7 Search Results for "Geissmann, Barbara"

Document
DOI: 10.4230/LIPIcs.WADS.2025.24
Computational Geometry with Probabilistically Noisy Primitive Operations

Authors: David Eppstein, Michael T. Goodrich, and Vinesh Sridhar

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
Much prior work has been done on designing computational geometry algorithms that handle input degeneracies, data imprecision, and arithmetic round-off errors. We take a new approach, inspired by the noisy sorting literature, and study computational geometry algorithms subject to noisy Boolean primitive operations in which, e.g., the comparison "is point q above line 𝓁?" returns the wrong answer with some fixed probability. We propose a novel technique called path-guided pushdown random walks that generalizes the results of noisy sorting. We apply this technique to solve point-location, plane-sweep, convex hulls in 2D and 3D, and Delaunay triangulations for noisy primitives in optimal time with high probability.
Cite as

David Eppstein, Michael T. Goodrich, and Vinesh Sridhar. Computational Geometry with Probabilistically Noisy Primitive Operations. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 24:1-24:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{eppstein_et_al:LIPIcs.WADS.2025.24,
  author =	{Eppstein, David and Goodrich, Michael T. and Sridhar, Vinesh},
  title =	{{Computational Geometry with Probabilistically Noisy Primitive Operations}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{24:1--24:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.24},
  URN =		{urn:nbn:de:0030-drops-242552},
  doi =		{10.4230/LIPIcs.WADS.2025.24},
  annote =	{Keywords: Computational geometry, noisy comparisons, random walks}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.100
Robust-Sorting and Applications to Ulam-Median

Authors: Ragesh Jaiswal, Amit Kumar, and Jatin Yadav

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
Sorting is one of the most basic primitives in many algorithms and data analysis tasks. Comparison-based sorting algorithms, like quick-sort and merge-sort, are known to be optimal when the outcome of each comparison is error-free. However, many real-world sorting applications operate in scenarios where the outcome of each comparison can be noisy. In this work, we explore settings where a bounded number of comparisons are potentially corrupted by erroneous agents, resulting in arbitrary, adversarial outcomes. We model the sorting problem as a query-limited tournament graph where edges involving erroneous nodes may yield arbitrary results. Our primary contribution is a randomized algorithm inspired by quick-sort that, in expectation, produces an ordering close to the true total order while only querying Õ(n) edges. We achieve a distance from the target order π within (3 + ε)|B|, where B is the set of erroneous nodes, balancing the competing objectives of minimizing both query complexity and misalignment with π. Our algorithm needs to carefully balance two aspects - identify a pivot that partitions the vertex set evenly and ensure that this partition is "truthful" and yet query as few "triangles" in the graph G as possible. Since the nodes in B can potentially hide in an intricate manner, our algorithm requires several technical steps that ensure that progress is made in each recursive step. Additionally, we demonstrate significant implications for the Ulam-k-Median problem. This is a classical clustering problem where the metric is defined on the set of permutations on a set of d elements. Chakraborty, Das, and Krauthgamer gave a (2-ε) FPT approximation algorithm for this problem, where the running time is super-linear in both n and d. We give the first (2-ε) FPT linear time approximation algorithm for this problem. Our main technical result gives a strengthening of the results in Chakraborty et al. by showing that a good 1-median solution can be obtained from a constant-size random sample of the input. We use our robust sorting framework to find a good solution from such a random sample. We feel that the notion of robust sorting should have applications in several such settings.
Cite as

Ragesh Jaiswal, Amit Kumar, and Jatin Yadav. Robust-Sorting and Applications to Ulam-Median. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 100:1-100:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jaiswal_et_al:LIPIcs.ICALP.2025.100,
  author =	{Jaiswal, Ragesh and Kumar, Amit and Yadav, Jatin},
  title =	{{Robust-Sorting and Applications to Ulam-Median}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{100:1--100:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.100},
  URN =		{urn:nbn:de:0030-drops-234774},
  doi =		{10.4230/LIPIcs.ICALP.2025.100},
  annote =	{Keywords: Sorting, clustering, query complexity}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2019.64
Dual-Mode Greedy Algorithms Can Save Energy

Authors: Barbara Geissmann, Stefano Leucci, Chih-Hung Liu, Paolo Penna, and Guido Proietti

Published in: LIPIcs, Volume 149, 30th International Symposium on Algorithms and Computation (ISAAC 2019)

Abstract
In real world applications, important resources like energy are saved by deliberately using so-called low-cost operations that are less reliable. Some of these approaches are based on a dual mode technology where it is possible to choose between high-energy operations (always correct) and low-energy operations (prone to errors), and thus enable to trade energy for correctness. In this work we initiate the study of algorithms for solving optimization problems that in their computation are allowed to choose between two types of operations: high-energy comparisons (always correct but expensive) and low-energy comparisons (cheaper but prone to errors). For the errors in low-energy comparisons, we assume the persistent setting, which usually makes it impossible to achieve optimal solutions without high-energy comparisons. We propose to study a natural complexity measure which accounts for the number of operations of either type separately. We provide a new family of algorithms which, for a fairly large class of maximization problems, return a constant approximation using only polylogarithmic many high-energy comparisons and only O(n log n) low-energy comparisons. This result applies to the class of p-extendible system s [Mestre, 2006], which includes several NP-hard problems and matroids as a special case (p=1). These algorithmic solutions relate to some fundamental aspects studied earlier in different contexts: (i) the approximation guarantee when only ordinal information is available to the algorithm; (ii) the fact that even such ordinal information may be erroneous because of low-energy comparisons and (iii) the ability to approximately sort a sequence of elements when comparisons are subject to persistent errors. Finally, our main result is quite general and can be parametrized and adapted to other error models.
Cite as

Barbara Geissmann, Stefano Leucci, Chih-Hung Liu, Paolo Penna, and Guido Proietti. Dual-Mode Greedy Algorithms Can Save Energy. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 64:1-64:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{geissmann_et_al:LIPIcs.ISAAC.2019.64,
  author =	{Geissmann, Barbara and Leucci, Stefano and Liu, Chih-Hung and Penna, Paolo and Proietti, Guido},
  title =	{{Dual-Mode Greedy Algorithms Can Save Energy}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{64:1--64:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Lu, Pinyan and Zhang, Guochuan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.64},
  URN =		{urn:nbn:de:0030-drops-115604},
  doi =		{10.4230/LIPIcs.ISAAC.2019.64},
  annote =	{Keywords: matroids, p-extendible systems, greedy algorithm, approximation algorithms, high-low energy}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2019.4
Routing in Stochastic Public Transit Networks

Authors: Barbara Geissmann and Lukas Gianinazzi

Published in: OASIcs, Volume 75, 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)

Abstract
We present robust, adaptive routing policies for time-varying networks (temporal graphs) in the presence of random edge-failures. Such a policy answers the following question: How can a traveler navigate a time-varying network where edges fail randomly in order to maximize the traveler’s preference with respect to the arrival time? Our routing policy is computable in near-linear time in the number of edges in the network (for the case when the edges fail independently of each other). Using our robust routing policy, we show how to travel in a public transit network where the vehicles experience delays. To validate our approach, we present experiments using real-world delay data from the public transit network of the city of Zurich. Our experiments show that we obtain significantly improved outcomes compared to a purely schedule-based policy: The traveler is on time 5-11 percentage points more often for most destinations and 20-40 percentage points more often for certain remote destinations. Our implementation shows that the approach is fast enough for real-time usage. It computes a policy for 1-hour long journeys in around 0.1 seconds.
Cite as

Barbara Geissmann and Lukas Gianinazzi. Routing in Stochastic Public Transit Networks. In 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019). Open Access Series in Informatics (OASIcs), Volume 75, pp. 4:1-4:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{geissmann_et_al:OASIcs.ATMOS.2019.4,
  author =	{Geissmann, Barbara and Gianinazzi, Lukas},
  title =	{{Routing in Stochastic Public Transit Networks}},
  booktitle =	{19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)},
  pages =	{4:1--4:18},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-128-3},
  ISSN =	{2190-6807},
  year =	{2019},
  volume =	{75},
  editor =	{Cacchiani, Valentina and Marchetti-Spaccamela, Alberto},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2019.4},
  URN =		{urn:nbn:de:0030-drops-114167},
  doi =		{10.4230/OASIcs.ATMOS.2019.4},
  annote =	{Keywords: Route Planning, Public Transit Network, Temporal Graphs}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.49
Optimal Sorting with Persistent Comparison Errors

Authors: Barbara Geissmann, Stefano Leucci, Chih-Hung Liu, and Paolo Penna

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
We consider the problem of sorting n elements in the case of persistent comparison errors. In this problem, each comparison between two elements can be wrong with some fixed (small) probability p, and comparisons cannot be repeated (Braverman and Mossel, SODA'08). Sorting perfectly in this model is impossible, and the objective is to minimize the dislocation of each element in the output sequence, that is, the difference between its true rank and its position. Existing lower bounds for this problem show that no algorithm can guarantee, with high probability, maximum dislocation and total dislocation better than Omega(log n) and Omega(n), respectively, regardless of its running time. In this paper, we present the first O(n log n)-time sorting algorithm that guarantees both O(log n) maximum dislocation and O(n) total dislocation with high probability. This settles the time complexity of this problem and shows that comparison errors do not increase its computational difficulty: a sequence with the best possible dislocation can be obtained in O(n log n) time and, even without comparison errors, Omega(n log n) time is necessary to guarantee such dislocation bounds. In order to achieve this optimality result, we solve two sub-problems in the persistent error comparisons model, and the respective methods have their own merits for further application. One is how to locate a position in which to insert an element in an almost-sorted sequence having O(log n) maximum dislocation in such a way that the dislocation of the resulting sequence will still be O(log n). The other is how to simultaneously insert m elements into an almost sorted sequence of m different elements, such that the resulting sequence of 2m elements remains almost sorted.
Cite as

Barbara Geissmann, Stefano Leucci, Chih-Hung Liu, and Paolo Penna. Optimal Sorting with Persistent Comparison Errors. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 49:1-49:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{geissmann_et_al:LIPIcs.ESA.2019.49,
  author =	{Geissmann, Barbara and Leucci, Stefano and Liu, Chih-Hung and Penna, Paolo},
  title =	{{Optimal Sorting with Persistent Comparison Errors}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{49:1--49:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.49},
  URN =		{urn:nbn:de:0030-drops-111706},
  doi =		{10.4230/LIPIcs.ESA.2019.49},
  annote =	{Keywords: approximate sorting, comparison errors, persistent errors}
}
Document
DOI: 10.4230/LIPIcs.STACS.2018.36
Optimal Dislocation with Persistent Errors in Subquadratic Time

Authors: Barbara Geissmann, Stefano Leucci, Chih-Hung Liu, and Paolo Penna

Published in: LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)

Abstract
We study the problem of sorting N elements in presence of persistent errors in comparisons: In this classical model, each comparison between two elements is wrong independently with some probability p, but repeating the same comparison gives always the same result. The best known algorithms for this problem have running time O(N^2) and achieve an optimal maximum dislocation of O(log N) for constant error probability. Note that no algorithm can achieve dislocation o(log N), regardless of its running time. In this work we present the first subquadratic time algorithm with optimal maximum dislocation: Our algorithm runs in tilde{O}(N^{3/2}) time and guarantees O(log N) maximum dislocation with high probability. Though the first version of our algorithm is randomized, it can be derandomized by extracting the necessary random bits from the results of the comparisons (errors).
Cite as

Barbara Geissmann, Stefano Leucci, Chih-Hung Liu, and Paolo Penna. Optimal Dislocation with Persistent Errors in Subquadratic Time. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 36:1-36:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{geissmann_et_al:LIPIcs.STACS.2018.36,
  author =	{Geissmann, Barbara and Leucci, Stefano and Liu, Chih-Hung and Penna, Paolo},
  title =	{{Optimal Dislocation with Persistent Errors in Subquadratic Time}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{36:1--36:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Niedermeier, Rolf and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.36},
  URN =		{urn:nbn:de:0030-drops-85266},
  doi =		{10.4230/LIPIcs.STACS.2018.36},
  annote =	{Keywords: sorting, recurrent comparison errors, maximum dislocation}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2017.38
Sorting with Recurrent Comparison Errors

Authors: Barbara Geissmann, Stefano Leucci, Chih-Hung Liu, and Paolo Penna

Published in: LIPIcs, Volume 92, 28th International Symposium on Algorithms and Computation (ISAAC 2017)

Abstract
We present a sorting algorithm for the case of recurrent random comparison errors. The algorithm essentially achieves simultaneously good properties of previous algorithms for sorting n distinct elements in this model. In particular, it runs in O(n^2) time, the maximum dislocation of the elements in the output is O(log n), while the total dislocation is O(n). These guarantees are the best possible since we prove that even randomized algorithms cannot achieve o(log n) maximum dislocation with high probability, or o(n) total dislocation in expectation, regardless of their running time.
Cite as

Barbara Geissmann, Stefano Leucci, Chih-Hung Liu, and Paolo Penna. Sorting with Recurrent Comparison Errors. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 38:1-38:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{geissmann_et_al:LIPIcs.ISAAC.2017.38,
  author =	{Geissmann, Barbara and Leucci, Stefano and Liu, Chih-Hung and Penna, Paolo},
  title =	{{Sorting with Recurrent Comparison Errors}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{38:1--38:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-054-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{92},
  editor =	{Okamoto, Yoshio and Tokuyama, Takeshi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.38},
  URN =		{urn:nbn:de:0030-drops-82652},
  doi =		{10.4230/LIPIcs.ISAAC.2017.38},
  annote =	{Keywords: sorting, recurrent comparison error, maximum and total dislocation}
}
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