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Listing all triangles in an undirected graph is a fundamental graph primitive with numerous applications. It is trivially solvable in time cubic in the number of vertices. It has seen a significant body of work contributing to both theoretical aspects (e.g., lower and upper bounds on running time, adaption to new computational models) as well as practical… (More)

Finding a vertex subset in a graph that satisfies a certain property is one of the most-studied topics in algorithmic graph theory. The focus herein is often on minimizing or maximizing the size of the solution, that is, the size of the desired vertex set. In several applications, however, we also want to limit the “exposure” of the solution to the rest of… (More)

- Till Fluschnik, Stefan Kratsch, Rolf Niedermeier, Manuel Sorge
- FSTTCS
- 2015

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… (More)

Bodlaender et al.’s [SIDMA 2014] cross-composition technique is a popular method for excluding polynomial-size problem kernels for NP-hard parameterized problems. We present a new technique exploiting triangle-based fractal structures for extending the range of applicability of cross-compositions. Our technique makes it possible to prove new… (More)

- Till Fluschnik, Steffen Kriewald, +4 authors Diego Rybski
- ISPRS Int. J. Geo-Information
- 2016

Human development has far-reaching impacts on the surface of the globe. The transformation of natural land cover occurs in different forms, and urban growth is one of the most eminent transformative processes. We analyze global land cover data and extract cities as defined by maximally connected urban clusters. The analysis of the city size distribution for… (More)

- Till Fluschnik, Manuel Sorge
- ArXiv
- 2016

We study the Minimum Shared Edges problem introduced by Omran et al. [Journal of Combinatorial Optimization, 2015] on planar graphs: Planar MSE asks, given a planar graph G = (V,E), two distinct vertices s, t ∈ V , and two integers p, k ∈ N, whether there are p s-t paths in G that share at most k edges, where an edges is called shared if it appears in at… (More)

Kernelization—a mathematical key concept for provably effective polynomial-time preprocessing of NP-hard problems—plays a central role in parameterized complexity and has triggered an extensive line of research. This is in part due to a lower bounds framework that allows to exclude polynomial-size kernels under the assumption of NP * coNP/poly. In this… (More)

Dynamic time warping constitutes a major tool for analyzing time series. In particular, computing a mean series of a given sample of series in dynamic time warping spaces (by minimizing the Fréchet function) is a challenging computational problem, so far solved by several heuristic, inexact strategies. We spot several inaccuracies in the literature on exact… (More)

Hyperbolicity measures, in terms of (distance) metrics, how close a given graph is to being a tree. Due to its relevance in modeling real-world networks, hyperbolicity has seen intensive research over the last years. Unfortunately, the best known algorithms for computing the hyperbolicity number of a graph (the smaller, the more tree-like) have running time… (More)