Jens M. Schmidt

Efficient extraction of multiple kuratowski subdivisions

A graph is planar if and only if it does not contain a Kuratowski subdivision. Hence such a subdivision can be used as a witness for non-planarity. Modern planarity testing algorithms allow to extract a single such witness in linear time. We present the first linear time algorithm which is able to extract multiple Kuratowski subdivisions at once. This is of particular interest for, e.g., Branch-and-Cut algorithms which require multiple such subdivisions to generate cut constraints. The algorithm is not only described theoretically, but we also present an experimental study of its implementation.

Interval Stabbing Problems in Small Integer Ranges

Given a set I of n intervals, a stabbing query consists of a point q and asks for all intervals in I that contain q. The Interval Stabbing Problem is to find a data structure that can handle stabbing queries efficiently. We propose a new, simple and optimal approach for different kinds of interval stabbing problems in a static setting where the query points and interval ends are in {1,...,O(n)}.

High-order punishment and the evolution of cooperation

The Prisoners Dilemma and the Public Goods Game are models to study mechanisms leading to the evolution of cooperation. From a simplified rational and egoistic perspective there should be no altruistic cooperation in these games at all. Previous studies observed circumstances under which cooperation can emerge. This paper demonstrates that high-order punishment opportunities can maintain a higher cooperation level in an agent based simulation of the evolution of cooperation.

Contractions, Removals, and Certifying 3-Connectivity in Linear Time

One of the most noted construction methods of

Every DFS Tree of a 3-Connected Graph Contains a Contractible Edge

3

An O ( n + m ) Certifying Triconnnectivity Algorithm for Hamiltonian Graphs

-vertex-connected graphs is due to Tutte and is based on the following fact: Any

Linear-Time Recognition of Map Graphs with Outerplanar Witness

3

The Mondshein Sequence

-vertex-connected graph

Certifying 3-connectivity in linear time

G=(V,E)

Construction Sequences and Certifying 3-connectivity

on more than