Clean Citation Style
{ "authors" : [{ "lastname":"Bläsius" , "initial":"T" , "url":"https://hpi.de/friedrich/publications/people/thomas-blaesius.html" , "mail":"thomas.blasius(at)hpi.de" }, { "lastname":"Casel" , "initial":"K" , "url":"https://hpi.de/friedrich/publications/people/katrin-casel.html" , "mail":"katrin.casel(at)hpi.de" }, { "lastname":"Chauhan" , "initial":"A" , "url":"https://hpi.de/friedrich/publications/people/ankit-chauhan.html" , "mail":"ankit.chauhan(at)hpi.de" }, { "lastname":"Cohen" , "initial":"S" , "url":"https://hpi.de/friedrich/publications/people/sarel-cohen.html" , "mail":"sarel.cohen(at)hpi.de" }, { "lastname":"Cseh" , "initial":"" , "url":"https://hpi.de/friedrich/publications/people/agnes-cseh.html" , "mail":"agnes.cseh(at)hpi.de" }, { "lastname":"Doskoč" , "initial":"V" , "url":"https://hpi.de/friedrich/publications/people/vanja-doskoc.html" , "mail":"vanja.doskoc(at)hpi.de" }, { "lastname":"Elijazyfer" , "initial":"Z" , "url":"https://hpi.de/friedrich/people/ziena-elijazyfer.html" , "mail":"ziena.elijazyfer(at)hpi.de" }, { "lastname":"Fischbeck" , "initial":"P" , "url":"https://hpi.de/friedrich/publications/people/philipp-fischbeck.html" , "mail":"philipp.fischbeck(at)hpi.de" }, { "lastname":"Friedrich" , "initial":"T" , "url":"https://hpi.de/friedrich/publications/people/tobias-friedrich.html" , "mail":"friedrich(at)hpi.de" }, { "lastname":"Göbel" , "initial":"A" , "url":"https://hpi.de/friedrich/publications/people/andreas-goebel.html" , "mail":"andreas.goebel(at)hpi.de" }, { "lastname":"Issac" , "initial":"D" , "url":"https://hpi.de/friedrich/publications/people/davis-issac.html" , "mail":"davis.issac(at)hpi.de" }, { "lastname":"Katzmann" , "initial":"M" , "url":"https://hpi.de/friedrich/publications/people/maximilian-katzmann.html" , "mail":"maximilian.katzmann(at)hpi.de" }, { "lastname":"Khazraei" , "initial":"A" , "url":"https://hpi.de/friedrich/publications/people/ardalan-khazraei.html" , "mail":"ardalan.khazraei(at)hpi.de" }, { "lastname":"Kötzing" , "initial":"T" , "url":"https://hpi.de/friedrich/publications/people/timo-koetzing.html" , "mail":"timo.koetzing(at)hpi.de" }, { "lastname":"Krejca" , "initial":"M" , "url":"https://hpi.de/friedrich/publications/people/martin-krejca.html" , "mail":"martin.krejca(at)hpi.de" }, { "lastname":"Krogmann" , "initial":"S" , "url":"https://hpi.de/friedrich/publications/people/simon-krogmann.html" , "mail":"simon.krogmann(at)hpi.de" }, { "lastname":"Krohmer" , "initial":"A" , "url":"https://hpi.de/friedrich/publications/people/anton-krohmer.html" , "mail":"none" }, { "lastname":"Kumar" , "initial":"N" , "url":"https://hpi.de/friedrich/publications/people/nikhil-kumar.html" , "mail":"nikhil.kumar(at)hpi.de" }, { "lastname":"Lagodzinski" , "initial":"G" , "url":"https://hpi.de/friedrich/publications/people/gregor-lagodzinski.html" , "mail":"gregor.lagodzinski(at)hpi.de" }, { "lastname":"Lenzner" , "initial":"P" , "url":"https://hpi.de/friedrich/publications/people/pascal-lenzner.html" , "mail":"pascal.lenzner(at)hpi.de" }, { "lastname":"Melnichenko" , "initial":"A" , "url":"https://hpi.de/friedrich/publications/people/anna-melnichenko.html" , "mail":"anna.melnichenko(at)hpi.de" }, { "lastname":"Molitor" , "initial":"L" , "url":"https://hpi.de/friedrich/publications/people/louise-molitor.html" , "mail":"louise.molitor(at)hpi.de" }, { "lastname":"Neubert" , "initial":"S" , "url":"https://hpi.de/friedrich/publications/people/stefan-neubert.html" , "mail":"stefan.neubert(at)hpi.de" }, { "lastname":"Pappik" , "initial":"M" , "url":"https://hpi.de/friedrich/publications/people/marcus-pappik.html" , "mail":"marcus.pappik(at)hpi.de" }, { "lastname":"Quinzan" , "initial":"F" , "url":"https://hpi.de/friedrich/publications/people/francesco-quinzan.html" , "mail":"francesco.quinzan(at)hpi.de" }, { "lastname":"Rizzo" , "initial":"M" , "url":"https://hpi.de/friedrich/publications/people/manuel-rizzo.html" , "mail":"manuel.rizzo(at)hpi.de" }, { "lastname":"Rothenberger" , "initial":"R" , "url":"https://hpi.de/friedrich/publications/people/ralf-rothenberger.html" , "mail":"ralf.rothenberger(at)hpi.de" }, { "lastname":"Schirneck" , "initial":"M" , "url":"https://hpi.de/friedrich/publications/people/martin-schirneck.html" , "mail":"martin.schirneck(at)hpi.de" }, { "lastname":"Seidel" , "initial":"K" , "url":"https://hpi.de/friedrich/publications/people/karen-seidel.html" , "mail":"karen.seidel(at)hpi.de" }, { "lastname":"Sutton" , "initial":"A" , "url":"https://hpi.de/friedrich/publications/people/andrew-m-sutton.html" , "mail":"none" }, { "lastname":"Weyand" , "initial":"C" , "url":"https://hpi.de/friedrich/publications/people/christopher-weyand.html" , "mail":"none" }]}
Bilò, Davide; Friedrich, Tobias; Lenzner, Pascal; Lowski, Stefanie; Melnichenko, AnnaSelfish Creation of Social Networks. Conference on Artificial Intelligence (AAAI) 2021
Understanding real-world networks has been a core research endeavor throughout the last two decades. Network Creation Games are a promising approach for this from a game-theoretic perspective. In these games, selfish agents corresponding to nodes in a network strategically decide which links to form to optimize their centrality. Many versions have been introduced and analyzed, but none of them fits to modeling the evolution of social networks. In real-world social networks, connections are often established by recommendations from common acquaintances or by a chain of such recommendations. Thus establishing and maintaining a contact with a friend of a friend is easier than connecting to complete strangers. This explains the high clustering, i.e., the abundance of triangles, in real-world social networks. We propose and analyze a network creation model inspired by real-world social networks. Edges are formed in our model via bilateral consent of both endpoints and the cost for establishing and maintaining an edge is proportional to the distance of the endpoints before establishing the connection. We provide results for generic cost functions, which essentially only must be convex functions in the distance of the endpoints without the respective edge. For this broad class of cost functions, we provide many structural properties of equilibrium networks and prove (almost) tight bounds on the diameter, the Price of Anarchy and the Price of Stability. Moreover, as a proof-of-concept we show via experiments that the created equilibrium networks of our model indeed closely mimics real-world social networks. We observe degree distributions that seem to follow a power-law, high clustering, and low diameters. This can be seen as a promising first step towards game-theoretic network creation models that predict networks featuring all core real-world properties.
Berger, Julian; Böther, Maximilian; Doskoč, Vanja; Gadea Harder, Jonathan; Klodt, Nicolas; Kötzing, Timo; Lötzsch, Winfried; Peters, Jannik; Schiller, Leon; Seifert, Lars; Wells, Armin; Wietheger, SimonLearning Languages with Decidable Hypotheses. Computability in Europe (CiE) 2021
Böther, Maximilian; Fischbeck, Philipp; Friedrich, Tobias; Krejca, Martin S.; Molitor, Louise; Schiller, LeonEvolutionary Minimization of Traffic Congestion. Genetic and Evolutionary Computation Conference (GECCO) 2021
Traffic congestion is a major issue that can be solved by suggesting drivers alternative routes they are willing to take. This concept has been formalized as a strategic routing problem in which a single alternative route is suggested to an existing one. We extend this formalization and introduce the Multiple-Routes problem, which is given a start and a destination and then aims at finding up to \(n\) different routes that the drivers strategically disperse over, minimizing the overall travel time of the system. Due to the NP-hard nature of the problem, we introduce the Multiple-Routes evolutionary algorithm (MREA) as a heuristic solver. We study several mutation and crossover operators and evaluate them on real-world data of the city of Berlin, Germany. We find that a combination of all operators yields the best result, improving the overall travel time by a factor between 1.8 and 3, in the median, compared to all drivers taking the fastest route. For the base case \(n=2\), we compare our MREA to the highly tailored optimal solver by Bläsius etal. [ATMOS 2020] and show that, in the median, our approach finds solutions of quality at least \(99.69\%\) of an optimal solution while only requiring \(40\%\) of the time.
Kißig, Otto; Taraz, Martin; Cohen, Sarel; Doskoč, Vanja; Friedrich, TobiasDrug Repurposing for Multiple COVID Strains using Collaborative Filtering. ICLR Workshop on Machine Learning for Preventing and Combating Pandemics (MLPCP@ICLR) 2021
Birnick, Johann; Bläsius, Thomas; Friedrich, Tobias; Naumann, Felix; Papenbrock, Thorsten; Schirneck, MartinHitting Set Enumeration with Partial Information for Unique Column Combination Discovery. Proceedings of the VLDB Endowment 2020: 2270 - 2283
Unique column combinations (UCCs) are a fundamental concept in relational databases. They identify entities in the data and support various data management activities. Still, UCCs are usually not explicitly defined and need to be discovered. State-of-the-art data profiling algorithms are able to efficiently discover UCCs in moderately sized datasets, but they tend to fail on large and, in particular, on wide datasets due to run time and memory limitations. In this paper, we introduce HPIValid, a novel UCC discovery algorithm that implements a faster and more resource-saving search strategy. HPIValid models the metadata discovery as a hitting set enumeration problem in hypergraphs. In this way, it combines efficient discovery techniques from data profiling research with the most recent theoretical insights into enumeration algorithms. Our evaluation shows that HPIValid is not only orders of magnitude faster than related work, it also has a much smaller memory footprint.
Bläsius, Thomas; Böther, Maximilian; Fischbeck, Philipp; Friedrich, Tobias; Gries, Alina; Hüffner, Falk; Kißig, Otto; Lenzner, Pascal; Molitor, Louise; Schiller, Leon; Wells, Armin; Witheger, SimonA Strategic Routing Framework and Algorithms for Computing Alternative Paths. Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS) 2020: 10:1--10:14
Traditional navigation services find the fastest route for a single driver. Though always using the fastest route seems desirable for every individual, selfish behavior can have undesirable effects such as higher energy consumption and avoidable congestion, even leading to higher overall and individual travel times. In contrast, strategic routing aims at optimizing the traffic for all agents regarding a global optimization goal. We introduce a framework to formalize real-world strategic routing scenarios as algorithmic problems and study one of them, which we call Single Alternative Path (SAP), in detail. There, we are given an original route between a single origin–destination pair. The goal is to suggest an alternative route to all agents that optimizes the overall travel time under the assumption that the agents distribute among both routes according to a psychological model, for which we introduce the concept of Pareto-conformity. We show that the SAP problem is NP-complete, even for such models. Nonetheless, assuming Pareto-conformity, we give multiple algorithms for different variants of SAP, using multi-criteria shortest path algorithms as subroutines.Moreover, we prove that several natural models are in fact Pareto-conform. The implementation and evaluation of our algorithms serve as a proof of concept, showing that SAP can be solved in reasonable time even though the algorithms have exponential running time in the worst case.
Friedrich, Tobias; Krejca, Martin S.; Lagodzinski, J. A. Gregor; Rizzo, Manuel; Zahn, ArthurMemetic Genetic Algorithms for Time Series Compression by Piecewise Linear Approximation. International Conference on Neural Information Processing (ICONIP) 2020: 592-604
Time series are sequences of data indexed by time. Such data are collected in various domains, often in massive amounts, such that storing them proves challenging. Thus, time series are commonly stored in a compressed format. An important compression approach is piecewise linear approximation (PLA), which only keeps a small set of time points and interpolates the remainder linearly. Picking a subset of time points such that the PLA minimizes the mean squared error to the original time series is a challenging task, naturally lending itself to heuristics. We propose the piecewise linear approximation genetic algorithm (PLA-GA) for compressing time series by PLA. The PLA-GA is a memetic \((\mu + \lambda)\) GA that makes use of two distinct operators tailored to time series compression. First, we add special individuals to the initial population that are derived using established PLA heuristics. Second, we propose a novel local search operator that greedily improves a compressed time series. We compare the PLA-GA empirically with existing evolutionary approaches and with a deterministic PLA algorithm, known as Bellman's algorithm, that is optimal for the restricted setting of sampling. In both cases, the PLA-GA approximates the original time series better and quicker. Further, it drastically outperforms Bellman's algorithm with increasing instance size with respect to run time until finding a solution of equal or better quality -- we observe speed-up factors between 7 and 100 for instances of 90,000 to 100,000 data points.
Echzell, Hagen; Friedrich, Tobias; Lenzner, Pascal; Melnichenko, AnnaFlow-Based Network Creation Games. International Joint Conference on Artificial Intelligence (IJCAI) 2020: 139-145
Network Creation Games (NCGs) model the creation of decentralized communication networks like the Internet. In such games strategic agents corresponding to network nodes selfishly decide with whom to connect to optimize some objective function. Past research intensively analyzed models where the agents strive for a central position in the network. This models agents optimizing the network for low-latency applications like VoIP. However, with today's abundance of streaming services it is important to ensure that the created network can satisfy the increased bandwidth demand. To the best of our knowledge, this natural problem of the decentralized strategic creation of networks with sufficient bandwidth has not yet been studied. We introduce Flow-Based NCGs where the selfish agents focus on bandwidth instead of latency. In essence, budget-constrained agents create network links to maximize their minimum or average network flow value to all other network nodes. Equivalently, this can also be understood as agents who create links to increase their connectivity and thus also the robustness of the network. For this novel type of NCG we prove that pure Nash equilibria exist, we give a simple algorithm for computing optimal networks, we show that the Price of Stability is~1 and we prove an (almost) tight bound of 2 on the Price of Anarchy. Last but not least, we show that our models do not admit a potential function.
Friedrich, Tobias; Krejca, Martin S.; Rothenberger, Ralf; Arndt, Tobias; Hafner, Danijar; Kellermeier, Thomas; Krogmann, Simon; Razmjou, ArminRouting for On-Street Parking Search using Probabilistic Data. AI Communications 2019: 113-124
A significant percentage of urban traffic is caused by the search for parking spots. One possible approach to improve this situation is to guide drivers along routes which are likely to have free parking spots. The task of finding such a route can be modeled as a probabilistic graph problem which is NP-complete. Thus, we propose heuristic approaches for solving this problem and evaluate them experimentally. For this, we use probabilities of finding a parking spot, which are based on publicly available empirical data from TomTom International B.V. Additionally, we propose a heuristic that relies exclusively on conventional road attributes. Our experiments show that this algorithm comes close to the baseline by a factor of 1.3 in our cost measure. Last, we complement our experiments with results from a field study, comparing the success rates of our algorithms against real human drivers.
Doerr, Benjamin; Fischbeck, Philipp; Frahnow, Clemens; Friedrich, Tobias; Kötzing, Timo; Schirneck, MartinIsland Models Meet Rumor Spreading. Algorithmica 2019: 886-915
Island models in evolutionary computation solve problems by a careful interplay of independently running evolutionary algorithms on the island and an exchange of good solutions between the islands. In this work, we conduct rigorous run time analyses for such island models trying to simultaneously obtain good run times and low communication effort. We improve the existing upper bounds for both measures (i) by improving the run time bounds via a careful analysis, (ii) by balancing individual computation and communication in a more appropriate manner, and (iii) by replacing the usual communicate-with-all approach with randomized rumor spreading. In the latter, each island contacts a randomly chosen neighbor. This epidemic communication paradigm is known to lead to very fast and robust information dissemination in many applications. Our results concern island models running simple (1+1) evolutionary algorithms to optimize the classic test functions OneMax and LeadingOnes. We investigate binary trees, d-dimensional tori, and complete graphs as communication topologies.
Bläsius, Thomas; Friedrich, Tobias; Lischeid, Julius; Meeks, Kitty; Schirneck, MartinEfficiently Enumerating Hitting Sets of Hypergraphs Arising in Data Profiling. Algorithm Engineering and Experiments (ALENEX) 2019: 130-143
We devise an enumeration method for inclusion-wise minimal hitting sets in hypergraphs. It has delay \(O(m^{k^\ast+1} \cdot n^2)\) and uses linear space. Hereby, \(n\) is the number of vertices, \(m\) the number of hyperedges, and \(k^\ast\) the rank of the transversal hypergraph. In particular, on classes of hypergraphs for which the cardinality \(k^\ast\) of the largest minimal hitting set is bounded, the delay is polynomial. The algorithm solves the extension problem for minimal hitting sets as a subroutine. We show that the extension problem is W[3]-complete when parameterised by the cardinality of the set which is to be extended. For the subroutine, we give an algorithm that is optimal under the exponential time hypothesis. Despite these lower bounds, we provide empirical evidence showing that the enumeration outperforms the theoretical worst-case guarantee on hypergraphs arising in the profiling of relational databases, namely, in the detection of unique column combinations.
Peters, Jannik; Stephan, Daniel; Amon, Isabel; Gawendowicz, Hans; Lischeid, Julius; Salabarria, Julius; Umland, Jonas; Werner, Felix; Krejca, Martin S.; Rothenberger, Ralf; Kötzing, Timo; Friedrich, TobiasMixed Integer Programming versus Evolutionary Computation for Optimizing a Hard Real-World Staff Assignment Problem. International Conference on Automated Planning and Scheduling (ICAPS) 2019: 541-554
Assigning staff to engagements according to hard constraints while optimizing several objectives is a task encountered by many companies on a regular basis. Simplified versions of such assignment problems are NP-hard. Despite this, a typical approach to solving them consists of formulating them as mixed integer programming (MIP) problems and using a state-of-the-art solver to get solutions that closely approximate the optimum. In this paper, we consider a complex real-world staff assignment problem encountered by the professional service company KPMG, with the goal of finding an algorithm that solves it faster and with a better solution than a commercial MIP solver. We follow the evolutionary algorithm (EA) metaheuristic and design a search heuristic which iteratively improves a solution using domain-specific mutation operators. Furthermore, we use a flow algorithm to optimally solve a subproblem, which tremendously reduces the search space for the EA. For our real-world instance of the assignment problem, given the same total time budget of \(100\) hours, a parallel EA approach finds a solution that is only \(1.7\)% away from an upper bound for the (unknown) optimum within under five hours, while the MIP solver Gurobi still has a gap of \(10.5\) %.
Bläsius, Thomas; Fischbeck, Philipp; Friedrich, Tobias; Schirneck, MartinUnderstanding the Effectiveness of Data Reduction in Public Transportation Networks. Workshop on Algorithms and Models for the Web Graph (WAW) 2019: 87-101
Given a public transportation network of stations and connections, we want to find a minimum subset of stations such that each connection runs through a selected station. Although this problem is NP-hard in general, real-world instances are regularly solved almost completely by a set of simple reduction rules. To explain this behavior, we view transportation networks as hitting set instances and identify two characteristic properties, locality and heterogeneity. We then devise a randomized model to generate hitting set instances with adjustable properties. While the heterogeneity does influence the effectiveness of the reduction rules, the generated instances show that locality is the significant factor. Beyond that, we prove that the effectiveness of the reduction rules is independent of the underlying graph structure. Finally, we show that high locality is also prevalent in instances from other domains, facilitating a fast computation of minimum hitting sets.
Echzell, Hagen; Friedrich, Tobias; Lenzner, Pascal; Molitor, Louise; Pappik, Marcus; Schöne, Friedrich; Sommer, Fabian; Stangl, DavidConvergence and Hardness of Strategic Schelling Segregation. Web and Internet Economics (WINE) 2019: 156-170
The phenomenon of residential segregation was captured by Schelling's famous segregation model where two types of agents are placed on a grid and an agent is content with her location if the fraction of her neighbors which have the same type as her is at least \(\tau\), for some \(0<\tau<1\). Discontent agents simply swap their location with a randomly chosen other discontent agent or jump to a random empty cell. We analyze a generalized game-theoretic model of Schelling segregation which allows more than two agent types and more general underlying graphs modeling the residential area. For this we show that both aspects heavily influence the dynamic properties and the tractability of finding an optimal placement. We map the boundary of when improving response dynamics (IRD), i.e., the natural approach for finding equilibrium states, are guaranteed to converge. For this we prove several sharp threshold results where guaranteed IRD convergence suddenly turns into the strongest possible non-convergence result: a violation of weak acyclicity. In particular, we show such threshold results also for Schelling's original model, which is in contrast to the standard assumption in many empirical papers. Furthermore, we show that in case of convergence, IRD find an equilibrium in \(O(m)\) steps, where \(m\) is the number of edges in the underlying graph and show that this bound is met in empirical simulations starting from random initial agent placements.
Bläsius, Thomas; Freiberger, Cedric; Friedrich, Tobias; Katzmann, Maximilian; Montenegro-Retana, Felix; Thieffry, MarianneEfficient Shortest Paths in Scale-Free Networks with Underlying Hyperbolic Geometry. International Colloquium on Automata, Languages, and Programming (ICALP) 2018: 20:1-20:14
A common way to accelerate shortest path algorithms on graphs is the use of a bidirectional search, which simultaneously explores the graph from the start and the destination. It has been observed recently that this strategy performs particularly well on scale-free real-world networks. Such networks typically have a heterogeneous degree distribution (e.g., a power-law distribution) and high clustering (i.e., vertices with a common neighbor are likely to be connected themselves). These two properties can be obtained by assuming an underlying hyperbolic geometry. To explain the observed behavior of the bidirectional search, we analyze its running time on hyperbolic random graphs and prove that it is \(\tilde{O}(n\)\(^{2 - 1/ \alpha}+\)\(n^{1/(2\alpha)}\)\(+ \delta_{\max})\) with high probability, where \(\alpha\)\(\in\)\((0.5, 1)\) controls the power-law exponent of the degree distribution, and \(\delta_{\max}\) is the maximum degree. This bound is sublinear, improving the obvious worst-case linear bound. Although our analysis depends on the underlying geometry, the algorithm itself is oblivious to it.
Frahnow, Clemens; Kötzing, TimoRing Migration Topology Helps Bypassing Local Optima. Parallel Problem Solving From Nature (PPSN) 2018: 129-140
Running several evolutionary algorithms in parallel and occasionally exchanging good solutions is referred to as island models. The idea is that the independence of the different islands leads to diversity, thus possibly exploring the search space better. Many theoretical analyses so far have found a complete (or sufficiently quickly expanding) topology as underlying migration graph most efficient for optimization, even though a quick dissemination of individuals leads to a loss of diversity. We suggest a simple fitness function Fork with two local optima parametrized by \(r \geq 2\) and a scheme for composite fitness functions. We show that, while the (1+1) EA gets stuck in a bad local optimum and incurs a run time of \(\Theta(n^{2r})\) fitness evaluations on Fork, island models with a complete topology can achieve a run time of \(\Theta(n^{1.5r})\) by making use of rare migrations in order to explore the search space more effectively. Finally, the ring topology, making use of rare migrations and a large diameter, can achieve a run time of \(\tilde{\Theta}(n^r)\), the black box complexity of Fork. This shows that the ring topology can be preferable over the complete topology in order to maintain diversity.
Bläsius, Thomas; Eube, Jan; Feldtkeller, Thomas; Friedrich, Tobias; Krejca, Martin S.; Lagodzinski, J. A. Gregor; Rothenberger, Ralf; Severin, Julius; Sommer, Fabian; Trautmann, JustinMemory-restricted Routing With Tiled Map Data. Systems, Man, and Cybernetics (SMC) 2018: 3347-3354
Modern routing algorithms reduce query time by depending heavily on preprocessed data. The recently developed Navigation Data Standard (NDS) enforces a separation between algorithms and map data, rendering preprocessing inapplicable. Furthermore, map data is partitioned into tiles with respect to their geographic coordinates. With the limited memory found in portable devices, the number of tiles loaded becomes the major factor for run time. We study routing under these restrictions and present new algorithms as well as empirical evaluations. Our results show that, on average, the most efficient algorithm presented uses more than 20 times fewer tile loads than a normal A*.
Bläsius, Thomas; Friedrich, Tobias; Katzmann, Maximilian; Krohmer, Anton; Striebel, JonathanTowards a Systematic Evaluation of Generative Network Models. Workshop on Algorithms and Models for the Web Graph (WAW) 2018: 99-114
Generative graph models play an important role in network science. Unlike real-world networks, they are accessible for mathematical analysis and the number of available networks is not limited. The explanatory power of results on generative models, however, heavily depends on how realistic they are. We present a framework that allows for a systematic evaluation of generative network models. It is based on the question whether real-world networks can be distinguished from generated graphs with respect to certain graph parameters. As a proof of concept, we apply our framework to four popular random graph models (Erdős-Rényi, Barabási-Albert, Chung-Lu, and hyperbolic random graphs). Our experiments for example show that all four models are bad representations for Facebook's social networks, while Chung-Lu and hyperbolic random graphs are good representations for other networks, with different strengths and weaknesses.
Doerr, Benjamin; Fischbeck, Philipp; Frahnow, Clemens; Friedrich, Tobias; Kötzing, Timo; Schirneck, MartinIsland Models Meet Rumor Spreading. Genetic and Evolutionary Computation Conference (GECCO) 2017: 1359-1366
Island models in evolutionary computation solve problems by a careful interplay of independently running evolutionary algorithms on the island and an exchange of good solutions between the islands. In this work, we conduct rigorous run time analyses for such island models trying to simultaneously obtain good run times and low communication effort. We improve the existing upper bounds for the communication effort (i) by improving the run time bounds via a careful analysis, (ii) by setting the balance between individual computation and communication in a more appropriate manner, and (iii) by replacing the usual communicate-with-all-neighbors approach with randomized rumor spreading, where each island contacts a randomly chosen neighbor. This epidemic communication paradigm is known to lead to very fast and robust information dissemination in many applications. Our results concern islands running simple (1+1) evolutionary algorithms, we regard d-dimensional tori and complete graphs as communication topologies, and optimize the classic test functions OneMax and LeadingOnes.
Friedrich, Tobias; Ihde, Sven; Keßler, Christoph; Lenzner, Pascal; Neubert, Stefan; Schumann, DavidEfficient Best Response Computation for Strategic Network Formation under Attack. Symposium on Algorithmic Game Theory (SAGT) 2017: 199-211
Inspired by real world examples, e.g. the Internet, researchers have introduced an abundance of strategic games to study natural phenomena in networks. Unfortunately, almost all of these games have the conceptual drawback of being computationally intractable, i.e. computing a best response strategy or checking if an equilibrium is reached is NP-hard. Thus, a main challenge in the field is to find tractable realistic network formation models. We address this challenge by investigating a very recently introduced model by Goyal et al. [WINE'16] which focuses on robust networks in the presence of a strong adversary who attacks (and kills) nodes in the network and lets this attack spread virus-like to neighboring nodes and their neighbors. Our main result is to establish that this natural model is one of the few exceptions which are both realistic and computationally tractable. In particular, we answer an open question of Goyal et al. by providing an efficient algorithm for computing a best response strategy, which implies that deciding whether the game has reached a Nash equilibrium can be done efficiently as well. Our algorithm essentially solves the problem of computing a minimal connection to a network which maximizes the reachability while hedging against severe attacks on the network infrastructure and may thus be of independent interest.
Friedrich, Tobias; Ihde, Sven; Keßler, Christoph; Lenzner, Pascal; Neubert, Stefan; Schumann, DavidBrief Announcement: Efficient Best Response Computation for Strategic Network Formation under Attack. Symposium on Parallelism in Algorithms and Architectures (SPAA) 2017: 321-323
Inspired by real world examples, e.g. the Internet, researchers have introduced an abundance of strategic games to study natural phenomena in networks. Unfortunately, almost all of these games have the conceptual drawback of being computationally intractable, i.e. computing a best response strategy or checking if an equilibrium is reached is NP-hard. Thus, a main challenge in the field is to find tractable realistic network formation models. We address this challenge by establishing that the recently introduced model by Goyal et al.[WINE'16], which focuses on robust networks in the presence of a strong adversary, is a rare exception which is both realistic and computationally tractable. In particular, we sketch an efficient algorithm for computing a best response strategy, which implies that deciding whether the game has reached a Nash equilibrium can be done efficiently as well. Our algorithm essentially solves the problem of computing a minimal connection to a network which maximizes the reachability while hedging against severe attacks on the network infrastructure.
Arndt, Tobias; Hafner, Danijar; Kellermeier, Thomas; Krogmann, Simon; Razmjou, Armin; Krejca, Martin S.; Rothenberger, Ralf; Friedrich, TobiasProbabilistic Routing for On-Street Parking Search. European Symposium on Algorithms (ESA) 2016: 6:1-6:13
An estimated \(30\%\) of urban traffic is caused by search for parking spots. Traffic could be reduced by suggesting effective routes leading along potential parking spots. In this paper, we formalize parking search as a probabilistic problem on a road graph and show that it is NP-complete. We explore heuristics that optimize for the driving duration and the walking distance to the destination. Routes are constrained to reach a certain probability threshold of finding a spot. Empirically estimated probabilities of successful parking attempts are provided by TomTom on a per-street basis. We release these probabilities as a dataset of about 80,000 roads covering the Berlin area. This allows to evaluate parking search algorithms on a real road network with realistic probabilities for the first time. However, for many other areas, parking probabilities are not openly available. Because they are effortful to collect, we propose an algorithm that relies on conventional road attributes only. Our experiments show that this algorithm comes close to the baseline by a factor of 1.3 in our cost measure. This leads to the conclusion that conventional road attributes may be sufficient to compute reasonably good parking search routes.
Kötzing, Timo; Schirneck, MartinTowards an Atlas of Computational Learning Theory. Symposium on Theoretical Aspects of Computer Science (STACS) 2016: 47:1-47:13
A major part of our knowledge about Computational Learning stems from comparisons of the learning power of different learning criteria. These comparisons inform about trade-offs between learning restrictions and, more generally, learning settings; furthermore, they inform about what restrictions can be observed without losing learning power. With this paper we propose that one main focus of future research in Computational Learning should be on a structured approach to determine the relations of different learning criteria. In particular, we propose that, for small sets of learning criteria, all pairwise relations should be determined; these relations can then be easily depicted as a map, a diagram detailing the relations. Once we have maps for many relevant sets of learning criteria, the collection of these maps is an Atlas of Computational Learning Theory, informing at a glance about the landscape of computational learning just as a geographical atlas informs about the earth. In this paper we work toward this goal by providing three example maps, one pertaining to partially set-driven learning, and two pertaining to strongly monotone learning. These maps can serve as blueprints for future maps of similar base structure.