TY - JOUR A1 - Friedrich, Tobias A1 - Kötzing, Timo A1 - Krejca, Martin Stefan A1 - Sutton, Andrew M. T1 - Robustness of Ant Colony Optimization to Noise JF - Evolutionary computation N2 - Recently, ant colony optimization (ACO) algorithms have proven to be efficient in uncertain environments, such as noisy or dynamically changing fitness functions. Most of these analyses have focused on combinatorial problems such as path finding. We rigorously analyze an ACO algorithm optimizing linear pseudo- Boolean functions under additive posterior noise. We study noise distributions whose tails decay exponentially fast, including the classical case of additive Gaussian noise. Without noise, the classical (mu + 1) EA outperforms any ACO algorithm, with smaller mu being better; however, in the case of large noise, the (mu + 1) EA fails, even for high values of mu (which are known to help against small noise). In this article, we show that ACO is able to deal with arbitrarily large noise in a graceful manner; that is, as long as the evaporation factor. is small enough, dependent on the variance s2 of the noise and the dimension n of the search space, optimization will be successful. We also briefly consider the case of prior noise and prove that ACO can also efficiently optimize linear functions under this noise model. KW - Ant colony optimization KW - Noisy Fitness KW - Theory KW - Run time analysis Y1 - 2016 U6 - https://doi.org/10.1162/EVCO_a_00178 SN - 1063-6560 SN - 1530-9304 VL - 24 SP - 237 EP - 254 PB - MIT Press CY - Cambridge ER - TY - JOUR A1 - Friedrich, Tobias A1 - Katzmann, Maximilian A1 - Krohmer, Anton T1 - Unbounded Discrepancy of Deterministic Random Walks on Grids JF - SIAM journal on discrete mathematics N2 - Random walks are frequently used in randomized algorithms. We study a derandomized variant of a random walk on graphs called the rotor-router model. In this model, instead of distributing tokens randomly, each vertex serves its neighbors in a fixed deterministic order. For most setups, both processes behave in a remarkably similar way: Starting with the same initial configuration, the number of tokens in the rotor-router model deviates only slightly from the expected number of tokens on the corresponding vertex in the random walk model. The maximal difference over all vertices and all times is called single vertex discrepancy. Cooper and Spencer [Combin. Probab. Comput., 15 (2006), pp. 815-822] showed that on Z(d), the single vertex discrepancy is only a constant c(d). Other authors also determined the precise value of c(d) for d = 1, 2. All of these results, however, assume that initially all tokens are only placed on one partition of the bipartite graph Z(d). We show that this assumption is crucial by proving that, otherwise, the single vertex discrepancy can become arbitrarily large. For all dimensions d >= 1 and arbitrary discrepancies l >= 0, we construct configurations that reach a discrepancy of at least l. KW - deterministic random walk KW - rotor-router model KW - single vertex discrepancy Y1 - 2018 U6 - https://doi.org/10.1137/17M1131088 SN - 0895-4801 SN - 1095-7146 VL - 32 IS - 4 SP - 2441 EP - 2452 PB - Society for Industrial and Applied Mathematics CY - Philadelphia ER - TY - JOUR A1 - Shi, Feng A1 - Schirneck, Friedrich Martin A1 - Friedrich, Tobias A1 - Kötzing, Timo A1 - Neumann, Frank T1 - Reoptimization time analysis of evolutionary algorithms on linear functions under dynamic uniform constraints JF - Algorithmica : an international journal in computer science N2 - Rigorous runtime analysis is a major approach towards understanding evolutionary computing techniques, and in this area linear pseudo-Boolean objective functions play a central role. Having an additional linear constraint is then equivalent to the NP-hard Knapsack problem, certain classes thereof have been studied in recent works. In this article, we present a dynamic model of optimizing linear functions under uniform constraints. Starting from an optimal solution with respect to a given constraint bound, we investigate the runtimes that different evolutionary algorithms need to recompute an optimal solution when the constraint bound changes by a certain amount. The classical (1+1) EA and several population-based algorithms are designed for that purpose, and are shown to recompute efficiently. Furthermore, a variant of the (1+(λ,λ))GA for the dynamic optimization problem is studied, whose performance is better when the change of the constraint bound is small. Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-605295 SN - 0178-4617 SN - 1432-0541 VL - 82 IS - 10 SP - 3117 EP - 3123 PB - Springer CY - New York ER - TY - JOUR A1 - Friedrich, Tobias A1 - Kötzing, Timo A1 - Krejca, Martin Stefan T1 - Unbiasedness of estimation-of-distribution algorithms JF - Theoretical computer science N2 - In the context of black-box optimization, black-box complexity is used for understanding the inherent difficulty of a given optimization problem. Central to our understanding of nature-inspired search heuristics in this context is the notion of unbiasedness. Specialized black-box complexities have been developed in order to better understand the limitations of these heuristics - especially of (population-based) evolutionary algorithms (EAs). In contrast to this, we focus on a model for algorithms explicitly maintaining a probability distribution over the search space: so-called estimation-of-distribution algorithms (EDAs). We consider the recently introduced n-Bernoulli-lambda-EDA framework, which subsumes, for example, the commonly known EDAs PBIL, UMDA, lambda-MMAS(IB), and cGA. We show that an n-Bernoulli-lambda-EDA is unbiased if and only if its probability distribution satisfies a certain invariance property under isometric automorphisms of [0, 1](n). By restricting how an n-Bernoulli-lambda-EDA can perform an update, in a way common to many examples, we derive conciser characterizations, which are easy to verify. We demonstrate this by showing that our examples above are all unbiased. (C) 2018 Elsevier B.V. All rights reserved. KW - Estimation-of-distribution algorithm KW - Unbiasedness KW - Theory Y1 - 2019 U6 - https://doi.org/10.1016/j.tcs.2018.11.001 SN - 0304-3975 SN - 1879-2294 VL - 785 SP - 46 EP - 59 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Friedrich, Tobias A1 - Krejca, Martin Stefan A1 - Rothenberger, Ralf A1 - Arndt, Tobias A1 - Hafner, Danijar A1 - Kellermeier, Thomas A1 - Krogmann, Simon A1 - Razmjou, Armin T1 - Routing for on-street parking search using probabilistic data JF - AI communications : AICOM ; the European journal on artificial intelligence N2 - 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. KW - Parking search KW - probabilistic routing KW - constrained optimization KW - field study Y1 - 2019 U6 - https://doi.org/10.3233/AIC-180574 SN - 0921-7126 SN - 1875-8452 VL - 32 IS - 2 SP - 113 EP - 124 PB - IOS Press CY - Amsterdam ER - TY - JOUR A1 - Chauhan, Ankit A1 - Friedrich, Tobias A1 - Rothenberger, Ralf T1 - Greed is good for deterministic scale-free networks JF - Algorithmica : an international journal in computer science N2 - Large real-world networks typically follow a power-law degree distribution. To study such networks, numerous random graph models have been proposed. However, real-world networks are not drawn at random. Therefore, Brach et al. (27th symposium on discrete algorithms (SODA), pp 1306-1325, 2016) introduced two natural deterministic conditions: (1) a power-law upper bound on the degree distribution (PLB-U) and (2) power-law neighborhoods, that is, the degree distribution of neighbors of each vertex is also upper bounded by a power law (PLB-N). They showed that many real-world networks satisfy both properties and exploit them to design faster algorithms for a number of classical graph problems. We complement their work by showing that some well-studied random graph models exhibit both of the mentioned PLB properties. PLB-U and PLB-N hold with high probability for Chung-Lu Random Graphs and Geometric Inhomogeneous Random Graphs and almost surely for Hyperbolic Random Graphs. As a consequence, all results of Brach et al. also hold with high probability or almost surely for those random graph classes. In the second part we study three classical NP-hard optimization problems on PLB networks. It is known that on general graphs with maximum degree Delta, a greedy algorithm, which chooses nodes in the order of their degree, only achieves a Omega (ln Delta)-approximation forMinimum Vertex Cover and Minimum Dominating Set, and a Omega(Delta)-approximation forMaximum Independent Set. We prove that the PLB-U property with beta>2 suffices for the greedy approach to achieve a constant-factor approximation for all three problems. We also show that these problems are APX-hard even if PLB-U, PLB-N, and an additional power-law lower bound on the degree distribution hold. Hence, a PTAS cannot be expected unless P = NP. Furthermore, we prove that all three problems are in MAX SNP if the PLB-U property holds. KW - random graphs KW - deterministic properties KW - power-law KW - approximation KW - APX-hardness Y1 - 2020 U6 - https://doi.org/10.1007/s00453-020-00729-z SN - 0178-4617 SN - 1432-0541 VL - 82 IS - 11 SP - 3338 EP - 3389 PB - Springer CY - New York ER - TY - JOUR A1 - Birnick, Johann A1 - Bläsius, Thomas A1 - Friedrich, Tobias A1 - Naumann, Felix A1 - Papenbrock, Thorsten A1 - Schirneck, Friedrich Martin T1 - Hitting set enumeration with partial information for unique column combination discovery JF - Proceedings of the VLDB Endowment N2 - 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. Y1 - 2020 U6 - https://doi.org/10.14778/3407790.3407824 SN - 2150-8097 VL - 13 IS - 11 SP - 2270 EP - 2283 PB - Association for Computing Machinery CY - [New York, NY] ER - TY - JOUR A1 - Quinzan, Francesco A1 - Göbel, Andreas A1 - Wagner, Markus A1 - Friedrich, Tobias T1 - Evolutionary algorithms and submodular functions BT - benefits of heavy-tailed mutations JF - Natural computing : an innovative journal bridging biosciences and computer sciences ; an international journal N2 - A core operator of evolutionary algorithms (EAs) is the mutation. Recently, much attention has been devoted to the study of mutation operators with dynamic and non-uniform mutation rates. Following up on this area of work, we propose a new mutation operator and analyze its performance on the (1 + 1) Evolutionary Algorithm (EA). Our analyses show that this mutation operator competes with pre-existing ones, when used by the (1 + 1) EA on classes of problems for which results on the other mutation operators are available. We show that the (1 + 1) EA using our mutation operator finds a (1/3)-approximation ratio on any non-negative submodular function in polynomial time. We also consider the problem of maximizing a symmetric submodular function under a single matroid constraint and show that the (1 + 1) EA using our operator finds a (1/3)-approximation within polynomial time. This performance matches that of combinatorial local search algorithms specifically designed to solve these problems and outperforms them with constant probability. Finally, we evaluate the performance of the (1 + 1) EA using our operator experimentally by considering two applications: (a) the maximum directed cut problem on real-world graphs of different origins, with up to 6.6 million vertices and 56 million edges and (b) the symmetric mutual information problem using a four month period air pollution data set. In comparison with uniform mutation and a recently proposed dynamic scheme, our operator comes out on top on these instances. KW - Evolutionary algorithms KW - Mutation operators KW - Submodular functions KW - Matroids Y1 - 2021 U6 - https://doi.org/10.1007/s11047-021-09841-7 SN - 1572-9796 VL - 20 IS - 3 SP - 561 EP - 575 PB - Springer Science + Business Media B.V. CY - Dordrecht ER - TY - JOUR A1 - Blaesius, Thomas A1 - Friedrich, Tobias A1 - Schirneck, Friedrich Martin T1 - The complexity of dependency detection and discovery in relational databases JF - Theoretical computer science N2 - Multi-column dependencies in relational databases come associated with two different computational tasks. The detection problem is to decide whether a dependency of a certain type and size holds in a given database, the discovery problem asks to enumerate all valid dependencies of that type. We settle the complexity of both of these problems for unique column combinations (UCCs), functional dependencies (FDs), and inclusion dependencies (INDs). We show that the detection of UCCs and FDs is W[2]-complete when parameterized by the solution size. The discovery of inclusion-wise minimal UCCs is proven to be equivalent under parsimonious reductions to the transversal hypergraph problem of enumerating the minimal hitting sets of a hypergraph. The discovery of FDs is equivalent to the simultaneous enumeration of the hitting sets of multiple input hypergraphs. We further identify the detection of INDs as one of the first natural W[3]-complete problems. The discovery of maximal INDs is shown to be equivalent to enumerating the maximal satisfying assignments of antimonotone, 3-normalized Boolean formulas. KW - data profiling KW - enumeration complexity KW - functional dependency KW - inclusion KW - dependency KW - parameterized complexity KW - parsimonious reduction KW - transversal hypergraph KW - Unique column combination KW - W[3]-completeness Y1 - 2021 U6 - https://doi.org/10.1016/j.tcs.2021.11.020 SN - 0304-3975 SN - 1879-2294 VL - 900 SP - 79 EP - 96 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Casel, Katrin A1 - Fischbeck, Philipp A1 - Friedrich, Tobias A1 - Göbel, Andreas A1 - Lagodzinski, J. A. Gregor T1 - Zeros and approximations of Holant polynomials on the complex plane JF - Computational complexity : CC N2 - We present fully polynomial time approximation schemes for a broad class of Holant problems with complex edge weights, which we call Holant polynomials. We transform these problems into partition functions of abstract combinatorial structures known as polymers in statistical physics. Our method involves establishing zero-free regions for the partition functions of polymer models and using the most significant terms of the cluster expansion to approximate them. Results of our technique include new approximation and sampling algorithms for a diverse class of Holant polynomials in the low-temperature regime (i.e. small external field) and approximation algorithms for general Holant problems with small signature weights. Additionally, we give randomised approximation and sampling algorithms with faster running times for more restrictive classes. Finally, we improve the known zero-free regions for a perfect matching polynomial. KW - Holant problems KW - approximate counting KW - partition functions KW - graph KW - polynomials Y1 - 2022 U6 - https://doi.org/10.1007/s00037-022-00226-5 SN - 1016-3328 SN - 1420-8954 VL - 31 IS - 2 PB - Springer CY - Basel ER -