7 Search Results for "Korman, Simon"

Document
DOI: 10.4230/LIPIcs.STACS.2026.16
To Buy or Not to Buy: Online Rent-Or-Buy on Node-Weighted Graphs

Authors: Sander Borst and Moritz Venzin

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
We study the rent-or-buy variant of the online Steiner forest problem on node- and edge-weighted graphs. For n-node graphs with at most ̄{n} nodes of non-zero weight, and at most k̃ different arriving terminal pairs, we obtain the following: - A deterministic, O(log n log ̄{n})-competitive algorithm against adaptive adversaries. This improves on the previous best, O(log⁴ n)-competitive algorithm obtained by the black-box reduction from [Yair Bartal et al., 2001] combined with the previously best deterministic algorithms for the simpler "buy-only" setting. - A deterministic, O(̄{n}log k̃)-competitive algorithm against adaptive adversaries. This generalizes the O(log k̃)-competitive algorithm for the purely edge-weighted setting from [Seeun Umboh, 2015]. - A randomized, O(log k̃ log ̄{n})-competitive algorithm against oblivious adversaries. All previous approaches were based on the randomized, black-box reduction from [Awerbuch et al., 2004] that achieves a O(log k̃ log n)-competitive ratio when combined with an algorithm for the "buy-only" setting. Our key technical ingredient is a novel charging scheme to an instance of online prize-collecting set cover. This allows us to extend the witness-technique of [Seeun Umboh, 2015] to the node-weighted setting and obtain refined guarantees with respect to ̄{n}, already in the much simpler "buy-only" setting.
Cite as

Sander Borst and Moritz Venzin. To Buy or Not to Buy: Online Rent-Or-Buy on Node-Weighted Graphs. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 16:1-16:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{borst_et_al:LIPIcs.STACS.2026.16,
  author =	{Borst, Sander and Venzin, Moritz},
  title =	{{To Buy or Not to Buy: Online Rent-Or-Buy on Node-Weighted Graphs}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{16:1--16:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.16},
  URN =		{urn:nbn:de:0030-drops-255054},
  doi =		{10.4230/LIPIcs.STACS.2026.16},
  annote =	{Keywords: online network design, node-weighted Steiner forest, derandomization}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.45
Fairness in the k-Server Problem

Authors: Mohammadreza Daneshvaramoli, Mohammad Hajiesmaili, Shahin Kamali, Helia Karisani, and Cameron Musco

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We initiate a formal study of fairness for the k-server problem, where the objective is not only to minimize the total movement cost, but also to distribute the cost equitably among servers. We first define a general notion of (α,β)-fairness, where, for parameters α ≥ 1 and β ≥ 0, no server incurs more than an α/k-fraction of the total cost plus an additive term β. We then show that fairness can be achieved without a loss in competitiveness in both the offline and online settings. In the offline setting, we give a deterministic algorithm that, for any ε > 0, transforms any optimal solution into an (α,β)-fair solution for α = 1 + ε and β = O(diam ⋅ log k / ε), while increasing the cost of the solution by just an additive O(diam ⋅ k log k / ε) term. Here diam is the diameter of the underlying metric space. We give a similar result in the online setting, showing that any competitive algorithm can be transformed into a randomized online algorithm that is fair with high probability against an oblivious adversary and still competitive up to a small loss. The above results leave open a significant question: can fairness be achieved in the online setting, either with a deterministic algorithm or a randomized algorithm, against a fully adaptive adversary? We make progress towards answering this question, showing that the classic deterministic Double Coverage Algorithm (DCA) is fair on line metrics and on tree metrics when k = 2. However, we also show a negative result: DCA fails to be fair for any non-vacuous parameters on general tree metrics. We further show that on uniform metrics (i.e., the paging problem), the deterministic First-In First-Out (FIFO) algorithm is fair. We show that any "marking algorithm", including the Least Recently Used (LRU) algorithm, also satisfies a weaker, but still meaningful notion of fairness.
Cite as

Mohammadreza Daneshvaramoli, Mohammad Hajiesmaili, Shahin Kamali, Helia Karisani, and Cameron Musco. Fairness in the k-Server Problem. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 45:1-45:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{daneshvaramoli_et_al:LIPIcs.ITCS.2026.45,
  author =	{Daneshvaramoli, Mohammadreza and Hajiesmaili, Mohammad and Kamali, Shahin and Karisani, Helia and Musco, Cameron},
  title =	{{Fairness in the k-Server Problem}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{45:1--45:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.45},
  URN =		{urn:nbn:de:0030-drops-253328},
  doi =		{10.4230/LIPIcs.ITCS.2026.45},
  annote =	{Keywords: k-server problem, online algorithms, fairness, competitive analysis}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2025.60
Brief Announcement: Distributed Sparsest Cut via Eigenvalue Estimation

Authors: Yannic Maus and Tijn de Vos

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
We give new, improved bounds for approximating the sparsest cut value or in other words the conductance ϕ of a graph in the CONGEST model. As our main result, we present an algorithm running in O(log² n/ϕ) rounds in which every vertex outputs a value ̃ ϕ satisfying ϕ ≤ ̃ ϕ ≤ √{2.01ϕ}. In most regimes, our algorithm improves significantly over the previously fastest algorithm for the problem [Chen, Meierhans, Probst Gutenberg, Saranurak; SODA 25]. Additionally, our result generalizes to k-way conductance. We obtain these results, by approximating the eigenvalues of the normalized Laplacian matrix L: = I-Deg^{-1/2}ADeg^ {-1/2}, where, A is the adjacency matrix and Deg is the diagonal matrix with the weighted degrees on the diagonal. We show our algorithms are near-optimal by proving a lower bound for computing the smallest non-trivial eigenvalue of L, even in the stronger LOCAL model The previous state of the art sparsest cut algorithm is in the technical realm of expander decompositions. Our algorithms, on the other hand, are relatively simple and easy to implement. At the core, they rely on the well-known power method, which comes down to repeatedly multiplying the Laplacian with a vector. This operation can be performed in a single round in the CONGEST model. All our algorithms apply to weighted, undirected graphs. Our lower bounds apply even in unweighted graphs.
Cite as

Yannic Maus and Tijn de Vos. Brief Announcement: Distributed Sparsest Cut via Eigenvalue Estimation. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 60:1-60:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{maus_et_al:LIPIcs.DISC.2025.60,
  author =	{Maus, Yannic and de Vos, Tijn},
  title =	{{Brief Announcement: Distributed Sparsest Cut via Eigenvalue Estimation}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{60:1--60:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.60},
  URN =		{urn:nbn:de:0030-drops-248763},
  doi =		{10.4230/LIPIcs.DISC.2025.60},
  annote =	{Keywords: CONGEST, Sparsest Cut, Laplacian, Eigenvalues, Spectral Graph Theory}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.34
Link Diameter, Radius and 2-Point Link Distance Queries in Polygonal Domains

Authors: Mart Hagedoorn and Valentin Polishchuk

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

Abstract
We show how to preprocess a polygonal domain with holes so that the link distance (the number of links in a minimum-link path) between two query points in the domain can be reported efficiently. Using our data structures, the link diameter of the domain (i.e., the maximum number of links that may be required in a minimum-link path between two points in the domain) as well as the link center and radius of the domain (i.e., the point minimizing the maximum link distance to the furthest point in the domain and this maximum link distance) can be found in polynomial time. We also give a simpler algorithm for finding the link diameter, not using the link distance query structures. Answering 2-point link distance queries and computing the link diameter/radius/center in polygonal domains have been open questions since these problems were studied for simple polygons in the 90’s.
Cite as

Mart Hagedoorn and Valentin Polishchuk. Link Diameter, Radius and 2-Point Link Distance Queries in Polygonal Domains. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 34:1-34:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hagedoorn_et_al:LIPIcs.WADS.2025.34,
  author =	{Hagedoorn, Mart and Polishchuk, Valentin},
  title =	{{Link Diameter, Radius and 2-Point Link Distance Queries in Polygonal Domains}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{34:1--34:15},
  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.2025.34},
  URN =		{urn:nbn:de:0030-drops-242659},
  doi =		{10.4230/LIPIcs.WADS.2025.34},
  annote =	{Keywords: Minimum-link paths, link distance, diameter, center, radius, 2-point distance queries}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.51
Parameterized Geometric Graph Modification with Disk Scaling

Authors: Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, Saket Saurabh, and Meirav Zehavi

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
The parameterized analysis of graph modification problems represents the most extensively studied area within Parameterized Complexity. Given a graph G and an integer k ∈ ℕ as input, the goal is to determine whether we can perform at most k operations on G to transform it into a graph belonging to a specified graph class ℱ. Typical operations are combinatorial and include vertex deletions and edge deletions, insertions, and contractions. However, in many real-world scenarios, when the input graph is constrained to be a geometric intersection graph, the modification of the graph is influenced by changes in the geometric properties of the underlying objects themselves, rather than by combinatorial modifications. It raises the question of whether vertex deletions or adjacency modifications are necessarily the most appropriate modification operations for studying modifications of geometric graphs. We propose the study of the disk intersection graph modification through the scaling of disks. This operation is typical in the realm of topology control but has not yet been explored in the context of Parameterized Complexity. We design parameterized algorithms and kernels for modifying to the most basic graph classes: edgeless, connected, and acyclic. Our technical contributions encompass a novel combination of linear programming, branching, and kernelization techniques, along with a fresh application of bidimensionality theory to analyze the area covered by disks, which may have broader applicability.
Cite as

Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, Saket Saurabh, and Meirav Zehavi. Parameterized Geometric Graph Modification with Disk Scaling. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 51:1-51:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fomin_et_al:LIPIcs.ITCS.2025.51,
  author =	{Fomin, Fedor V. and Golovach, Petr A. and Inamdar, Tanmay and Saurabh, Saket and Zehavi, Meirav},
  title =	{{Parameterized Geometric Graph Modification with Disk Scaling}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{51:1--51:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.51},
  URN =		{urn:nbn:de:0030-drops-226795},
  doi =		{10.4230/LIPIcs.ITCS.2025.51},
  annote =	{Keywords: parameterized algorithms, kernelization, spreading points, distant representatives, unit disk packing}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.9
Deleting and Testing Forbidden Patterns in Multi-Dimensional Arrays

Authors: Omri Ben-Eliezer, Simon Korman, and Daniel Reichman

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Abstract
Analyzing multi-dimensional data is a fundamental problem in various areas of computer science. As the amount of data is often huge, it is desirable to obtain sublinear time algorithms to understand local properties of the data. We focus on the natural problem of testing pattern freeness: given a large d-dimensional array A and a fixed d-dimensional pattern P over a finite alphabet Gamma, we say that A is P-free if it does not contain a copy of the forbidden pattern P as a consecutive subarray. The distance of A to P-freeness is the fraction of the entries of A that need to be modified to make it P-free. For any epsilon > 0 and any large enough pattern P over any alphabet - other than a very small set of exceptional patterns - we design a tolerant tester that distinguishes between the case that the distance is at least epsilon and the case that the distance is at most a_d epsilon, with query complexity and running time c_d epsilon^{-1}, where a_d < 1 and c_d depend only on the dimension d. These testers only need to access uniformly random blocks of samples from the input A. To analyze the testers we establish several combinatorial results, including the following d-dimensional modification lemma, which might be of independent interest: For any large enough d-dimensional pattern P over any alphabet (excluding a small set of exceptional patterns for the binary case), and any d-dimensional array A containing a copy of P, one can delete this copy by modifying one of its locations without creating new P-copies in A. Our results address an open question of Fischer and Newman, who asked whether there exist efficient testers for properties related to tight substructures in multi-dimensional structured data.
Cite as

Omri Ben-Eliezer, Simon Korman, and Daniel Reichman. Deleting and Testing Forbidden Patterns in Multi-Dimensional Arrays. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{beneliezer_et_al:LIPIcs.ICALP.2017.9,
  author =	{Ben-Eliezer, Omri and Korman, Simon and Reichman, Daniel},
  title =	{{Deleting and Testing Forbidden Patterns in Multi-Dimensional Arrays}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{9:1--9:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.9},
  URN =		{urn:nbn:de:0030-drops-74427},
  doi =		{10.4230/LIPIcs.ICALP.2017.9},
  annote =	{Keywords: Property testing, Sublinear algorithms, Pattern matching}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2016.30
Time-Space Trade-offs for Triangulating a Simple Polygon

Authors: Boris Aronov, Matias Korman, Simon Pratt, André van Renssen, and Marcel Roeloffzen

Published in: LIPIcs, Volume 53, 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)

Abstract
An s-workspace algorithm is an algorithm that has read-only access to the values of the input, write-only access to the output, and only uses O(s) additional words of space. We give a randomized s-workspace algorithm for triangulating a simple polygon P of n vertices, for any s up to n. The algorithm runs in O(n^2/s+n(log s)log^5(n/s)) expected time using O(s) variables, for any s up to n. In particular, the algorithm runs in O(n^2/s) expected time for most values of s.
Cite as

Boris Aronov, Matias Korman, Simon Pratt, André van Renssen, and Marcel Roeloffzen. Time-Space Trade-offs for Triangulating a Simple Polygon. In 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 53, pp. 30:1-30:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{aronov_et_al:LIPIcs.SWAT.2016.30,
  author =	{Aronov, Boris and Korman, Matias and Pratt, Simon and van Renssen, André and Roeloffzen, Marcel},
  title =	{{Time-Space Trade-offs for Triangulating a Simple Polygon}},
  booktitle =	{15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)},
  pages =	{30:1--30:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-011-8},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{53},
  editor =	{Pagh, Rasmus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2016.30},
  URN =		{urn:nbn:de:0030-drops-60522},
  doi =		{10.4230/LIPIcs.SWAT.2016.30},
  annote =	{Keywords: simple polygon, triangulation, shortest path, time-space trade-off}
}
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