Algorithmik und Komplexitätstheorie
Institut für Softwaretechnik und Theoretische Informatik
Fakultät Elektrotechnik und Informatik
Technische Universität Berlin
Sekr. TEL 5-1
Ernst Reuter Platz 7
D-10587 Berlin
Email: till.fluschnik 'at' tu-berlin 'dot' de
PhD student
© Till Fluschnik

Publications.

2017.

Authors Title Journal Conference arxiv
TF, Piotr Skowron, Mervin Triphaus, Kai Wilker Fair Knapsack
abstract

We study the following multiagent variant of the knapsack problem. We are given a set of items, a set of voters, and a value of the budget; each item is endowed with a cost and each voter assigns to each item a certain value. The goal is to select a subset of items with the total cost not exceeding the budget, in a way that is consistent with the voters' preferences. Since the preferences of the voters over the items can vary significantly, we need a way of aggregating these preferences, in order to select the socially most preferred valid knapsack. We study three approaches to aggregating voters preferences, which are motivated by the literature on multiwinner elections and fair allocation. This way we introduce the concepts of individually best, diverse, and fair knapsack. We study computational complexity (including parameterized complexity, and complexity under restricted domains) of computing the aforementioned concepts of multiagent knapsacks.

arXiv
Philipp Zschoche, TF, Hendrik Molter, and Rolf Niedermeier The Computational Complexity of Finding Separators in Temporal Graphs
abstract

Vertex separators, that is, vertex sets whose deletion disconnects two distinguished vertices in a graph, play a pivotal role in algorithmic graph theory. For instance, the concept of tree decompositions of graphs is tightly connected to the separator concept. For many realistic models of the real world, however, it is necessary to consider graphs whose edge set changes with time. More specifically, the edges are labeled with time stamps. In the literature, these graphs are referred to as temporal graphs, temporal networks, time-varying networks, edge-scheduled networks, etc. While there is an extensive literature on separators in "static" graphs, much less is known for the temporal setting. Building on previous work (e.g., Kempe et al. [STOC '00]), for the first time we systematically investigate the (parameterized) complexity of finding separators in temporal graphs. Doing so, we discover a rich landscape of computationally (fixed-parameter) tractable and intractable cases. In particular, we shed light on the so far seemingly overlooked fact that two frequently used models of temporal separation may lead to quite significant differences in terms of computational complexity. More specifically, considering paths in temporal graphs one may distinguish between strict paths (the time stamps along a path are strictly increasing) and non-strict paths (the time stamps along a path are monotonically non-decreasing). We observe that the corresponding strict case of temporal separators leads to several computationally much easier to handle cases than the non-strict case does.

arXiv
Markus Brill, TF, Vincent Froese, Brijnesh Jain, Rolf Niedermeier, and David Schultz Exact Mean Computation in Dynamic Time Warping Spaces
abstract

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 Fr\'echet function) is a challenging computational problem, so far solved by several heuristic, inexact strategies. We spot several inaccuracies in the literature on exact mean computation in dynamic time warping spaces. Our contributions comprise an exact dynamic program computing a mean (useful for benchmarking and evaluating known heuristics). Empirical evaluations reveal significant deficits of the state-of-the-art heuristics in terms of their output quality. Finally, we give an exact polynomial-time algorithm for the special case of binary time series.

arXiv
TF, George B. Mertzios, and André Nichterlein Kernelization Lower Bounds for Finding Constant Size Subgraphs
abstract

Kernelization is an important tool in parameterized algorithmics. The goal is to reduce the input instance of a parameterized problem in polynomial time to an equivalent instance of the same problem such that the size of the reduced instance only depends on the parameter and not on the size of the original instance. In this paper, we provide a first conceptual study on limits of kernelization for several polynomial-time solvable problems. For instance, we consider the problem of finding a triangle with negative sum of edge weights parameterized by the maximum degree of the input graph. We prove that a linear-time computable strict kernel of truly subcubic size for this problem violates the popular APSP-conjecture.

arXiv
TF, Marco Morik, and Manuel Sorge The Complexity of Routing with Few Collisions
abstract

We study the computational complexity of routing multiple objects through a network in such a way that only few collisions occur: Given a graph G with two distinct terminal vertices and two positive integers p and k, the question is whether one can connect the terminals by at least p routes (e.g. paths) such that at most k edges are time-wise shared among them. We study three types of routes: traverse each vertex at most once (paths), each edge at most once (trails), or no such restrictions (walks). We prove that for paths and trails the problem is NP-complete on undirected and directed graphs even if k is constant or the maximum vertex degree in the input graph is constant. For walks, however, it is solvable in polynomial time on undirected graphs for arbitrary k and on directed graphs if k is constant. We additionally study for all route types a variant of the problem where the maximum length of a route is restricted by some given upper bound. We prove that this length-restricted variant has the same complexity classification with respect to paths and trails, but for walks it becomes NP-complete on undirected graphs.

FCT 2017: 10472:257–270 arXiv (bib-dblp)
Matthias Bentert, TF, André Nichterlein, and Rolf Niedermeier Parameterized Aspects of Triangle Enumeration
abstract

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 aspects (e.g. algorithms tuned for large graphs). Motivated by the fact that the worst-case running time is cubic, we perform a systematic parameterized complexity study of triangle enumeration, providing both positive results (new enumerative kernelizations, “subcubic” parameterized solving algorithms) as well as negative results (uselessness in terms of possibility of “faster” parameterized algorithms of certain parameters such as diameter).

FCT 2017: 10472:96–110, (Best Student Paper Award) arXiv (bib-dblp)
TF, Christian Komusiewicz, George B. Mertzios, André Nichterlein, Rolf Niedermeier, and Nimrod Talmon When can Graph Hyperbolicity be computed in Linear Time? WADS 2017: 10389:397–408 arXiv
TF, Meike Hatzel, Steffen Härtlein, Hendrik Molter, and Henning Seidler The Minimum Shared Edges Problem on Grid-like Graphs
abstract

We study the 𝖭𝖯-hard Minimum Shared Edges (MSE) problem on graphs: decide whether it is possible to route p paths from a start vertex to a target vertex in a given graph while using at most k edges more than once. We show that MSE can be decided on bounded (i.e. finite) grids in linear time when both dimensions are either small or large compared to the number p of paths. On the contrary, we show that MSE remains 𝖭𝖯-hard on subgraphs of bounded grids. Finally, we study MSE from a parametrised complexity point of view. It is known that MSE is fixed-parameter tractable with respect to the number p of paths. We show that, under standard complexity-theoretical assumptions, the problem parametrised by the combined parameter k, p, maximum degree, diameter, and treewidth does not admit a polynomial-size problem kernel, even when restricted to planar graphs.

WG 2017: 10520:249–262 arXiv
Henning Fernau, TF, Danny Hermelin, Andreas Krebs, Hendrik Molter, and Rolf Niedermeier Diminishable Parameterized Problems and Strict Polynomial Kernelization arXiv

2016.

Authors Title Journal Conference arxiv
René van Bevern, TF, George B. Mertzios, Hendrik Molter, Manuel Sorge, and Ondřej Suchý The parameterized complexity of finding secluded solutions to some classical optimization problems on graphs under review IPEC 2016: 5:1-5:16 arXiv (2017)
TF, Steffen Kriewald, Anselmo García Cantú Ros, Bin Zhou, Dominik E. Reusser, Jürgen P. Kropp, and Diego Rybski The Size Distribution, Scaling Properties and Spatial Organization of Urban Clusters: A Global and Regional Perspective IJGI, ISPRS Int. J. Geo-Inf. 2016, 5(7), 110
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arxiv (2014)
TF, Danny Hermelin, André Nichterlein, and Rolf Niedermeier Fractals for Kernelization Lower Bounds, With an Application to Length-Bounded Cut Problems under review ICALP 2016: (55)25:1-25:14 arxiv (2015)
TF and Manuel Sorge The Minimum Shared Edges Problem on Planar Graphs
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arXiv
Ramana Venkata Gudipudi, TF, Anselmo García Cantú Ros, Carsten Walther, and Jürgen P. Kropp City Density and CO2 Efficiency
abstract

Cities play a vital role in the global climate change mitigation agenda. City population density is one of the key factors that influence urban energy consumption and the subsequent GHG emissions. However, previous research on the relationship between population density and GHG emissions led to contradictory results due to urban/rural definition conundrum and the varying methodologies for estimating GHG emissions. This work addresses these ambiguities by employing the City Clustering Algorithm (CCA) and utilizing the gridded CO2 emissions data. Our results, derived from the analysis of all inhabited areas in the US, show a sub-linear relationship between population density and the total emissions (i.e. the sum of on-road and building emissions) on a per capita basis. Accordingly, we find that doubling the population density would entail a reduction in the total CO2 emissions in buildings and on-road sectors typically by at least 42%. Moreover, we find that population density exerts a higher influence on on-road emissions than buildings emissions. From an energy consumption point of view, our results suggest that on-going urban sprawl will lead to an increase in on-road energy consumption in cities and therefore stresses the importance of developing adequate local policy measures to limit urban sprawl.

Energy Policy, (91)352–361
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2015.

Authors Title Journal Conference arxiv
TF, Stefan Kratsch, Rolf Niedermeier, and Manuel Sorge The Parameterized Complexity of the Minimum Shared Edges Problem under review FSTTCS 2015: 448-462 arxiv (2016)

2014.

Authors Title Journal Conference arxiv
Anselmo García Cantú Ros, TF, and Jürgen P. Kropp Variance-based control of regime shifts: bistability and oscillations under review
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arXiv

Theses.

Master Thesis.

TF. The Parameterized Complexity of Finding Paths with Shared Edges. TU Berlin.

Bachelor Thesis.

TF. Kritisches Verhalten eines verdünnten zufälligen Polymers. TU Berlin.


Participant.

2017.

43rd International Workshop on Graph-Theoretic Concepts in Computer Science (WG'17). In Eindhoven, The Netherlands, June 21-23, 2017.

2015.

Workshop on Kernelization (WORKER) 2015. In Nordfjordeid, Norway. June 2015.
© Till Fluschnik


Talks.

2017.

15th Algorithms and Data Structures Symposium (WADS) . St. John's, Newfundland, Canada, July 31-August 2
© Till Fluschnik

2016.

72. Workshop über Algorithmen und Komplexität . Leibniz Universität Hannover, Institut für Theoretische Informatik.
© Till Fluschnik
11th International Symposium on Parameterized and Exact Computation (IPEC 2016) . In Aarhus, Denmark, August 24-26.
© Till Fluschnik
43rd International Colloquium on Automata, Languages and Programming (ICALP 2016). In Rome, Italy. July 2016.
© Till Fluschnik

2015.

35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015). In Bangalore, India. December 2015.
© Till Fluschnik
7th Workshop on Graph Classes, Optimization, and Width Parameters (GROW). In Aussois, France. October 2015. Slides.
© Till Fluschnik
The size distribution, scaling properties and spatial organization of urban clusters: a global and regional perspective. Verhandlungen der Deutschen Physikalischen Gesellschaft, AKE 14: Physics of Sustainability and Human-Nature Interactions I, at TU Berlin, Germany. March 2015.

Co-Supervised Theses.

2017.

Max-Jonathan Luckow. Paths under Neighborhood Constraints — Algorithms and Complexity. TU Berlin, April 2017, Bachelor thesis.

2016.

Matthias Bentert. Parametrised Algorithms for Finding Triangles in Graphs - Detection, Counting and Enumeration. TU Berlin, December 2016, Master thesis.

Maximilian Stahlberg. Finding the Most Vital Edges for Shortest Paths - Algorithms and Complexity for Special Graph Classes. TU Berlin, February, 2016. Bachelor thesis.

Marco Morik. The Complexity of Routing with Collision Avoidance. TU Berlin, June, 2016. Bachelor thesis.


Misc.

Script Recommendations (for Lectures etc.).

Analysis (and more) Scripts by Dirk Ferus (only in German).

Scripts by Wolfgang König (in the context of probabilistic theory, only in German): in particular, Wahrscheinlichkeitstheorie I+II and Stochastische Algorithmen.

Script by Stefan Felsner (together with students) about Graph theory (only in German)

Book Recommendations.

Martin Aigner and Günter M. Ziegler: Proof from THE BOOK

Links.

TÜV Rheinland Berlin Marathon-Relay

Orthodromic Spatial Clustering