09171 Abstracts Collection -- Adaptive, Output Sensitive, Online and Parameterized Algorithms

From 19.01. to 24.04.2009, the Dagstuhl Seminar 09171 ``Adaptive, Output Sensitive, Online and Parameterized Algorithms \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

The Parameterized Complexity of the Minimum Shared Edges Problem

We study the NP-complete Minimum Shared Edges (MSE) problem. Given an undirected graph, a source and a sink vertex, and two integers p and k, the question is whether there are p paths in the graph connecting the source with the sink and sharing at most k edges. Herein, an edge is shared if it appears in at least two paths. We show that MSE is W[1]-hard when parameterized by the treewidth of the input graph and the number k of shared edges combined. We show that MSE is fixed-parameter tractable with respect to p, but does not admit a polynomial-size kernel (unless NP is contained in coNP/poly). In the proof of the fixed-parameter tractability of MSE parameterized by p, we employ the treewidth reduction technique due to Marx, O'Sullivan, and Razgon [ACM TALG 2013].Comment: 35 pages, 16 figure

Parliamentary Voting Procedures: Agenda Control, Manipulation, and Uncertainty

We study computational problems for two popular parliamentary voting procedures: the amendment procedure and the successive procedure. While finding successful manipulations or agenda controls is tractable for both procedures, our real-world experimental results indicate that most elections cannot be manipulated by a few voters and agenda control is typically impossible. If the voter preferences are incomplete, then finding which alternatives can possibly win is NP-hard for both procedures. Whilst deciding if an alternative necessarily wins is coNP-hard for the amendment procedure, it is polynomial-time solvable for the successive one

High-Multiplicity Fair Allocation Using Parametric Integer Linear Programming

Using insights from parametric integer linear programming, we significantly improve on our previous work [Proc. ACM EC 2019] on high-multiplicity fair allocation. Therein, answering an open question from previous work, we proved that the problem of finding envy-free Pareto-efficient allocations of indivisible items is fixed-parameter tractable with respect to the combined parameter "number of agents" plus "number of item types." Our central improvement, compared to this result, is to break the condition that the corresponding utility and multiplicity values have to be encoded in unary required there. Concretely, we show that, while preserving fixed-parameter tractability, these values can be encoded in binary, thus greatly expanding the range of feasible values.Comment: 15 pages; Published in the Proceedings of ECAI-202