New Races in Parameterized Algorithmics

Towards Fully Multivariate Algorithmics: Some New Results and Directions in Parameter Ecology

This paper reports on three recent research directions that begin to explore the subject of fully multivariate algorithmics, meaning by this the largely uncharted theoretical landscape that lies beyond parameterized complexity and algorithmics — itself a natural two-dimensional generalization of the familiar one-dimensional framework of P versus NP .

Reflections on Multivariate Algorithmics and Problem Parameterization

Research on parameterized algorithmics for NP-hard problems has steadily grown over the last years. We survey and discuss how parameterized complexity analysis naturally develops into the field of multivariate algorithmics. Correspondingly, we describe how to perform a systematic investigation and exploitation of the “parameter space” of computationally hard problems. Algorithms and Complexity;...

Parameterized Algorithmics: A Graph-Theoretic Approach

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 aggregati...

Parametric Duality: Kernel Sizes & Algorithmics

We derive certain properties for problems which are parameterized tractable both in their “primal” and in their “dual” parameterization. In particular, we derive the first ever lower bounds result for kernel sizes of parameterized problems. We discuss various consequences of this result. Moreover, we explain how to get improved non-parameterized algorithms from known parameterized algorithms by...