few vertices as possible from G such that the resulting graph has maximum vertex degree d. Our main result is to prove that Bounded-Degree Vertex Deletion is W[1]-hard with respect to the parameter treewidth. As a side result, we obtain that the NP-hard Vector Dominating Set problem is W[1]-hard with respect to the parameter treewidth. On the positive side, we show that Bounded-Degree Vertex Deletion becomes fixed-parameter tractable when parameterized by the combined parameter treewidth and number of vertices to delete, and when parametrized by the feedback edge set number.

Partial Kernelization for Rank Aggregation: Theory and Experiments

Rank Aggregation is important in many areas ranging from web search over databases to bioinformatics. The underlying decision problem Kemeny Score is NP-complete even in case of four input rankings to be aggregated into a “median ranking”. We study efficient polynomial-time data reduction rules that allow us to find optimal median rankings. On the theoretical side, we improve a result for a “partial problem kernel” from quadratic to linear size. On the practical side, we provide encouraging experimental results with data based on web search and sport competitions, e.g., computing optimal median rankings for real-world instances with more than 100 candidates within milliseconds.

The complexity of finding a large subgraph under anonymity constraints

We define and analyze an anonymization problem in undirected graphs, which is motivated by certain privacy issues in social networks. The goal is to remove a small number of vertices from the graph such that in the resulting subgraph every occurring vertex degree occurs many times.

Elections with Few Candidates: Prices, Weights, and Covering Problems

We show that a number of election-related problems with prices such as, for example, bribery are fixed-parameter tractable in

The Complexity of Degree Anonymization by Vertex Addition

{\mathsf {FPT}}

Studies in Computational Aspects of Voting

when parameterized by the number of candidates. For bribery, this resolves a nearly 10-year old family of open problems. Our results follow by a general technique that formulates voting problems as covering problems and extends the classic approach of using integer linear programming and the algorithm of Lenstrai¾?[19]. In this context, our central result is that Weighted Set Multicover parameterized by the universe size is fixed-parameter tractable. Our approach is also applicable to weighted electoral control for Approval voting. We improve previously known