23 Search Results for "Bienkowski, Marcin"

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.STACS.2026.79
Mind the Gap. Doubling Constant Parametrization of Weighted Problems: TSP, Max-Cut, and More

Authors: Mihail Stoian

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

Abstract
Despite much research, hard weighted problems still resist super-polynomial improvements over their textbook solution. On the other hand, the unweighted versions of these problems have recently witnessed the sought-after speedups. Currently, the only way to repurpose the algorithm of the unweighted version for the weighted version is to employ a polynomial embedding of the input weights. This, however, introduces a pseudo-polynomial factor into the running time, which becomes impractical for arbitrarily weighted instances. In this paper, we introduce a new way to repurpose the algorithm of the unweighted problem. Specifically, we show that the time complexity of several well-known NP-hard problems operating over the (min, +) and (max, +) semirings, such as TSP, Weighted Max-Cut, and Edge-Weighted k-Clique, is proportional to that of their unweighted versions when the set of input weights has small doubling. We achieve this by a meta-algorithm that converts the input weights into polynomially bounded integers using the recent constructive Freiman’s theorem by Randolph and Węgrzycki [ESA 2024] before applying the polynomial embedding.
Cite as

Mihail Stoian. Mind the Gap. Doubling Constant Parametrization of Weighted Problems: TSP, Max-Cut, and More. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 79:1-79:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{stoian:LIPIcs.STACS.2026.79,
  author =	{Stoian, Mihail},
  title =	{{Mind the Gap. Doubling Constant Parametrization of Weighted Problems: TSP, Max-Cut, and More}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{79:1--79:19},
  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.2026.79},
  URN =		{urn:nbn:de:0030-drops-255680},
  doi =		{10.4230/LIPIcs.STACS.2026.79},
  annote =	{Keywords: doubling constant parametrization, weighted problems, traveling salesman, weighted max-cut, edge-weighted k-clique}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.27
Online Makespan Scheduling Under Scenarios

Authors: Ekin Ergen

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We consider a natural extension of online makespan scheduling on identical parallel machines by introducing scenarios. A scenario is a subset of jobs, and the task of our problem is to find a global assignment of the jobs to machines so that the maximum makespan under a scenario, i.e., the maximum makespan of any schedule restricted to a scenario, is minimized. For varying values of the number of scenarios and machines, we explore the competitiveness of online algorithms. We prove tight and near-tight bounds, several of which are achieved through novel constructions. In particular, we leverage the interplay between the unit processing time case of our problem and the hypergraph coloring problem both ways: We use hypergraph coloring techniques to steer an adversarial family of instances proving lower bounds for our problem, which in turn leads to lower bounds for several variants of online hypergraph coloring.
Cite as

Ekin Ergen. Online Makespan Scheduling Under Scenarios. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 27:1-27:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ergen:LIPIcs.ESA.2025.27,
  author =	{Ergen, Ekin},
  title =	{{Online Makespan Scheduling Under Scenarios}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{27:1--27:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.27},
  URN =		{urn:nbn:de:0030-drops-244950},
  doi =		{10.4230/LIPIcs.ESA.2025.27},
  annote =	{Keywords: online scheduling, scenario-based model, online algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.76
A 3.3904-Competitive Online Algorithm for List Update with Uniform Costs

Authors: Mateusz Basiak, Marcin Bienkowski, Martin Böhm, Marek Chrobak, Łukasz Jeż, Jiří Sgall, and Agnieszka Tatarczuk

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We consider the List Update problem where the cost of each swap is assumed to be 1. This is in contrast to the "standard" model, in which an algorithm is allowed to swap the requested item with previous items for free. We construct an online algorithm Full-Or-Partial-Move (FPM), whose competitive ratio is at most 3.3904, improving over the previous best known bound of 4.
Cite as

Mateusz Basiak, Marcin Bienkowski, Martin Böhm, Marek Chrobak, Łukasz Jeż, Jiří Sgall, and Agnieszka Tatarczuk. A 3.3904-Competitive Online Algorithm for List Update with Uniform Costs. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 76:1-76:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{basiak_et_al:LIPIcs.ESA.2025.76,
  author =	{Basiak, Mateusz and Bienkowski, Marcin and B\"{o}hm, Martin and Chrobak, Marek and Je\.{z}, {\L}ukasz and Sgall, Ji\v{r}{\'\i} and Tatarczuk, Agnieszka},
  title =	{{A 3.3904-Competitive Online Algorithm for List Update with Uniform Costs}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{76:1--76:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.76},
  URN =		{urn:nbn:de:0030-drops-245442},
  doi =		{10.4230/LIPIcs.ESA.2025.76},
  annote =	{Keywords: List update, work functions, amortized analysis, online algorithms, competitive analysis}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.25
Covering a Few Submodular Constraints and Applications

Authors: Tanvi Bajpai, Chandra Chekuri, and Pooja Kulkarni

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

Abstract
We consider the problem of covering multiple submodular constraints. Given a finite ground set N, a cost function c: N → ℝ_+, r monotone submodular functions f_1,f_2,…,f_r over N and requirements b_1,b_2,…,b_r the goal is to find a minimum cost subset S ⊆ N such that f_i(S) ≥ b_i for 1 ≤ i ≤ r. When r = 1 this is the well-known Submodular Set Cover problem. Previous work [Chekuri et al., 2022] considered the setting when r is large and developed bi-criteria approximation algorithms, and approximation algorithms for the important special case when each f_i is a weighted coverage function. These are fairly general models and capture several concrete and interesting problems as special cases. The approximation ratios for these problem are at least Ω(log r) which is unavoidable when r is part of the input. In this paper, motivated by some recent applications, we consider the problem when r is a fixed constant and obtain two main results. When the f_i are weighted coverage functions from a deletion-closed set system we obtain a (1+ε)(e/(e-1))(1+β)-approximation where β is the approximation ratio for the underlying set cover instances via the natural LP. Second, for covering multiple submodular constraints we obtain a randomized bi-criteria approximation algorithm that for any given integer α ≥ 1 outputs a set S such that f_i(S) ≥ (1-1/e^α-ε)b_i for each i ∈ [r] and 𝔼[c(S)] ≤ (1+ε)α ⋅ OPT. These results show that one can obtain nearly as good an approximation for any fixed r as what one would achieve for r = 1. We also demonstrate applications of our results to implicit covering problems such as fair facility location.
Cite as

Tanvi Bajpai, Chandra Chekuri, and Pooja Kulkarni. Covering a Few Submodular Constraints and Applications. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 25:1-25:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bajpai_et_al:LIPIcs.APPROX/RANDOM.2025.25,
  author =	{Bajpai, Tanvi and Chekuri, Chandra and Kulkarni, Pooja},
  title =	{{Covering a Few Submodular Constraints and Applications}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{25:1--25:22},
  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.2025.25},
  URN =		{urn:nbn:de:0030-drops-243917},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.25},
  annote =	{Keywords: covering, linear programming, rounding, fairness}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.77
Minimizing Recourse in an Adaptive Balls and Bins Game

Authors: Adi Fine, Haim Kaplan, and Uri Stemmer

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

Abstract
We consider a simple load-balancing game between an algorithm and an adaptive adversary. In a simplified version of this game, the adversary observes the assignment of jobs to machines and selects a machine to kill. The algorithm must then restart the jobs from the failed machine on other machines. The adversary repeats this process, observing the new assignment and eliminating another machine, and so on. The adversary aims to force the algorithm to perform many restarts, while we seek a robust algorithm that minimizes restarts regardless of the adversary’s strategy. This game was recently introduced by Bhattacharya et al. for designing a 3-spanner with low recourse against an adaptive adversary. We prove that a simple algorithm, which assigns each job to a randomly chosen live bin, incurs O(n log n) recourse against an adaptive adversary. This enables us to construct a much simpler 3-spanner with a recourse that is smaller by a factor of O(log² n) compared to the previous construction, without increasing the update time or the size of the spanner. This motivates a careful examination of the range of attacks an adaptive adversary can deploy against simple algorithms before resorting to more complex ones. As our case study demonstrates, this attack space may not be as large as it initially appears, enabling the development of robust algorithms that are both simpler and easier to analyze.
Cite as

Adi Fine, Haim Kaplan, and Uri Stemmer. Minimizing Recourse in an Adaptive Balls and Bins Game. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 77:1-77:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fine_et_al:LIPIcs.ICALP.2025.77,
  author =	{Fine, Adi and Kaplan, Haim and Stemmer, Uri},
  title =	{{Minimizing Recourse in an Adaptive Balls and Bins Game}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{77:1--77:19},
  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.2025.77},
  URN =		{urn:nbn:de:0030-drops-234544},
  doi =		{10.4230/LIPIcs.ICALP.2025.77},
  annote =	{Keywords: Adaptive adversary, load-balancing game, balls-and-bins, randomized algorithms, dynamic 3-spanner, dynamic graph algorithms, adversarial robustness}
}
Document
DOI: 10.4230/LIPIcs.SAND.2025.4
On b-Matching and Fully-Dynamic Maximum k-Edge Coloring

Authors: Antoine El-Hayek, Kathrin Hanauer, and Monika Henzinger

Published in: LIPIcs, Volume 330, 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)

Abstract
Given a graph G that undergoes a sequence of edge insertions and deletions, we study the Maximum k-Edge Coloring problem (MkEC): Having access to k different colors, color as many edges of G as possible such that no two adjacent edges share the same color. While this problem is different from simply maintaining a b-matching with b = k, the two problems are related. However, maximum b-matching can be solved efficiently in the static setting, whereas MkEC is NP-hard and even APX-hard for k ≥ 2. We present new results on both problems: For b-matching, we show a new integrality gap result and we adapt Wajc’s matching sparsification scheme [David Wajc, 2020] for the case where b is a constant. Using these as basis, we give three new algorithms for the dynamic MkEC problem: Our MatchO algorithm builds on the dynamic (2+ε)-approximation algorithm of Bhattacharya, Gupta, and Mohan [Sayan Bhattacharya et al., 2017] for b-matching and achieves a (2+ε)(k+1)/k-approximation in O(poly(log n, ε^-1)) update time against an oblivious adversary. Our MatchA algorithm builds on the dynamic (7+ε)-approximation algorithm by Bhattacharya, Henzinger, and Italiano [Sayan Bhattacharya et al., 2015] for fractional b-matching and achieves a (7+ε)(3k+3)/(3k-1)-approximation in O(poly(log n, ε^-1)) update time against an adaptive adversary. Moreover, our reductions use the dynamic b-matching algorithm as a black box, so any future improvement in the approximation ratio for dynamic b-matching will automatically translate into a better approximation ratio for our algorithms. Finally, we present a greedy algorithm with O(Δ+k) update time, which guarantees a 2.16 approximation factor.
Cite as

Antoine El-Hayek, Kathrin Hanauer, and Monika Henzinger. On b-Matching and Fully-Dynamic Maximum k-Edge Coloring. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 4:1-4:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{elhayek_et_al:LIPIcs.SAND.2025.4,
  author =	{El-Hayek, Antoine and Hanauer, Kathrin and Henzinger, Monika},
  title =	{{On b-Matching and Fully-Dynamic Maximum k-Edge Coloring}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{4:1--4:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-368-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{330},
  editor =	{Meeks, Kitty and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.4},
  URN =		{urn:nbn:de:0030-drops-230571},
  doi =		{10.4230/LIPIcs.SAND.2025.4},
  annote =	{Keywords: dynamic algorithm, graph algorithm, matching, b-matching, edge coloring}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.18
Online Disjoint Set Covers: Randomization Is Not Necessary

Authors: Marcin Bienkowski, Jarosław Byrka, and Łukasz Jeż

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
In the online disjoint set covers problem, the edges of a hypergraph are revealed online, and the goal is to partition them into a maximum number of disjoint set covers. That is, n nodes of a hypergraph are given at the beginning, and then a sequence of hyperedges (subsets of [n]) is presented to an algorithm. For each hyperedge, an online algorithm must assign a color (an integer). Once an input terminates, the gain of the algorithm is the number of colors that correspond to valid set covers (i.e., the union of hyperedges that have that color contains all n nodes). We present a deterministic online algorithm that is O(log² n)-competitive, exponentially improving on the previous bound of O(n) and matching the performance of the best randomized algorithm by Emek et al. [ESA 2019]. For color selection, our algorithm uses a novel potential function, which can be seen as an online counterpart of the derandomization method of conditional probabilities and pessimistic estimators. There are only a few cases where derandomization has been successfully used in the field of online algorithms. In contrast to previous approaches, our result extends to the following new challenges: (i) the potential function derandomizes not only the Chernoff bound, but also the coupon collector’s problem, (ii) the value of Opt of the maximization problem is not bounded a priori, and (iii) we do not produce a fractional solution first, but work directly on the input.
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Marcin Bienkowski, Jarosław Byrka, and Łukasz Jeż. Online Disjoint Set Covers: Randomization Is Not Necessary. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 18:1-18:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bienkowski_et_al:LIPIcs.STACS.2025.18,
  author =	{Bienkowski, Marcin and Byrka, Jaros{\l}aw and Je\.{z}, {\L}ukasz},
  title =	{{Online Disjoint Set Covers: Randomization Is Not Necessary}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{18:1--18:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine 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.2025.18},
  URN =		{urn:nbn:de:0030-drops-228433},
  doi =		{10.4230/LIPIcs.STACS.2025.18},
  annote =	{Keywords: Disjoint Set Covers, Derandomization, pessimistic Estimator, potential Function, online Algorithms, competitive Analysis}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.74
Nearly-Optimal Algorithm for Non-Clairvoyant Service with Delay

Authors: Noam Touitou

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
We consider the online service with delay problem, in which a server traverses a metric space to serve requests that arrive over time. Requests gather individual delay cost while awaiting service, penalizing service latency; an algorithm seeks to minimize both its movement cost and the total delay cost. Algorithms for the problem (on general metric spaces) are only known for the clairvoyant model, where the algorithm knows future delay cost in advance (e.g., Azar et al., STOC'17; Azar and Touitou, FOCS'19; Touitou, STOC'23). However, in the non-clairvoyant setting, only negative results are known: where n is the size of the metric space and m is the number of requests, there are lower bounds of Ω(√n) and Ω(√m) on competitiveness (Azar et al., STOC'17), that hold even for randomized algorithms (Le et al., SODA'23). In this paper, we present the first algorithm for non-clairvoyant online service with delay. Our algorithm is deterministic and O(min{√n log n, √m log m})-competitive; combined with the lower bounds of Azar et al., this settles the correct competitive ratio for the problem up to logarithmic factors, in terms of both n and m.
Cite as

Noam Touitou. Nearly-Optimal Algorithm for Non-Clairvoyant Service with Delay. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 74:1-74:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{touitou:LIPIcs.STACS.2025.74,
  author =	{Touitou, Noam},
  title =	{{Nearly-Optimal Algorithm for Non-Clairvoyant Service with Delay}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{74:1--74:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine 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.2025.74},
  URN =		{urn:nbn:de:0030-drops-228995},
  doi =		{10.4230/LIPIcs.STACS.2025.74},
  annote =	{Keywords: Online, Delay, Deadlines, k-server, Non-clairvoyant}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.59
Online Matching with Delays and Size-Based Costs

Authors: Yasushi Kawase and Tomohiro Nakayoshi

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
In this paper, we introduce the problem of Online Matching with Delays and Size-based Costs (OMDSC). The OMDSC problem involves m requests arriving online. At any time, a group can be formed by matching any number of requests that have been received but remain unmatched. The cost associated with each group is determined by the waiting time for each request within the group and size-dependent cost. The size-dependent cost is specified by a penalty function. Our goal is to partition all the incoming requests into multiple groups while minimizing the total associated cost. This problem is an extension of the TCP acknowledgment problem proposed by Dooly et al. (J. ACM, 2001). It generalizes the cost model for sending acknowledgments. This study reveals the competitive ratios for a fundamental case, in which the penalty function takes only values of either 0 or 1. We classify such penalty functions into three distinct cases: (i) a fixed penalty of 1 regardless of the group size, (ii) a penalty of 0 if and only if the group size is a multiple of a specific integer k, and (iii) other situations. The problem in case (i) is equivalent to the TCP acknowledgment problem, for which Dooly et al. proposed a 2-competitive algorithm. For case (ii), we first show that natural algorithms that match all remaining requests are Ω(√k)-competitive. We then propose an O(log k / log log k)-competitive deterministic algorithm by carefully managing the match size and timing, and prove its optimality. For any penalty function in case (iii), we demonstrate the non-existence of a competitive online algorithm. Additionally, we discuss competitive ratios for other typical penalty functions that are not restricted to take values of 0 or 1.
Cite as

Yasushi Kawase and Tomohiro Nakayoshi. Online Matching with Delays and Size-Based Costs. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 59:1-59:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kawase_et_al:LIPIcs.STACS.2025.59,
  author =	{Kawase, Yasushi and Nakayoshi, Tomohiro},
  title =	{{Online Matching with Delays and Size-Based Costs}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{59:1--59:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine 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.2025.59},
  URN =		{urn:nbn:de:0030-drops-228846},
  doi =		{10.4230/LIPIcs.STACS.2025.59},
  annote =	{Keywords: Online matching, competitive analysis, delayed service}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.81
Online Balanced Allocation of Dynamic Components

Authors: Rajmohan Rajaraman and Omer Wasim

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

Abstract
We introduce Online Balanced Allocation of Dynamic Components (OBADC), a problem motivated by the practical challenge of dynamic resource allocation for large-scale distributed applications. In OBADC, we need to allocate a dynamic set of at most k𝓁 vertices (representing processes) in 𝓁 > 0 clusters. We consider an over-provisioned setup in which each cluster can hold at most k(1+ε) vertices, for an arbitrary constant ε > 0. The communication requirements among the vertices are modeled by the notion of a dynamically changing component, which is a subset of vertices that need to be co-located in the same cluster. At each time t, a request r_t of one of the following types arrives: 1) insertion of a vertex v forming a singleton component v at unit cost. 2) merge of (u,v) requiring that the components containing u and v be merged and co-located thereafter. 3) deletion of an existing vertex v at zero cost. Before serving any request, an algorithm can migrate vertices from one cluster to another, at a unit migration cost per vertex. We seek an online algorithm to minimize the total migration cost incurred for an arbitrary request sequence σ = (r_t)_{t > 0}, while simultaneously minimizing the number of clusters utilized. We analyze competitiveness with respect to an optimal clairvoyant offline algorithm with identical (over-provisioned) capacity constraints. We give an O(log k)-competitive algorithm for OBADC, and a matching lower-bound. The number of clusters utilized by our algorithm is always within a (2+ε) factor of the minimum. Furthermore, in a resource augmented setting where the optimal offline algorithm is constrained to capacity k per cluster, our algorithm obtains O(log k) competitiveness and utilizes a number of clusters within (1+ε) factor of the minimum. We also consider OBADC in the context of machine-learned predictions, where for each newly inserted vertex v at time t: i) with probability η > 0, the set of vertices (that exist at time t) in the component of v is revealed and, ii) with probability 1-η, no information is revealed. For OBADC with predictions, we give a O(1)-consistent and O(min(log 1/(η), log k))-robust algorithm.
Cite as

Rajmohan Rajaraman and Omer Wasim. Online Balanced Allocation of Dynamic Components. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 81:1-81:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{rajaraman_et_al:LIPIcs.ITCS.2025.81,
  author =	{Rajaraman, Rajmohan and Wasim, Omer},
  title =	{{Online Balanced Allocation of Dynamic Components}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{81:1--81:23},
  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.2025.81},
  URN =		{urn:nbn:de:0030-drops-227090},
  doi =		{10.4230/LIPIcs.ITCS.2025.81},
  annote =	{Keywords: online algorithms, competitive ratio, algorithms with predictions}
}
Document
DOI: 10.4230/LIPIcs.STACS.2024.14
A Subquadratic Bound for Online Bisection

Authors: Marcin Bienkowski and Stefan Schmid

Published in: LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)

Abstract
The online bisection problem is a natural dynamic variant of the classic optimization problem, where one has to dynamically maintain a partition of n elements into two clusters of cardinality n/2. During runtime, an online algorithm is given a sequence of requests, each being a pair of elements: an inter-cluster request costs one unit while an intra-cluster one is free. The algorithm may change the partition, paying a unit cost for each element that changes its cluster. This natural problem admits a simple deterministic O(n²)-competitive algorithm [Avin et al., DISC 2016]. While several significant improvements over this result have been obtained since the original work, all of them either limit the generality of the input or assume some form of resource augmentation (e.g., larger clusters). Moreover, the algorithm of Avin et al. achieves the best known competitive ratio even if randomization is allowed. In this paper, we present the first randomized online algorithm that breaks this natural quadratic barrier and achieves a competitive ratio of Õ(n^{23/12}) without resource augmentation and for an arbitrary sequence of requests.
Cite as

Marcin Bienkowski and Stefan Schmid. A Subquadratic Bound for Online Bisection. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bienkowski_et_al:LIPIcs.STACS.2024.14,
  author =	{Bienkowski, Marcin and Schmid, Stefan},
  title =	{{A Subquadratic Bound for Online Bisection}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{14:1--14:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.14},
  URN =		{urn:nbn:de:0030-drops-197247},
  doi =		{10.4230/LIPIcs.STACS.2024.14},
  annote =	{Keywords: Bisection, Graph Partitioning, online balanced Repartitioning, online Algorithms, competitive Analysis}
}
Document
DOI: 10.4230/LIPIcs.STACS.2024.15
An Improved Approximation Algorithm for Dynamic Minimum Linear Arrangement

Authors: Marcin Bienkowski and Guy Even

Published in: LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)

Abstract
The dynamic offline linear arrangement problem deals with reordering n elements subject to a sequence of edge requests. The input consists of a sequence of m edges (i.e., unordered pairs of elements). The output is a sequence of permutations (i.e., bijective mapping of the elements to n equidistant points). In step t, the order of the elements is changed to the t-th permutation, and then the t-th request is served. The cost of the output consists of two parts per step: request cost and rearrangement cost. The former is the current distance between the endpoints of the request, while the latter is proportional to the number of adjacent element swaps required to move from one permutation to the consecutive permutation. The goal is to find a minimum cost solution. We present a deterministic O(log n log log n)-approximation algorithm for this problem, improving over a randomized O(log² n)-approximation by Olver et al. [Neil Olver et al., 2018]. Our algorithm is based on first solving spreading-metric LP relaxation on a time-expanded graph, applying a tree decomposition on the basis of the LP solution, and finally converting the tree decomposition to a sequence of permutations. The techniques we employ are general and have the potential to be useful for other dynamic graph optimization problems.
Cite as

Marcin Bienkowski and Guy Even. An Improved Approximation Algorithm for Dynamic Minimum Linear Arrangement. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 15:1-15:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bienkowski_et_al:LIPIcs.STACS.2024.15,
  author =	{Bienkowski, Marcin and Even, Guy},
  title =	{{An Improved Approximation Algorithm for Dynamic Minimum Linear Arrangement}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{15:1--15:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.15},
  URN =		{urn:nbn:de:0030-drops-197252},
  doi =		{10.4230/LIPIcs.STACS.2024.15},
  annote =	{Keywords: Minimum Linear Arrangement, dynamic Variant, Optimization Problems, Graph Problems, approximation Algorithms}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.45
Online Facility Location with Linear Delay

Authors: Marcin Bienkowski, Martin Böhm, Jarosław Byrka, and Jan Marcinkowski

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)

Abstract
In the problem of online facility location with delay, a sequence of n clients appear in the metric space, and they need to be eventually connected to some open facility. The clients do not have to be connected immediately, but such a choice comes with a certain penalty: each client incurs a waiting cost (equal to the difference between its arrival and its connection time). At any point in time, an algorithm may decide to open a facility and connect any subset of clients to it. That is, an algorithm needs to balance three types of costs: cost of opening facilities, costs of connecting clients, and the waiting costs of clients. We study a natural variant of this problem, where clients may be connected also to an already open facility, but such action incurs an extra cost: an algorithm pays for waiting of the facility (a cost incurred separately for each such "late" connection). This is reminiscent of online matching with delays, where both sides of the connection incur a waiting cost. We call this variant two-sided delay to differentiate it from the previously studied one-sided delay, where clients may connect to a facility only at its opening time. We present an O(1)-competitive deterministic algorithm for the two-sided delay variant. Our approach is an extension of the approach used by Jain, Mahdian and Saberi [STOC 2002] for analyzing the performance of offline algorithms for facility location. To this end, we substantially simplify the part of the original argument in which a bound on the sequence of factor-revealing LPs is derived. We then show how to transform our O(1)-competitive algorithm for the two-sided delay variant to O(log n / log log n)-competitive deterministic algorithm for one-sided delays. This improves the known O(log n) bound by Azar and Touitou [FOCS 2020]. We note that all previous online algorithms for problems with delays in general metrics have at least logarithmic ratios.
Cite as

Marcin Bienkowski, Martin Böhm, Jarosław Byrka, and Jan Marcinkowski. Online Facility Location with Linear Delay. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 45:1-45:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bienkowski_et_al:LIPIcs.APPROX/RANDOM.2022.45,
  author =	{Bienkowski, Marcin and B\"{o}hm, Martin and Byrka, Jaros{\l}aw and Marcinkowski, Jan},
  title =	{{Online Facility Location with Linear Delay}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{45:1--45:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.45},
  URN =		{urn:nbn:de:0030-drops-171678},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.45},
  annote =	{Keywords: online facility location, network design problems, facility location with delay, JMS algorithm, competitive analysis, factor revealing LP}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.28
Traveling Repairperson, Unrelated Machines, and Other Stories About Average Completion Times

Authors: Marcin Bienkowski, Artur Kraska, and Hsiang-Hsuan Liu

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
We present a unified framework for minimizing average completion time for many seemingly disparate online scheduling problems, such as the traveling repairperson problems (TRP), dial-a-ride problems (DARP), and scheduling on unrelated machines. We construct a simple algorithm that handles all these scheduling problems, by computing and later executing auxiliary schedules, each optimizing a certain function on already seen prefix of the input. The optimized function resembles a prize-collecting variant of the original scheduling problem. By a careful analysis of the interplay between these auxiliary schedules, and later employing the resulting inequalities in a factor-revealing linear program, we obtain improved bounds on the competitive ratio for all these scheduling problems. In particular, our techniques yield a 4-competitive deterministic algorithm for all previously studied variants of online TRP and DARP, and a 3-competitive one for the scheduling on unrelated machines (also with precedence constraints). This improves over currently best ratios for these problems that are 5.14 and 4, respectively. We also show how to use randomization to further reduce the competitive ratios to 1+2/ln 3 < 2.821 and 1+1/ln 2 < 2.443, respectively. The randomized bounds also substantially improve the current state of the art. Our upper bound for DARP contradicts the lower bound of 3 given by Fink et al. (Inf. Process. Lett. 2009); we pinpoint a flaw in their proof.
Cite as

Marcin Bienkowski, Artur Kraska, and Hsiang-Hsuan Liu. Traveling Repairperson, Unrelated Machines, and Other Stories About Average Completion Times. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 28:1-28:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bienkowski_et_al:LIPIcs.ICALP.2021.28,
  author =	{Bienkowski, Marcin and Kraska, Artur and Liu, Hsiang-Hsuan},
  title =	{{Traveling Repairperson, Unrelated Machines, and Other Stories About Average Completion Times}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{28:1--28:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.28},
  URN =		{urn:nbn:de:0030-drops-140977},
  doi =		{10.4230/LIPIcs.ICALP.2021.28},
  annote =	{Keywords: traveling repairperson problem, dial-a-ride, machine scheduling, unrelated machines, minimizing completion time, competitive analysis, factor-revealing LP}
}
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