8 Search Results for "Fr�hbis-Kr�ger, Anne"

Document
DOI: 10.4230/DagRep.13.6.55
Challenges in Benchmarking Optimization Heuristics (Dagstuhl Seminar 23251)

Authors: Anne Auger, Peter A. N. Bosman, Pascal Kerschke, Darrell Whitley, and Lennart Schäpermeier

Published in: Dagstuhl Reports, Volume 13, Issue 6 (2024)

Abstract
This report documents the program and outcomes of the Dagstuhl Seminar 23251 "Challenges in Benchmarking Optimization Heuristics". In the domain of optimization heuristics, a stable basis for fairly evaluating the performance of optimization algorithms and other solution approaches - commonly referred to as "benchmarking" - is fundamental to ensuring steady scientific progress. Although many pitfalls are well known in the community, the development of sound benchmarking protocols is slow, and the adoption of community-wide recognized and implementable standards requires lasting and joint efforts among research groups. This seminar brought together people from diverse backgrounds and fostered discussions among different optimization communities, focusing on how to cope with "horse racing papers", landscape analysis techniques for understanding problem instances, and discussions about the overarching goals of benchmarking.
Cite as

Anne Auger, Peter A. N. Bosman, Pascal Kerschke, Darrell Whitley, and Lennart Schäpermeier. Challenges in Benchmarking Optimization Heuristics (Dagstuhl Seminar 23251). In Dagstuhl Reports, Volume 13, Issue 6, pp. 55-80, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{auger_et_al:DagRep.13.6.55,
  author =	{Auger, Anne and Bosman, Peter A. N. and Kerschke, Pascal and Whitley, Darrell and Sch\"{a}permeier, Lennart},
  title =	{{Challenges in Benchmarking Optimization Heuristics (Dagstuhl Seminar 23251)}},
  pages =	{55--80},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2024},
  volume =	{13},
  number =	{6},
  editor =	{Auger, Anne and Bosman, Peter A. N. and Kerschke, Pascal and Whitley, Darrell and Sch\"{a}permeier, Lennart},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.13.6.55},
  URN =		{urn:nbn:de:0030-drops-196383},
  doi =		{10.4230/DagRep.13.6.55},
  annote =	{Keywords: benchmarking, design of search heuristics, optimization, real-world applications, understanding problem complexity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.28
Faster Approximate Covering of Subcurves Under the Fréchet Distance

Authors: Frederik Brüning, Jacobus Conradi, and Anne Driemel

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
Subtrajectory clustering is an important variant of the trajectory clustering problem, where the start and endpoints of trajectory patterns within the collected trajectory data are not known in advance. We study this problem in the form of a set cover problem for a given polygonal curve: find the smallest number k of representative curves such that any point on the input curve is contained in a subcurve that has Fréchet distance at most a given Δ to a representative curve. We focus on the case where the representative curves are line segments and approach this NP-hard problem with classical techniques from the area of geometric set cover: we use a variant of the multiplicative weights update method which was first suggested by Brönniman and Goodrich for set cover instances with small VC-dimension. We obtain a bicriteria-approximation algorithm that computes a set of O(klog(k)) line segments that cover a given polygonal curve of n vertices under Fréchet distance at most O(Δ). We show that the algorithm runs in Õ(k² n + k n³) time in expectation and uses Õ(k n + n³) space. For input curves that are c-packed and lie in the plane, we bound the expected running time by Õ(k² c² n) and the space by Õ(kn + c² n). In addition, we present a variant of the algorithm that uses implicit weight updates on the candidate set and thereby achieves near-linear running time in n without any assumptions on the input curve, while keeping the same approximation bounds. This comes at the expense of a small (polylogarithmic) dependency on the relative arclength.
Cite as

Frederik Brüning, Jacobus Conradi, and Anne Driemel. Faster Approximate Covering of Subcurves Under the Fréchet Distance. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 28:1-28:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bruning_et_al:LIPIcs.ESA.2022.28,
  author =	{Br\"{u}ning, Frederik and Conradi, Jacobus and Driemel, Anne},
  title =	{{Faster Approximate Covering of Subcurves Under the Fr\'{e}chet Distance}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{28:1--28:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.28},
  URN =		{urn:nbn:de:0030-drops-169660},
  doi =		{10.4230/LIPIcs.ESA.2022.28},
  annote =	{Keywords: Clustering, Set cover, Fr\'{e}chet distance, Approximation algorithms}
}
Document
DOI: 10.4230/DagRep.12.2.87
Theory of Randomized Optimization Heuristics (Dagstuhl Seminar 22081)

Authors: Anne Auger, Carlos M. Fonseca, Tobias Friedrich, Johannes Lengler, and Armand Gissler

Published in: Dagstuhl Reports, Volume 12, Issue 2 (2022)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 22081 "Theory of Randomized Optimization Heuristics". This seminar is part of a biennial seminar series. This year, we focused on connections between classical topics of the community, such as Evolutionary Algorithms and Strategies (EA, ES), Estimation-of-Distribution Algorithms (EDA) and Evolutionary Multi-Objective Optimization (EMO), and related fields like Stochastic Gradient Descent (SGD) and Bayesian Optimization (BO). The mixture proved to be extremely successful. Already the first talk turned into a two hour long, vivid and productive plenary discussion. The seminar was smaller than previous versions (due to corona regulations), but its intensity more than made up for the smaller size.
Cite as

Anne Auger, Carlos M. Fonseca, Tobias Friedrich, Johannes Lengler, and Armand Gissler. Theory of Randomized Optimization Heuristics (Dagstuhl Seminar 22081). In Dagstuhl Reports, Volume 12, Issue 2, pp. 87-102, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@Article{auger_et_al:DagRep.12.2.87,
  author =	{Auger, Anne and Fonseca, Carlos M. and Friedrich, Tobias and Lengler, Johannes and Gissler, Armand},
  title =	{{Theory of Randomized Optimization Heuristics (Dagstuhl Seminar 22081)}},
  pages =	{87--102},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2022},
  volume =	{12},
  number =	{2},
  editor =	{Auger, Anne and Fonseca, Carlos M. and Friedrich, Tobias and Lengler, Johannes and Gissler, Armand},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.12.2.87},
  URN =		{urn:nbn:de:0030-drops-169325},
  doi =		{10.4230/DagRep.12.2.87},
  annote =	{Keywords: black-box optimization, derivative-free optimization, evolutionary and genetic algorithms, randomized search algorithms, stochastic gradient descent, theoretical computer science}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.46
On Computing the k-Shortcut Fréchet Distance

Authors: Jacobus Conradi and Anne Driemel

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
The Fréchet distance is a popular measure of dissimilarity for polygonal curves. It is defined as a min-max formulation that considers all direction-preserving continuous bijections of the two curves. Because of its susceptibility to noise, Driemel and Har-Peled introduced the shortcut Fréchet distance in 2012, where one is allowed to take shortcuts along one of the curves, similar to the edit distance for sequences. We analyse the parameterized version of this problem, where the number of shortcuts is bounded by a parameter k. The corresponding decision problem can be stated as follows: Given two polygonal curves T and B of at most n vertices, a parameter k and a distance threshold δ, is it possible to introduce k shortcuts along B such that the Fréchet distance of the resulting curve and the curve T is at most δ? We study this problem for polygonal curves in the plane. We provide a complexity analysis for this problem with the following results: (i) assuming the exponential-time-hypothesis (ETH), there exists no algorithm with running time bounded by n^o(k); (ii) there exists a decision algorithm with running time in O(k n^{2k+2} log n). In contrast, we also show that efficient approximate decider algorithms are possible, even when k is large. We present a (3+ε)-approximate decider algorithm with running time in O(k n² log² n) for fixed ε. In addition, we can show that, if k is a constant and the two curves are c-packed for some constant c, then the approximate decider algorithm runs in near-linear time.
Cite as

Jacobus Conradi and Anne Driemel. On Computing the k-Shortcut Fréchet Distance. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 46:1-46:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{conradi_et_al:LIPIcs.ICALP.2022.46,
  author =	{Conradi, Jacobus and Driemel, Anne},
  title =	{{On Computing the k-Shortcut Fr\'{e}chet Distance}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{46:1--46:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.46},
  URN =		{urn:nbn:de:0030-drops-163875},
  doi =		{10.4230/LIPIcs.ICALP.2022.46},
  annote =	{Keywords: Fr\'{e}chet distance, Partial similarity, Conditional lower bounds, Approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2022.36
On the Discrete Fréchet Distance in a Graph

Authors: Anne Driemel, Ivor van der Hoog, and Eva Rotenberg

Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)

Abstract
The Fréchet distance is a well-studied similarity measure between curves that is widely used throughout computer science. Motivated by applications where curves stem from paths and walks on an underlying graph (such as a road network), we define and study the Fréchet distance for paths and walks on graphs. When provided with a distance oracle of G with O(1) query time, the classical quadratic-time dynamic program can compute the Fréchet distance between two walks P and Q in a graph G in O(|P|⋅|Q|) time. We show that there are situations where the graph structure helps with computing Fréchet distance: when the graph G is planar, we apply existing (approximate) distance oracles to compute a (1+ε)-approximation of the Fréchet distance between any shortest path P and any walk Q in O(|G|log|G|/√ε+|P|+|Q|/ε) time. We generalise this result to near-shortest paths, i.e. κ-straight paths, as we show how to compute a (1+ε)-approximation between a κ-straight path P and any walk Q in O(|G|log|G|/√ε+|P|+(κ|Q|)/ε) time. Our algorithmic results hold for both the strong and the weak discrete Fréchet distance over the shortest path metric in G. Finally, we show that additional assumptions on the input, such as our assumption on path straightness, are indeed necessary to obtain truly subquadratic running time. We provide a conditional lower bound showing that the Fréchet distance, or even its 1.01-approximation, between arbitrary paths in a weighted planar graph cannot be computed in O((|P|⋅|Q|)^{1-δ}) time for any δ > 0 unless the Orthogonal Vector Hypothesis fails. For walks, this lower bound holds even when G is planar, unit-weight and has O(1) vertices.
Cite as

Anne Driemel, Ivor van der Hoog, and Eva Rotenberg. On the Discrete Fréchet Distance in a Graph. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 36:1-36:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{driemel_et_al:LIPIcs.SoCG.2022.36,
  author =	{Driemel, Anne and van der Hoog, Ivor and Rotenberg, Eva},
  title =	{{On the Discrete Fr\'{e}chet Distance in a Graph}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{36:1--36:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.36},
  URN =		{urn:nbn:de:0030-drops-160448},
  doi =		{10.4230/LIPIcs.SoCG.2022.36},
  annote =	{Keywords: Fr\'{e}chet, graphs, planar, complexity analysis}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2019.28
The VC Dimension of Metric Balls Under Fréchet and Hausdorff Distances

Authors: Anne Driemel, Jeff M. Phillips, and Ioannis Psarros

Published in: LIPIcs, Volume 129, 35th International Symposium on Computational Geometry (SoCG 2019)

Abstract
The Vapnik-Chervonenkis dimension provides a notion of complexity for systems of sets. If the VC dimension is small, then knowing this can drastically simplify fundamental computational tasks such as classification, range counting, and density estimation through the use of sampling bounds. We analyze set systems where the ground set X is a set of polygonal curves in R^d and the sets {R} are metric balls defined by curve similarity metrics, such as the Fréchet distance and the Hausdorff distance, as well as their discrete counterparts. We derive upper and lower bounds on the VC dimension that imply useful sampling bounds in the setting that the number of curves is large, but the complexity of the individual curves is small. Our upper bounds are either near-quadratic or near-linear in the complexity of the curves that define the ranges and they are logarithmic in the complexity of the curves that define the ground set.
Cite as

Anne Driemel, Jeff M. Phillips, and Ioannis Psarros. The VC Dimension of Metric Balls Under Fréchet and Hausdorff Distances. In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 28:1-28:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{driemel_et_al:LIPIcs.SoCG.2019.28,
  author =	{Driemel, Anne and Phillips, Jeff M. and Psarros, Ioannis},
  title =	{{The VC Dimension of Metric Balls Under Fr\'{e}chet and Hausdorff Distances}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{28:1--28:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-104-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{129},
  editor =	{Barequet, Gill and Wang, Yusu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2019.28},
  URN =		{urn:nbn:de:0030-drops-104329},
  doi =		{10.4230/LIPIcs.SoCG.2019.28},
  annote =	{Keywords: VC dimension, Fr\'{e}chet distance, Hausdorff distance}
}
Document
DOI: 10.4230/OASIcs.GCB.2013.46
Reconstructing Consensus Bayesian Network Structures with Application to Learning Molecular Interaction Networks

Authors: Holger Fröhlich and Gunnar W. Klau

Published in: OASIcs, Volume 34, German Conference on Bioinformatics 2013

Abstract
Bayesian Networks are an established computational approach for data driven network inference. However, experimental data is limited in its availability and corrupted by noise. This leads to an unavoidable uncertainty about the correct network structure. Thus sampling or bootstrap based strategies are applied to obtain edge frequencies. In a more general sense edge frequencies can also result from integrating networks learned on different datasets or via different inference algorithms. Subsequently one typically wants to derive a biological interpretation from the results in terms of a consensus network. We here propose a log odds based edge score on the basis of the expected false positive rate and thus avoid the selection of a subjective edge frequency cutoff. Computing a score optimal consensus network in our new model amounts to solving the maximum weight acyclic subdigraph problem. We use a branch-and-cut algorithm based on integer linear programming for this task. Our empirical studies on simulated and real data demonstrate a consistently improved network reconstruction accuracy compared to two threshold based strategies.
Cite as

Holger Fröhlich and Gunnar W. Klau. Reconstructing Consensus Bayesian Network Structures with Application to Learning Molecular Interaction Networks. In German Conference on Bioinformatics 2013. Open Access Series in Informatics (OASIcs), Volume 34, pp. 46-55, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{frohlich_et_al:OASIcs.GCB.2013.46,
  author =	{Fr\"{o}hlich, Holger and Klau, Gunnar W.},
  title =	{{Reconstructing Consensus Bayesian Network Structures with Application to Learning Molecular Interaction Networks}},
  booktitle =	{German Conference on Bioinformatics 2013},
  pages =	{46--55},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-59-0},
  ISSN =	{2190-6807},
  year =	{2013},
  volume =	{34},
  editor =	{Bei{\ss}barth, Tim and Kollmar, Martin and Leha, Andreas and Morgenstern, Burkhard and Schultz, Anne-Kathrin and Waack, Stephan and Wingender, Edgar},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.GCB.2013.46},
  URN =		{urn:nbn:de:0030-drops-42273},
  doi =		{10.4230/OASIcs.GCB.2013.46},
  annote =	{Keywords: Bayesian Networks, Network Reverse Engineering, Minimum Feedback Arc Set, Maximum Acyclic Subgraph, Molecular Interaction Networks}
}
Document
DOI: 10.4230/DagSemProc.06271.7
Computational Aspects of the Resolution of Singularities

Authors: Anne Frühbis-Krüger

Published in: Dagstuhl Seminar Proceedings, Volume 6271, Challenges in Symbolic Computation Software (2006)

Abstract
The task of resolution of singularities has been one of the central topics in Algebraic Geometry for many decades. After results in low dimension in the first half of the 20th century, it was Hironaka's monumental article in 1964 which solved the porblem in the general case in chareacteristic zero. The case of characteristic $p > 0$ is still unsolved except in partial results in low dimension. But Hironaka's proof did not put an end to the interest in characteric zero, instead it shifted the focus toward the task of finding a more constructive approach. Such algorithmic approaches appeared at the end of the 1980's independently by Villamayor and by Bierstone and Milman. In this talk we consider the computational tasks arising from Villamayor's algorithm and present an implementation.
Cite as

Anne Frühbis-Krüger. Computational Aspects of the Resolution of Singularities. In Challenges in Symbolic Computation Software. Dagstuhl Seminar Proceedings, Volume 6271, pp. 1-8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{fruhbiskruger:DagSemProc.06271.7,
  author =	{Fr\"{u}hbis-Kr\"{u}ger, Anne},
  title =	{{Computational Aspects of the Resolution of Singularities}},
  booktitle =	{Challenges in Symbolic Computation Software},
  pages =	{1--8},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6271},
  editor =	{Wolfram Decker and Mike Dewar and Erich Kaltofen and Stephen Watt},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.06271.7},
  URN =		{urn:nbn:de:0030-drops-7713},
  doi =		{10.4230/DagSemProc.06271.7},
  annote =	{Keywords: Resolution of Singularities, algorithmic desingularization,}
}
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