Reflections on Multivariate Algorithmics and Problem Parameterization

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 .

Multivariate Algorithmics for Finding Cohesive Subnetworks

Community detection is an important task in the analysis of biological, social or technical networks. We survey different models of cohesive graphs, commonly referred to as clique relaxations, that are used in the detection of network communities. For each clique relaxation, we give an overview of basic model properties and of the complexity of the problem of finding large cohesive subgraphs un...

The Drama of Divine Providence: Reflections on the Problem of Evil

This article studies the problem of evil in Abrahamic religions and philosophical traditions, and tries to restate their solutions in a contemporary language. The author aims at affirming traditional Abrahamic approaches to theodicy that preserve divine omnipotence, benevolence, and omniscience, but without denying the reality of evil.

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...

Multivariate Algorithmics in Biological Data Analysis