7 Search Results for "Manokaran, Rajsekar"

Document
DOI: 10.4230/OASIcs.ATMOS.2025.4
Visualization of Event Graphs for Train Schedules

Authors: Johann Hartleb, Marie Schmidt, Samuel Wolf, and Alexander Wolff

Published in: OASIcs, Volume 137, 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)

Abstract
Train timetables can be represented as event graphs, where events correspond to a train passing through a location at a certain point in time. A visual representation of an event graph is important for many applications such as dispatching and (the development of) dispatching software. A common way to represent event graphs are time-space diagrams. In such a diagram, key locations are visualized on the y-axis and time on the x-axis of a coordinate system. A train’s movement is then represented as a connected sequence of line segments in this coordinate system. This visualization allows for an easy detection of infrastructure conflicts and safety distance violations. However, time-space diagrams are usually used only to depict event graphs that are restricted to corridors, where an obvious ordering of the locations exists. In this paper, we consider the visualization of general event graphs in time-space diagrams, where the challenge is to find an ordering of the locations that produces readable drawings. We argue that this means to minimize the number of turns, i.e., the total number of changes in y-direction. To this end, we establish a connection between this problem and Maximum Betweenness. Then we develop a preprocessing strategy to reduce the instance size. We also propose a parameterized algorithm and integer linear programming formulations. We experimentally evaluate the preprocessing strategy and the integer programming formulations on a real-world dataset. Our best algorithm solves every instance in the dataset in less than a second. This suggests that turn-optimal time-space diagrams can be computed in real time.
Cite as

Johann Hartleb, Marie Schmidt, Samuel Wolf, and Alexander Wolff. Visualization of Event Graphs for Train Schedules. In 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025). Open Access Series in Informatics (OASIcs), Volume 137, pp. 4:1-4:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hartleb_et_al:OASIcs.ATMOS.2025.4,
  author =	{Hartleb, Johann and Schmidt, Marie and Wolf, Samuel and Wolff, Alexander},
  title =	{{Visualization of Event Graphs for Train Schedules}},
  booktitle =	{25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)},
  pages =	{4:1--4:20},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-404-8},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{137},
  editor =	{Sauer, Jonas and Schmidt, Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2025.4},
  URN =		{urn:nbn:de:0030-drops-247607},
  doi =		{10.4230/OASIcs.ATMOS.2025.4},
  annote =	{Keywords: Graph Drawing, Event Graphs, Integer Linear Programming, Parameterized Algorithms, Treewidth}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.30
Algorithmic Contiguity from Low-Degree Conjecture and Applications in Correlated Random Graphs

Authors: Zhangsong Li

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
In this paper, assuming a natural strengthening of the low-degree conjecture, we provide evidence of computational hardness for two problems: (1) the (partial) matching recovery problem in the sparse correlated Erdős-Rényi graphs G(n,q;ρ) when the edge-density q = n^{-1+o(1)} and the correlation ρ < √{α} lies below the Otter’s threshold, this resolves a remaining problem in [Jian Ding et al., 2023]; (2) the detection problem between a pair of correlated sparse stochastic block model S(n,λ/n;k,ε;s) and a pair of independent stochastic block models S(n,λs/n;k,ε) when ε² λ s < 1 lies below the Kesten-Stigum (KS) threshold and s < √α lies below the Otter’s threshold, this resolves a remaining problem in [Guanyi Chen et al., 2024]. One of the main ingredient in our proof is to derive certain forms of algorithmic contiguity between two probability measures based on bounds on their low-degree advantage. To be more precise, consider the high-dimensional hypothesis testing problem between two probability measures ℙ and ℚ based on the sample Y. We show that if the low-degree advantage Adv_{≤D}(dℙ/dℚ) = O(1), then (assuming the low-degree conjecture) there is no efficient algorithm A such that ℚ(A(Y) = 0) = 1-o(1) and ℙ(A(Y) = 1) = Ω(1). This framework provides a useful tool for performing reductions between different inference tasks.
Cite as

Zhangsong Li. Algorithmic Contiguity from Low-Degree Conjecture and Applications in Correlated Random Graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 30:1-30:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{li:LIPIcs.APPROX/RANDOM.2025.30,
  author =	{Li, Zhangsong},
  title =	{{Algorithmic Contiguity from Low-Degree Conjecture and Applications in Correlated Random Graphs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{30:1--30:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.30},
  URN =		{urn:nbn:de:0030-drops-243965},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.30},
  annote =	{Keywords: Algorithmic Contiguity, Low-degree Conjecture, Correlated Random Graphs}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.18
A Randomized Rounding Approach for DAG Edge Deletion

Authors: Sina Kalantarzadeh, Nathan Klein, and Victor Reis

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
In the DAG Edge Deletion problem, we are given an edge-weighted directed acyclic graph and a parameter k, and the goal is to delete the minimum weight set of edges so that the resulting graph has no paths of length k. This problem, which has applications to scheduling, was introduced in 2015 by Kenkre, Pandit, Purohit, and Saket. They gave a k-approximation and showed that it is UGC-Hard to approximate better than ⌊0.5k⌋ for any constant k ≥ 4 using a work of Svensson from 2012. The approximation ratio was improved to 2/3(k+1) by Klein and Wexler in 2016. In this work, we introduce a randomized rounding framework based on distributions over vertex labels in [0,1]. The most natural distribution is to sample labels independently from the uniform distribution over [0,1]. We show this leads to a (2-√2)(k+1) ≈ 0.585(k+1)-approximation. By using a modified (but still independent) label distribution, we obtain a 0.549(k+1)-approximation for the problem, as well as show that no independent distribution over labels can improve our analysis to below 0.542(k+1). Finally, we show a 0.5(k+1)-approximation for bipartite graphs and for instances with structured LP solutions. Whether this ratio can be obtained in general is open.
Cite as

Sina Kalantarzadeh, Nathan Klein, and Victor Reis. A Randomized Rounding Approach for DAG Edge Deletion. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 18:1-18:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kalantarzadeh_et_al:LIPIcs.APPROX/RANDOM.2025.18,
  author =	{Kalantarzadeh, Sina and Klein, Nathan and Reis, Victor},
  title =	{{A Randomized Rounding Approach for DAG Edge Deletion}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{18:1--18:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.18},
  URN =		{urn:nbn:de:0030-drops-243840},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.18},
  annote =	{Keywords: Approximation Algorithms, Randomized Algorithms, Linear Programming, Graph Algorithms, Scheduling}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.19
On the Constant-Factor Approximability of Minimum Cost Constraint Satisfaction Problems

Authors: Ian DeHaan, Neng Huang, and Euiwoong Lee

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
We study minimum cost constraint satisfaction problems (MinCostCSP) through the algebraic lens. We show that for any constraint language Γ which has the dual discriminator operation as a polymorphism, there exists a |D|-approximation algorithm for MinCostCSP(Γ) where D is the domain. Complementing our algorithmic result, we show that any constraint language Γ where MinCostCSP(Γ) admits a constant-factor approximation must have a near-unanimity (NU) polymorphism unless P = NP, extending a similar result by Dalmau et al. on MinCSPs. These results imply a dichotomy of constant-factor approximability for constraint languages that contain all permutation relations (a natural generalization for Boolean CSPs that allow variable negation): either MinCostCSP(Γ) has an NU polymorphism and is |D|-approximable, or it does not have any NU polymorphism and is NP-hard to approximate within any constant factor. Finally, we present a constraint language which has a majority polymorphism, but is nonetheless NP-hard to approximate within any constant factor assuming the Unique Games Conjecture, showing that the condition of having an NU polymorphism is in general not sufficient unless UGC fails.
Cite as

Ian DeHaan, Neng Huang, and Euiwoong Lee. On the Constant-Factor Approximability of Minimum Cost Constraint Satisfaction Problems. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 19:1-19:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dehaan_et_al:LIPIcs.APPROX/RANDOM.2025.19,
  author =	{DeHaan, Ian and Huang, Neng and Lee, Euiwoong},
  title =	{{On the Constant-Factor Approximability of Minimum Cost Constraint Satisfaction Problems}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{19:1--19:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.19},
  URN =		{urn:nbn:de:0030-drops-243851},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.19},
  annote =	{Keywords: Constraint satisfaction problems, approximation algorithms, polymorphisms}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.24
Temporal Valued Constraint Satisfaction Problems

Authors: Manuel Bodirsky, Édouard Bonnet, and Žaneta Semanišinová

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
We study the computational complexity of the valued constraint satisfaction problem (VCSP) for every valued structure over ℚ that is preserved by all order-preserving bijections. Such VCSPs will be called temporal, in analogy to the (classical) constraint satisfaction problem: a relational structure is preserved by all order-preserving bijections if and only if all its relations have a first-order definition in (ℚ; <), and the CSPs for such structures are called temporal CSPs. Many optimization problems that have been studied intensively in the literature can be phrased as a temporal VCSP. We prove that a temporal VCSP is in P, or NP-complete. Our analysis uses the concept of fractional polymorphisms. This is the first dichotomy result for VCSPs over infinite domains which is complete in the sense that it treats all valued structures that contain a given automorphism group.
Cite as

Manuel Bodirsky, Édouard Bonnet, and Žaneta Semanišinová. Temporal Valued Constraint Satisfaction Problems. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 24:1-24:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bodirsky_et_al:LIPIcs.MFCS.2025.24,
  author =	{Bodirsky, Manuel and Bonnet, \'{E}douard and Semani\v{s}inov\'{a}, \v{Z}aneta},
  title =	{{Temporal Valued Constraint Satisfaction Problems}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{24:1--24:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.24},
  URN =		{urn:nbn:de:0030-drops-241311},
  doi =		{10.4230/LIPIcs.MFCS.2025.24},
  annote =	{Keywords: Constraint Satisfaction Problems, valued CSPs, temporal CSPs, fractional polymorphisms, complexity dichotomy, min CSPs}
}
Document
DOI: 10.4230/OASIcs.Manzini.12
Wheeler Graphs and Wheeler Languages

Authors: Nicola Cotumaccio, Giovanna D'Agostino, Daniel Gibney, Alberto Policriti, Nicola Prezza, and Sharma V. Thankachan

Published in: OASIcs, Volume 131, The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday (2025)

Abstract
Suffix sorting stands at the core of the most efficient solutions for indexed pattern matching: the suffix tree, the suffix array, compressed indexes based on the Burrows-Wheeler transform, and so on. In [Gagie, Manzini, Sirén, TCS 2017] this concept was extended to labeled graphs, obtaining the rich class of Wheeler graphs. This work opened a very fruitful line of research, ultimately generating results able to bridge the fields of compressed data structures, graph theory, and regular language theory. In a Wheeler graph, nodes are sorted according to the alphabetic order of their incoming labels, propagating this order through pairs of equally-labeled edges. This apparently-simple definition makes it possible to solve on Wheeler graphs problems (including, but not limited to: compression, subpath queries, NFA equivalence, determinization, minimization) that on general labeled graphs are extremely hard to solve, and induces a rich structure in the class of regular languages (Wheeler languages) recognized by automata whose state transition is a Wheeler graph. The goal of this survey is to provide a summary of (and intuitions behind) the results on Wheeler graphs that appeared in the literature since their introduction, in addition to a discussion of interesting problems that are still open in the field.
Cite as

Nicola Cotumaccio, Giovanna D'Agostino, Daniel Gibney, Alberto Policriti, Nicola Prezza, and Sharma V. Thankachan. Wheeler Graphs and Wheeler Languages. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 12:1-12:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cotumaccio_et_al:OASIcs.Manzini.12,
  author =	{Cotumaccio, Nicola and D'Agostino, Giovanna and Gibney, Daniel and Policriti, Alberto and Prezza, Nicola and Thankachan, Sharma V.},
  title =	{{Wheeler Graphs and Wheeler Languages}},
  booktitle =	{The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
  pages =	{12:1--12:28},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-390-4},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{131},
  editor =	{Ferragina, Paolo and Gagie, Travis and Navarro, Gonzalo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Manzini.12},
  URN =		{urn:nbn:de:0030-drops-239205},
  doi =		{10.4230/OASIcs.Manzini.12},
  annote =	{Keywords: Wheeler languages, Wheeler graphs, pattern matching, indexing, compressed data structures}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2015.341
Improved NP-Inapproximability for 2-Variable Linear Equations

Authors: Johan Håstad, Sangxia Huang, Rajsekar Manokaran, Ryan O’Donnell, and John Wright

Published in: LIPIcs, Volume 40, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)

Abstract
An instance of the 2-Lin(2) problem is a system of equations of the form "x_i + x_j = b (mod 2)". Given such a system in which it's possible to satisfy all but an epsilon fraction of the equations, we show it is NP-hard to satisfy all but a C*epsilon fraction of the equations, for any C < 11/8 = 1.375 (and any 0 < epsilon <= 1/8). The previous best result, standing for over 15 years, had 5/4 in place of 11/8. Our result provides the best known NP-hardness even for the Unique Games problem, and it also holds for the special case of Max-Cut. The precise factor 11/8 is unlikely to be best possible; we also give a conjecture concerning analysis of Boolean functions which, if true, would yield a larger hardness factor of 3/2. Our proof is by a modified gadget reduction from a pairwise-independent predicate. We also show an inherent limitation to this type of gadget reduction. In particular, any such reduction can never establish a hardness factor C greater than 2.54. Previously, no such limitation on gadget reductions was known.
Cite as

Johan Håstad, Sangxia Huang, Rajsekar Manokaran, Ryan O’Donnell, and John Wright. Improved NP-Inapproximability for 2-Variable Linear Equations. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 40, pp. 341-360, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{hastad_et_al:LIPIcs.APPROX-RANDOM.2015.341,
  author =	{H\r{a}stad, Johan and Huang, Sangxia and Manokaran, Rajsekar and O’Donnell, Ryan and Wright, John},
  title =	{{Improved NP-Inapproximability for 2-Variable Linear Equations}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)},
  pages =	{341--360},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-89-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{40},
  editor =	{Garg, Naveen and Jansen, Klaus and Rao, Anup and Rolim, Jos\'{e} D. P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2015.341},
  URN =		{urn:nbn:de:0030-drops-53112},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2015.341},
  annote =	{Keywords: approximability, unique games, linear equation, gadget, linear programming}
}
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