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Space-Efficient Fault-Tolerant Diameter Oracles [article]

Davide Bilò, Sarel Cohen, Tobias Friedrich, Martin Schirneck
2021 arXiv   pre-print
We design f-edge fault-tolerant diameter oracles (f-FDOs). We preprocess a given graph G on n vertices and m edges, and a positive integer f, to construct a data structure that, when queried with a set F of |F| ≤ f edges, returns the diameter of G-F. For a single failure (f=1) in an unweighted directed graph of diameter D, there exists an approximate FDO by Henzinger et al. [ITCS 2017] with stretch (1+ε), constant query time, space O(m), and a combinatorial preprocessing time of O(mn +
more » ... /ε)).We present an FDO for directed graphs with the same stretch, query time, and space. It has a preprocessing time of O(mn + n^2/ε). The preprocessing time nearly matches a conditional lower bound for combinatorial algorithms, also by Henzinger et al. With fast matrix multiplication, we achieve a preprocessing time of O(n^2.5794 + n^2/ε). We further prove an information-theoretic lower bound showing that any FDO with stretch better than 3/2 requires Ω(m) bits of space. For multiple failures (f>1) in undirected graphs with non-negative edge weights, we give an f-FDO with stretch (f+2), query time O(f^2log^2n), O(fn) space, and preprocessing time O(fm). We complement this with a lower bound excluding any finite stretch in o(fn) space. We show that for unweighted graphs with polylogarithmic diameter and up to f = o(log n/ loglog n) failures, one can swap approximation for query time and space. We present an exact combinatorial f-FDO with preprocessing time mn^1+o(1), query time n^o(1), and space n^2+o(1). When using fast matrix multiplication instead, the preprocessing time can be improved to n^ω+o(1), where ω < 2.373 is the matrix multiplication exponent.
arXiv:2107.03485v1 fatcat:3a2l7rvbifdyzjiu4q23fhf7uu

Near-Optimal Deterministic Single-Source Distance Sensitivity Oracles [article]

Davide Bilò, Sarel Cohen, Tobias Friedrich, Martin Schirneck
2021 arXiv   pre-print
Bender and Martin Farach-Colton. The LCA Problem Revisited. Aaron Bernstein and David R. Karger. Improved Distance Sensitivity Oracles via Random Sampling.  ... 
arXiv:2106.15731v1 fatcat:dqagqwfywna2vdmoshlyoec2bi

The Complexity of Dependency Detection and Discovery in Relational Databases [article]

Thomas Bläsius, Tobias Friedrich, Martin Schirneck
2021 arXiv   pre-print
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
more » ... 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.
arXiv:2103.13331v1 fatcat:tyocbt3hwzf3lgjlr3zlb4tqii

Fixed-Parameter Sensitivity Oracles [article]

Davide Bilò, Katrin Casel, Keerti Choudhary, Sarel Cohen, Tobias Friedrich, J.A. Gregor Lagodzinski, Martin Schirneck, Simon Wietheger
2021 arXiv   pre-print
doi:10.1137/17M1148566. 6 Davide Bilò, Sarel Cohen, Tobias Friedrich, and Martin Schirneck. Space-Efficient Fault- Tolerant Diameter Oracles.  ...  MFCS.2021.18. 7 Davide Bilò, Sarel Cohen, Tobias Friedrich, and Martin Schirneck. Near-Optimal Deterministic Single-Source Distance Sensitivity Oracles.  ... 
arXiv:2112.03059v1 fatcat:ooac3rw4szh63icloztu7jdymm

Deterministic Sensitivity Oracles for Diameter, Eccentricities and All Pairs Distances [article]

Davide Bilò, Keerti Choudhary, Sarel Cohen, Tobias Friedrich, Martin Schirneck
2022 arXiv   pre-print
We construct data structures for extremal and pairwise distances in directed graphs in the presence of transient edge failures. Henzinger et al. [ITCS 2017] initiated the study of fault-tolerant (sensitivity) oracles for the diameter and vertex eccentricities. We extend this with a special focus on space efficiency. We present several new data structures, among them the first fault-tolerant eccentricity oracle for dual failures in subcubic space. We further prove lower bounds that show limits
more » ... approximation vs. space and diameter vs. space trade-offs for fault-tolerant oracles. They highlight key differences between data structures for undirected and directed graphs. Initially, our oracles are randomized leaning on a sampling technique frequently used in sensitivity analysis. Building on the work of Alon, Chechik, and Cohen [ICALP 2019] as well as Karthik and Parter [SODA 2021], we develop a hierarchical framework to derandomize fault-tolerant data structures. We first apply it to our own diameter and eccentricity oracles and then show its versatility by derandomizing algorithms from the literature: the distance sensitivity oracle of Ren [JCSS 2022] and the Single-Source Replacement Path algorithm of Chechik and Magen [ICALP 2020]. This way, we obtain the first deterministic distance sensitivity oracle with subcubic preprocessing time.
arXiv:2204.10679v1 fatcat:nm2dizmc7rddbhy6gu4co43wom

The Minimization of Random Hypergraphs [article]

Thomas Bläsius, Tobias Friedrich, Martin Schirneck
2020 arXiv   pre-print
Acknowledgments The authors thank Benjamin Doerr, Timo Kötzing, and Martin Krejca for the fruitful discussions on the Chernoff-Hoeffding theorem, including valuable pointers to the literature.  ... 
arXiv:1910.00308v3 fatcat:rqzd4tdnvvewdah4zekdvjlyky

timeXplain – A Framework for Explaining the Predictions of Time Series Classifiers [article]

Felix Mujkanovic, Vanja Doskoč, Martin Schirneck, Patrick Schäfer, Tobias Friedrich
2020 arXiv   pre-print
Modern time series classifiers display impressive predictive capabilities, yet their decision-making processes mostly remain black boxes to the user. At the same time, model-agnostic explainers, such as the recently proposed SHAP, promise to make the predictions of machine learning models interpretable, provided there are well-designed domain mappings. We bring both worlds together in our timeXplain framework, extending the reach of explainable artificial intelligence to time series
more » ... on and value prediction. We present novel domain mappings for the time and the frequency domain as well as series statistics and analyze their explicative power as well as their limits. We employ timeXplain in a large-scale experimental comparison of several state-of-the-art time series classifiers and discover similarities between seemingly distinct classification concepts such as residual neural networks and elastic ensembles.
arXiv:2007.07606v1 fatcat:irscxix22bgc7djjkgxrgrxaje

The Minimization of Random Hypergraphs

Thomas Bläsius, Tobias Friedrich, Martin Schirneck, Peter Sanders, Grzegorz Herman, Fabrizio Grandoni
2020 European Symposium on Algorithms  
Schirneck want to maximize the entropy and the same is true for the vertices inside an edge.  ... 
doi:10.4230/lipics.esa.2020.21 dblp:conf/esa/Blasius0S20 fatcat:6am5wp4ig5am3ffzxrhfbcaj7a

Normal Forms in Semantic Language Identification

Timo Kötzing, Martin Schirneck, Karen Seidel
2017 International Conference on Algorithmic Learning Theory  
As a side note, SemWb is in fact the semantic closure of what Kötzing and Schirneck (2016) defined as witness-based.  ...  In the case of SMon, the result was known before (Kötzing and Schirneck, 2016) . Corollary 19 (i) If δ ∈ {Caut Tar , SemWb, SemConv, SMon, WMon}, [TxtPsdδBc] = [TxtSdδBc].  ... 
dblp:conf/alt/KotzingSS17 fatcat:7nd7esrsjrfn3jpax4arps3rwm

Fast Building Block Assembly by Majority Vote Crossover

Tobias Friedrich, Timo Kötzing, Martin S. Krejca, Samadhi Nallaperuma, Frank Neumann, Martin Schirneck
2016 Proceedings of the 2016 on Genetic and Evolutionary Computation Conference - GECCO '16  
Different works have shown how crossover can help with building block assembly. Typically, crossover might get lucky to select good building blocks from each parent, but these lucky choices are usually rare. In this work we consider a crossover operator which works on three parent individuals. In each component, the offspring inherits the value present in the majority of the parents; thus, we call this crossover operator majority vote. We show that, if good components are sufficiently prevalent
more » ... in the individuals, majority vote creates an optimal individual with high probability. Furthermore, we show that this process can be amplified: as long as components are good independently and with probability at least 1/2+δ, we require only O log δ −1 + log log n successive stages of majority vote to create an optimal individual with high probability! We show how this applies in two scenarios. The first scenario is the Jump test function. With sufficient diversity, we get an optimization time of O(n log n) even for jump sizes as large as O(n 1/2−ε ). Our second scenario is a family of vertex cover instances. Majority vote optimizes this family efficiently, while local searches fail and only highly specialized two-parent crossovers are successful.
doi:10.1145/2908812.2908884 dblp:conf/gecco/FriedrichKKNNS16 fatcat:nkhp46jtw5auhfor4uh7o4glpu

Efficiently Enumerating Hitting Sets of Hypergraphs Arising in Data Profiling [chapter]

Thomas Bläsius, Tobias Friedrich, Julius Lischeid, Kitty Meeks, Martin Schirneck
2019 2019 Proceedings of the Twenty-First Workshop on Algorithm Engineering and Experiments (ALENEX)  
The first one was given by Chen and Zhang in the context of supply chain management [12] ; Bläsius, Friedrich, and Schirneck added the discovery of inclusion dependencies in relational data [7] .  ... 
doi:10.1137/1.9781611975499.11 dblp:conf/alenex/Blasius0LMS19 fatcat:etvgphwm4ne3domx67nddmu3hq

Correction to: Reoptimization Time Analysis of Evolutionary Algorithms on Linear Functions Under Dynamic Uniform Constraints

Feng Shi, Martin Schirneck, Tobias Friedrich, Timo Kötzing, Frank Neumann
2020 Algorithmica  
In the article Reoptimization Time Analysis of Evolutionary Algorithms on Linear Functions Under Dynamic Uniform Constraints, we claimed a worst-case runtime of O(nD log D) and O(nD) for the Multi-Objective Evolutionary Algorithm and the Multi-Objective ( +( , )) Genetic Algorithm, respectively, on linear profit functions under dynamic uniform constraint, where D = |B − B * | denotes the difference between the original constraint bound B and the new one B * . The technique used to prove these
more » ... sults contained an error. We correct this mistake and show a weaker bound of O(nD 2 ) for both algorithms instead. The Multi-Objective Evolutionary Algorithm In Theorem 9 of the original article [4], we claimed a bound of O(nD log D) for the expected reoptimization time of the Multi-Objective Evolutionary Algorithm (MOEA), where D = |B − B * | denotes the difference between the original constraint bound B and the new one B * . Its proof was based on the notion of candidate solutions x for which there is an optimum x * (assuming B ≤ B * ) such that In other words, an optimum can be created from a candidate by only flipping 0-bits. We used drift analysis on the potential function The original article can be found online at https ://doi.
doi:10.1007/s00453-020-00739-x fatcat:e54qrl43vrehhah67fdqfjs52e

The Parameterized Complexity of Dependency Detection in Relational Databases

Thomas Bläsius, Tobias Friedrich, Martin Schirneck, Marc Herbstritt
2017 International Symposium on Parameterized and Exact Computation  
We study the parameterized complexity of classical problems that arise in the profiling of relational data. Namely, we characterize the complexity of detecting unique column combinations (candidate keys), functional dependencies, and inclusion dependencies with the solution size as parameter. While the discovery of uniques and functional dependencies, respectively, turns out to be W [2]-complete, the detection of inclusion dependencies is one of the first natural problems proven to be complete
more » ... or the class W [3]. As a side effect, our reductions give insights into the complexity of enumerating all minimal unique column combinations or functional dependencies.
doi:10.4230/lipics.ipec.2016.6 dblp:conf/iwpec/Blasius0S16 fatcat:rhgnl2vh4fh7jer6nkdtdhzjgq

Analysis of the (1 + 1) EA on subclasses of linear functions under uniform and linear constraints

Tobias Friedrich, Timo Kötzing, J.A. Gregor Lagodzinski, Frank Neumann, Martin Schirneck
2018 Theoretical Computer Science  
After the embargo period  via non-commercial hosting platforms such as their institutional repository  via commercial sites with which Elsevier has an agreement In all cases accepted manuscripts should:  link to the formal publication via its DOI  bear a CC-BY-NC-ND licensethis is easy to do  if aggregated with other manuscripts, for example in a repository or other site, be
doi:10.1016/j.tcs.2018.04.051 fatcat:afejh6l43be75grs5j7zdj5ghy

Efficiently Enumerating Hitting Sets of Hypergraphs Arising in Data Profiling [article]

Thomas Bläsius, Tobias Friedrich, Julius Lischeid, Kitty Meeks, Martin Schirneck
2021 arXiv   pre-print
The first one was given by Chen and Zhang [19] in the context of supply chain management and Bläsius, Friedrich, and Schirneck [9] added the detection of inclusion dependencies in relational data.  ...  Bläsius, Friedrich, and Schirneck [9] improved upon the Turing-equivalence in [30] by giving a parsimonious, inclusion-preserving reduction also in the opposite direction, that is, from hitting sets  ... 
arXiv:1805.01310v3 fatcat:zm626hj75javxjnay5it4ligse
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