17 Search Results for "Antoniadis, Antonios"

Document
DOI: 10.4230/LIPIcs.MFCS.2025.12
Online Knapsack Problems with Estimates

Authors: Jakub Balabán, Matthias Gehnen, Henri Lotze, Finn Seesemann, and Moritz Stocker

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

Abstract
Imagine you are a computer scientist who enjoys attending conferences or workshops within the year. Sadly, your travel budget is limited, so you must select a subset of events you can travel to. When you are aware of all possible events and their costs at the beginning of the year, you can select the subset of the possible events that maximizes your happiness and is within your budget. On the other hand, if you are blind about the options, you will likely have a hard time when trying to decide if you want to register somewhere or not, and will likely regret decisions you made in the future. These scenarios can be modeled by knapsack variants, either by an offline or an online problem. However, both scenarios are somewhat unrealistic: Usually, you will not know the exact costs of each workshop at the beginning of the year. The online version, however, is too pessimistic, as you might already know which options there are and how much they cost roughly. At some point, you have to decide whether to register for some workshop, but then you are aware of the conference fee and the flight and hotel prices. We model this problem within the setting of online knapsack problems with estimates: in the beginning, you receive a list of potential items with their estimated size as well as the accuracy of the estimates. Then, the items are revealed one by one in an online fashion with their actual size, and you need to decide whether to take one or not. In this article, we show a best-possible algorithm for each estimate accuracy δ (i.e., when each actual item size can deviate by ± δ from the announced size) for both the simple knapsack (also known as subset sum problem) and the simple knapsack with removability.
Cite as

Jakub Balabán, Matthias Gehnen, Henri Lotze, Finn Seesemann, and Moritz Stocker. Online Knapsack Problems with Estimates. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 12:1-12:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{balaban_et_al:LIPIcs.MFCS.2025.12,
  author =	{Balab\'{a}n, Jakub and Gehnen, Matthias and Lotze, Henri and Seesemann, Finn and Stocker, Moritz},
  title =	{{Online Knapsack Problems with Estimates}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{12:1--12:19},
  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.2025.12},
  URN =		{urn:nbn:de:0030-drops-241190},
  doi =		{10.4230/LIPIcs.MFCS.2025.12},
  annote =	{Keywords: Knapsack, Online Knapsack, Removability, Estimate, Prediction}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.58
A New Impossibility Result for Online Bipartite Matching Problems

Authors: Flavio Chierichetti, Mirko Giacchini, Alessandro Panconesi, and Andrea Vattani

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

Abstract
Online Bipartite Matching with random user arrival is a fundamental problem in the online advertisement ecosystem. Over the last 30 years, many algorithms and impossibility results have been developed for this problem. In particular, the latest impossibility result was established by Manshadi, Oveis Gharan and Saberi [Manshadi et al., 2011] in 2011. Since then, several algorithms have been published in an effort to narrow the gap between the upper and the lower bounds on the competitive ratio. In this paper we show that no algorithm can achieve a competitive ratio better than 1- e/(e^e) = 0.82062…, improving upon the 0.823 upper bound presented in [Manshadi et al., 2011]. Our construction is simple to state, accompanied by a fully analytic proof, and yields a competitive ratio bound intriguingly similar to 1 - 1/e, the optimal competitive ratio for the fully adversarial Online Bipartite Matching problem. Although the tightness of our upper bound remains an open question, we show that our construction is extremal in a natural class of instances.
Cite as

Flavio Chierichetti, Mirko Giacchini, Alessandro Panconesi, and Andrea Vattani. A New Impossibility Result for Online Bipartite Matching Problems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 58:1-58:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chierichetti_et_al:LIPIcs.ICALP.2025.58,
  author =	{Chierichetti, Flavio and Giacchini, Mirko and Panconesi, Alessandro and Vattani, Andrea},
  title =	{{A New Impossibility Result for Online Bipartite Matching Problems}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{58:1--58:20},
  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.2025.58},
  URN =		{urn:nbn:de:0030-drops-234354},
  doi =		{10.4230/LIPIcs.ICALP.2025.58},
  annote =	{Keywords: Bipartite Matching, Random Graphs, Competitive Ratio}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.94
A Nearly Optimal Deterministic Algorithm for Online Transportation Problem

Authors: Tsubasa Harada and Toshiya Itoh

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

Abstract
For the online transportation problem with m server sites, it has long been known that the competitive ratio of any deterministic algorithm is at least 2m-1. Kalyanasundaram and Pruhs conjectured in 1998 that a deterministic (2m-1)-competitive algorithm exists for this problem, a conjecture that has remained open for over two decades. In this paper, we propose a new deterministic algorithm for the online transportation problem and show that it achieves a competitive ratio of at most 8m-5. This is the first O(m)-competitive deterministic algorithm, coming close to the lower bound of 2m-1 within a constant factor.
Cite as

Tsubasa Harada and Toshiya Itoh. A Nearly Optimal Deterministic Algorithm for Online Transportation Problem. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 94:1-94:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{harada_et_al:LIPIcs.ICALP.2025.94,
  author =	{Harada, Tsubasa and Itoh, Toshiya},
  title =	{{A Nearly Optimal Deterministic Algorithm for Online Transportation Problem}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{94:1--94:17},
  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.2025.94},
  URN =		{urn:nbn:de:0030-drops-234712},
  doi =		{10.4230/LIPIcs.ICALP.2025.94},
  annote =	{Keywords: Online algorithms, Competitive analysis, Online metric matching, Online weighted matching, Online minimum weight perfect matching, Online transportation problem, Online facility assignment, Greedy algorithm}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.53
A PTAS for TSP with Neighbourhoods over Parallel Line Segments

Authors: Benyamin Ghaseminia and Mohammad R. Salavatipour

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
We consider the Travelling Salesman Problem with Neighbourhoods (TSPN) on the Euclidean plane (ℝ²) and present a Polynomial-Time Approximation Scheme (PTAS) when the neighbourhoods are parallel line segments with lengths between [1, λ] for any constant value λ ≥ 1. In TSPN (which generalizes classic TSP), each client represents a set (or neighbourhood) of points in a metric and the goal is to find a minimum cost TSP tour that visits at least one point from each client set. In the Euclidean setting, each neighbourhood is a region on the plane. TSPN is significantly more difficult than classic TSP even in the Euclidean setting, as it captures group TSP. A notable case of TSPN is when each neighbourhood is a line segment. Although there are PTASs for when neighbourhoods are fat objects (with limited overlap), TSPN over line segments is APX-hard even if all the line segments have unit length. For parallel (unit) line segments, the best approximation factor is 3√2 from more than two decades ago. The PTAS we present in this paper settles the approximability of this case of the problem. Our algorithm finds a (1 + ε)-factor approximation for an instance of the problem for n segments with lengths in [1,λ] in time n^O(λ/ε³).
Cite as

Benyamin Ghaseminia and Mohammad R. Salavatipour. A PTAS for TSP with Neighbourhoods over Parallel Line Segments. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 53:1-53:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ghaseminia_et_al:LIPIcs.SoCG.2025.53,
  author =	{Ghaseminia, Benyamin and Salavatipour, Mohammad R.},
  title =	{{A PTAS for TSP with Neighbourhoods over Parallel Line Segments}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{53:1--53:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.53},
  URN =		{urn:nbn:de:0030-drops-232058},
  doi =		{10.4230/LIPIcs.SoCG.2025.53},
  annote =	{Keywords: Approximation Scheme, TSP Neighbourhood, Parallel line segments}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.62
On Approximability of 𝓁₂² Min-Sum Clustering

Authors: Karthik C. S., Euiwoong Lee, Yuval Rabani, Chris Schwiegelshohn, and Samson Zhou

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
The 𝓁₂² min-sum k-clustering problem is to partition an input set into clusters C_1,…,C_k to minimize ∑_{i=1}^k ∑_{p,q ∈ C_i} ‖p-q‖₂². Although 𝓁₂² min-sum k-clustering is NP-hard, it is not known whether it is NP-hard to approximate 𝓁₂² min-sum k-clustering beyond a certain factor. In this paper, we give the first hardness-of-approximation result for the 𝓁₂² min-sum k-clustering problem. We show that it is NP-hard to approximate the objective to a factor better than 1.056 and moreover, assuming a balanced variant of the Johnson Coverage Hypothesis, it is NP-hard to approximate the objective to a factor better than 1.327. We then complement our hardness result by giving a fast PTAS for 𝓁₂² min-sum k-clustering. Specifically, our algorithm runs in time O(n^{1+o(1)}d⋅ 2^{(k/ε)^O(1)}), which is the first nearly linear time algorithm for this problem. We also consider a learning-augmented setting, where the algorithm has access to an oracle that outputs a label i ∈ [k] for input point, thereby implicitly partitioning the input dataset into k clusters that induce an approximately optimal solution, up to some amount of adversarial error α ∈ [0,1/2). We give a polynomial-time algorithm that outputs a (1+γα)/(1-α)²-approximation to 𝓁₂² min-sum k-clustering, for a fixed constant γ > 0.
Cite as

Karthik C. S., Euiwoong Lee, Yuval Rabani, Chris Schwiegelshohn, and Samson Zhou. On Approximability of 𝓁₂² Min-Sum Clustering. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 62:1-62:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{karthikc.s._et_al:LIPIcs.SoCG.2025.62,
  author =	{Karthik C. S. and Lee, Euiwoong and Rabani, Yuval and Schwiegelshohn, Chris and Zhou, Samson},
  title =	{{On Approximability of 𝓁₂² Min-Sum Clustering}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{62:1--62:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.62},
  URN =		{urn:nbn:de:0030-drops-232142},
  doi =		{10.4230/LIPIcs.SoCG.2025.62},
  annote =	{Keywords: Clustering, hardness of approximation, polynomial-time approximation schemes, learning-augmented algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.44
Learning-Augmented Streaming Algorithms for Approximating MAX-CUT

Authors: Yinhao Dong, Pan Peng, and Ali Vakilian

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

Abstract
We study learning-augmented streaming algorithms for estimating the value of MAX-CUT in a graph. In the classical streaming model, while a 1/2-approximation for estimating the value of MAX-CUT can be trivially achieved with O(1) words of space, Kapralov and Krachun [STOC’19] showed that this is essentially the best possible: for any ε > 0, any (randomized) single-pass streaming algorithm that achieves an approximation ratio of at least 1/2 + ε requires Ω(n / 2^poly(1/ε)) space. We show that it is possible to surpass the 1/2-approximation barrier using just O(1) words of space by leveraging a (machine learned) oracle. Specifically, we consider streaming algorithms that are equipped with an ε-accurate oracle that for each vertex in the graph, returns its correct label in {-1, +1}, corresponding to an optimal MAX-CUT solution in the graph, with some probability 1/2 + ε, and the incorrect label otherwise. Within this framework, we present a single-pass algorithm that approximates the value of MAX-CUT to within a factor of 1/2 + Ω(ε²) with probability at least 2/3 for insertion-only streams, using only poly(1/ε) words of space. We also extend our algorithm to fully dynamic streams while maintaining a space complexity of poly(1/ε,log n) words.
Cite as

Yinhao Dong, Pan Peng, and Ali Vakilian. Learning-Augmented Streaming Algorithms for Approximating MAX-CUT. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 44:1-44:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dong_et_al:LIPIcs.ITCS.2025.44,
  author =	{Dong, Yinhao and Peng, Pan and Vakilian, Ali},
  title =	{{Learning-Augmented Streaming Algorithms for Approximating MAX-CUT}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{44:1--44:24},
  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.2025.44},
  URN =		{urn:nbn:de:0030-drops-226728},
  doi =		{10.4230/LIPIcs.ITCS.2025.44},
  annote =	{Keywords: Learning-Augmented Algorithms, Graph Streaming Algorithms, MAX-CUT}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.9
Computing Smallest Convex Intersecting Polygons

Authors: Antonios Antoniadis, Mark de Berg, Sándor Kisfaludi-Bak, and Antonis Skarlatos

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

Abstract
A polygon C is an intersecting polygon for a set O of objects in ℝ² if C intersects each object in O, where the polygon includes its interior. We study the problem of computing the minimum-perimeter intersecting polygon and the minimum-area convex intersecting polygon for a given set O of objects. We present an FPTAS for both problems for the case where O is a set of possibly intersecting convex polygons in the plane of total complexity n. Furthermore, we present an exact polynomial-time algorithm for the minimum-perimeter intersecting polygon for the case where O is a set of n possibly intersecting segments in the plane. So far, polynomial-time exact algorithms were only known for the minimum perimeter intersecting polygon of lines or of disjoint segments.
Cite as

Antonios Antoniadis, Mark de Berg, Sándor Kisfaludi-Bak, and Antonis Skarlatos. Computing Smallest Convex Intersecting Polygons. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 9:1-9:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{antoniadis_et_al:LIPIcs.ESA.2022.9,
  author =	{Antoniadis, Antonios and de Berg, Mark and Kisfaludi-Bak, S\'{a}ndor and Skarlatos, Antonis},
  title =	{{Computing Smallest Convex Intersecting Polygons}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{9:1--9:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.9},
  URN =		{urn:nbn:de:0030-drops-169470},
  doi =		{10.4230/LIPIcs.ESA.2022.9},
  annote =	{Keywords: convex hull, imprecise points, computational geometry}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2022.9
A Novel Prediction Setup for Online Speed-Scaling

Authors: Antonios Antoniadis, Peyman Jabbarzade, and Golnoosh Shahkarami

Published in: LIPIcs, Volume 227, 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)

Abstract
Given the rapid rise in energy demand by data centers and computing systems in general, it is fundamental to incorporate energy considerations when designing (scheduling) algorithms. Machine learning can be a useful approach in practice by predicting the future load of the system based on, for example, historical data. However, the effectiveness of such an approach highly depends on the quality of the predictions and can be quite far from optimal when predictions are sub-par. On the other hand, while providing a worst-case guarantee, classical online algorithms can be pessimistic for large classes of inputs arising in practice. This paper, in the spirit of the new area of machine learning augmented algorithms, attempts to obtain the best of both worlds for the classical, deadline based, online speed-scaling problem: Based on the introduction of a novel prediction setup, we develop algorithms that (i) obtain provably low energy-consumption in the presence of adequate predictions, and (ii) are robust against inadequate predictions, and (iii) are smooth, i.e., their performance gradually degrades as the prediction error increases.
Cite as

Antonios Antoniadis, Peyman Jabbarzade, and Golnoosh Shahkarami. A Novel Prediction Setup for Online Speed-Scaling. In 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 227, pp. 9:1-9:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{antoniadis_et_al:LIPIcs.SWAT.2022.9,
  author =	{Antoniadis, Antonios and Jabbarzade, Peyman and Shahkarami, Golnoosh},
  title =	{{A Novel Prediction Setup for Online Speed-Scaling}},
  booktitle =	{18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)},
  pages =	{9:1--9:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-236-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{227},
  editor =	{Czumaj, Artur and Xin, Qin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2022.9},
  URN =		{urn:nbn:de:0030-drops-161693},
  doi =		{10.4230/LIPIcs.SWAT.2022.9},
  annote =	{Keywords: learning augmented algorithms, speed-scaling, energy-efficiency, scheduling theory, online algorithms}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2022.10
On the Approximability of the Traveling Salesman Problem with Line Neighborhoods

Authors: Antonios Antoniadis, Sándor Kisfaludi-Bak, Bundit Laekhanukit, and Daniel Vaz

Published in: LIPIcs, Volume 227, 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)

Abstract
We study the variant of the Euclidean Traveling Salesman problem where instead of a set of points, we are given a set of lines as input, and the goal is to find the shortest tour that visits each line. The best known upper and lower bounds for the problem in ℝ^d, with d ≥ 3, are NP-hardness and an O(log³ n)-approximation algorithm which is based on a reduction to the group Steiner tree problem. We show that TSP with lines in ℝ^d is APX-hard for any d ≥ 3. More generally, this implies that TSP with k-dimensional flats does not admit a PTAS for any 1 ≤ k ≤ d-2 unless P = NP, which gives a complete classification regarding the existence of polynomial time approximation schemes for these problems, as there are known PTASes for k = 0 (i.e., points) and k = d-1 (hyperplanes). We are able to give a stronger inapproximability factor for d = O(log n) by showing that TSP with lines does not admit a (2-ε)-approximation in d dimensions under the Unique Games Conjecture. On the positive side, we leverage recent results on restricted variants of the group Steiner tree problem in order to give an O(log² n)-approximation algorithm for the problem, albeit with a running time of n^{O(log log n)}.
Cite as

Antonios Antoniadis, Sándor Kisfaludi-Bak, Bundit Laekhanukit, and Daniel Vaz. On the Approximability of the Traveling Salesman Problem with Line Neighborhoods. In 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 227, pp. 10:1-10:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{antoniadis_et_al:LIPIcs.SWAT.2022.10,
  author =	{Antoniadis, Antonios and Kisfaludi-Bak, S\'{a}ndor and Laekhanukit, Bundit and Vaz, Daniel},
  title =	{{On the Approximability of the Traveling Salesman Problem with Line Neighborhoods}},
  booktitle =	{18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)},
  pages =	{10:1--10:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-236-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{227},
  editor =	{Czumaj, Artur and Xin, Qin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2022.10},
  URN =		{urn:nbn:de:0030-drops-161706},
  doi =		{10.4230/LIPIcs.SWAT.2022.10},
  annote =	{Keywords: Traveling Salesman with neighborhoods, Group Steiner Tree, Geometric approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2021.51
Skeletons and Minimum Energy Scheduling

Authors: Antonios Antoniadis, Gunjan Kumar, and Nikhil Kumar

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

Abstract
Consider the problem where n jobs, each with a release time, a deadline and a required processing time are to be feasibly scheduled in a single- or multi-processor setting so as to minimize the total energy consumption of the schedule. A processor has two available states: a sleep state where no energy is consumed but also no processing can take place, and an active state which consumes energy at a rate of one, and in which jobs can be processed. Transitioning from the active to the sleep does not incur any further energy cost, but transitioning from the sleep to the active state requires q energy units. Jobs may be preempted and (in the multi-processor case) migrated. The single-processor case of the problem is known to be solvable in polynomial time via an involved dynamic program, whereas the only known approximation algorithm for the multi-processor case attains an approximation factor of 3 and is based on rounding the solution to a linear programming relaxation of the problem. In this work, we present efficient and combinatorial approximation algorithms for both the single- and the multi-processor setting. Before, only an algorithm based on linear programming was known for the multi-processor case. Our algorithms build upon the concept of a skeleton, a basic (and not necessarily feasible) schedule that captures the fact that some processor(s) must be active at some time point during an interval. Finally, we further demonstrate the power of skeletons by providing a 2-approximation algorithm for the multiprocessor case, thus improving upon the recent breakthrough 3-approximation result. Our algorithm is based on a novel rounding scheme of a linear-programming relaxation of the problem which incorporates skeletons.
Cite as

Antonios Antoniadis, Gunjan Kumar, and Nikhil Kumar. Skeletons and Minimum Energy Scheduling. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 51:1-51:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{antoniadis_et_al:LIPIcs.ISAAC.2021.51,
  author =	{Antoniadis, Antonios and Kumar, Gunjan and Kumar, Nikhil},
  title =	{{Skeletons and Minimum Energy Scheduling}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{51:1--51:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.51},
  URN =		{urn:nbn:de:0030-drops-154849},
  doi =		{10.4230/LIPIcs.ISAAC.2021.51},
  annote =	{Keywords: scheduling, energy-efficiency, approximation algorithms, dynamic programming, combinatorial algorithms}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.17
Breaking the Barrier Of 2 for the Competitiveness of Longest Queue Drop

Authors: Antonios Antoniadis, Matthias Englert, Nicolaos Matsakis, and Pavel Veselý

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

Abstract
We consider the problem of managing the buffer of a shared-memory switch that transmits packets of unit value. A shared-memory switch consists of an input port, a number of output ports, and a buffer with a specific capacity. In each time step, an arbitrary number of packets arrive at the input port, each packet designated for one output port. Each packet is added to the queue of the respective output port. If the total number of packets exceeds the capacity of the buffer, some packets have to be irrevocably rejected. At the end of each time step, each output port transmits a packet in its queue and the goal is to maximize the number of transmitted packets. The Longest Queue Drop (LQD) online algorithm accepts any arriving packet to the buffer. However, if this results in the buffer exceeding its memory capacity, then LQD drops a packet from the back of whichever queue is currently the longest, breaking ties arbitrarily. The LQD algorithm was first introduced in 1991, and is known to be 2-competitive since 2001. Although LQD remains the best known online algorithm for the problem and is of practical interest, determining its true competitiveness is a long-standing open problem. We show that LQD is 1.707-competitive, establishing the first (2-ε) upper bound for the competitive ratio of LQD, for a constant ε > 0.
Cite as

Antonios Antoniadis, Matthias Englert, Nicolaos Matsakis, and Pavel Veselý. Breaking the Barrier Of 2 for the Competitiveness of Longest Queue Drop. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 17:1-17:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{antoniadis_et_al:LIPIcs.ICALP.2021.17,
  author =	{Antoniadis, Antonios and Englert, Matthias and Matsakis, Nicolaos and Vesel\'{y}, Pavel},
  title =	{{Breaking the Barrier Of 2 for the Competitiveness of Longest Queue Drop}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{17:1--17:20},
  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.2021.17},
  URN =		{urn:nbn:de:0030-drops-140864},
  doi =		{10.4230/LIPIcs.ICALP.2021.17},
  annote =	{Keywords: buffer management, online scheduling, online algorithms, longest queue drop}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.8
On the Complexity of Anchored Rectangle Packing

Authors: Antonios Antoniadis, Felix Biermeier, Andrés Cristi, Christoph Damerius, Ruben Hoeksma, Dominik Kaaser, Peter Kling, and Lukas Nölke

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

Abstract
In the Anchored Rectangle Packing (ARP) problem, we are given a set of points P in the unit square [0,1]^2 and seek a maximum-area set of axis-aligned interior-disjoint rectangles S, each of which is anchored at a point p in P. In the most prominent variant - Lower-Left-Anchored Rectangle Packing (LLARP) - rectangles are anchored in their lower-left corner. Freedman [W. T. Tutte (Ed.), 1969] conjectured in 1969 that, if (0,0) in P, then there is a LLARP that covers an area of at least 0.5. Somewhat surprisingly, this conjecture remains open to this day, with the best known result covering an area of 0.091 [Dumitrescu and Tóth, 2015]. Maybe even more surprisingly, it is not known whether LLARP - or any ARP-problem with only one anchor - is NP-hard. In this work, we first study the Center-Anchored Rectangle Packing (CARP) problem, where rectangles are anchored in their center. We prove NP-hardness and provide a PTAS. In fact, our PTAS applies to any ARP problem where the anchor lies in the interior of the rectangles. Afterwards, we turn to the LLARP problem and investigate two different resource-augmentation settings: In the first we allow an epsilon-perturbation of the input P, whereas in the second we permit an epsilon-overlap between rectangles. For the former setting, we give an algorithm that covers at least as much area as an optimal solution of the original problem. For the latter, we give an (1 - epsilon)-approximation.
Cite as

Antonios Antoniadis, Felix Biermeier, Andrés Cristi, Christoph Damerius, Ruben Hoeksma, Dominik Kaaser, Peter Kling, and Lukas Nölke. On the Complexity of Anchored Rectangle Packing. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 8:1-8:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{antoniadis_et_al:LIPIcs.ESA.2019.8,
  author =	{Antoniadis, Antonios and Biermeier, Felix and Cristi, Andr\'{e}s and Damerius, Christoph and Hoeksma, Ruben and Kaaser, Dominik and Kling, Peter and N\"{o}lke, Lukas},
  title =	{{On the Complexity of Anchored Rectangle Packing}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{8:1--8:14},
  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.2019.8},
  URN =		{urn:nbn:de:0030-drops-111297},
  doi =		{10.4230/LIPIcs.ESA.2019.8},
  annote =	{Keywords: anchored rectangle, rectangle packing, resource augmentation, PTAS, NP, hardness}
}
Document
DOI: 10.4230/LIPIcs.STACS.2018.5
Approximating Airports and Railways

Authors: Anna Adamaszek, Antonios Antoniadis, Amit Kumar, and Tobias Mömke

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

Abstract
In this paper we consider the airport and railway problem (AR), which combines capacitated facility location with network design, both in the general metric and the two-dimensional Euclidean space. An instance of the airport and railway problem consists of a set of points in the corresponding metric, together with a non-negative weight for each point, and a parameter k. The points represent cities, the weights denote costs of opening an airport in the corresponding city, and the parameter k is a maximum capacity of an airport. The goal is to construct a minimum cost network of airports and railways connecting all the cities, where railways correspond to edges connecting pairs of points, and the cost of a railway is equal to the distance between the corresponding points. The network is partitioned into components, where each component contains an open airport, and spans at most k cities. For the Euclidean case, any points in the plane can be used as Steiner vertices of the network. We obtain the first bicriteria approximation algorithm for AR for the general metric case, which yields a 4-approximate solution with a resource augmentation of the airport capacity k by a factor of 2. More generally, for any parameter 0 < p <= 1 where pk is an integer we develop a (4/3)(2 + 1/p)-approximation algorithm for metric AR with a resource augmentation by a factor of 1 + p. Furthermore, we obtain the first constant factor approximation algorithm that does not resort to resource augmentation for AR in the Euclidean plane. Additionally, for the Euclidean setting we provide a quasi-polynomial time approximation scheme for the same problem with a resource augmentation by a factor of 1 + mu on the airport capacity, for any fixed mu > 0.
Cite as

Anna Adamaszek, Antonios Antoniadis, Amit Kumar, and Tobias Mömke. Approximating Airports and Railways. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 5:1-5:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{adamaszek_et_al:LIPIcs.STACS.2018.5,
  author =	{Adamaszek, Anna and Antoniadis, Antonios and Kumar, Amit and M\"{o}mke, Tobias},
  title =	{{Approximating Airports and Railways}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{5:1--5:13},
  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.2018.5},
  URN =		{urn:nbn:de:0030-drops-85183},
  doi =		{10.4230/LIPIcs.STACS.2018.5},
  annote =	{Keywords: Network Design, Facility Location, Approximation Algorithms, PTAS, Metric, Euclidean}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.31
A QPTAS for the General Scheduling Problem with Identical Release Dates

Authors: Antonios Antoniadis, Ruben Hoeksma, Julie Meißner, José Verschae, and Andreas Wiese

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

Abstract
The General Scheduling Problem (GSP) generalizes scheduling problems with sum of cost objectives such as weighted flow time and weighted tardiness. Given a set of jobs with processing times, release dates, and job dependent cost functions, we seek to find a minimum cost preemptive schedule on a single machine. The best known algorithm for this problem and also for weighted flow time/tardiness is an O(loglog P)-approximation (where P denotes the range of the job processing times), while the best lower bound shows only strong NP-hardness. When release dates are identical there is also a gap: the problem remains strongly NP-hard and the best known approximation algorithm has a ratio of e+\epsilon (running in quasi-polynomial time). We reduce the latter gap by giving a QPTAS if the numbers in the input are quasi-polynomially bounded, ruling out the existence of an APX-hardness proof unless NP\subseteq DTIME(2^polylog(n)). Our techniques are based on the QPTAS known for the UFP-Cover problem, a particular case of GSP where we must pick a subset of intervals (jobs) on the real line with associated heights and costs. If an interval is selected, its height will help cover a given demand on any point contained within the interval. We reduce our problem to a generalization of UFP-Cover and use a sophisticated divide-and-conquer procedure with interdependent non-symmetric subproblems. We also present a pseudo-polynomial time approximation scheme for two variants of UFP-Cover. For the case of agreeable intervals we give an algorithm based on a new dynamic programming approach which might be useful for other problems of this type. The second one is a resource augmentation setting where we are allowed to slightly enlarge each interval.
Cite as

Antonios Antoniadis, Ruben Hoeksma, Julie Meißner, José Verschae, and Andreas Wiese. A QPTAS for the General Scheduling Problem with Identical Release Dates. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{antoniadis_et_al:LIPIcs.ICALP.2017.31,
  author =	{Antoniadis, Antonios and Hoeksma, Ruben and Mei{\ss}ner, Julie and Verschae, Jos\'{e} and Wiese, Andreas},
  title =	{{A QPTAS for the General Scheduling Problem with Identical Release Dates}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{31:1--31:14},
  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.2017.31},
  URN =		{urn:nbn:de:0030-drops-74575},
  doi =		{10.4230/LIPIcs.ICALP.2017.31},
  annote =	{Keywords: Generalized Scheduling, QPTAS, Unsplittable Flows}
}
Document
DOI: 10.4230/LIPIcs.STACS.2016.6
Airports and Railways: Facility Location Meets Network Design

Authors: Anna Adamaszek, Antonios Antoniadis, and Tobias Mömke

Published in: LIPIcs, Volume 47, 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)

Abstract
We introduce a new framework of Airport and Railway Problems, which combines capacitated facility location with network design. In this framework we are given a graph with weights on the vertices and on the edges, together with a parameter k. The vertices of the graph represent cities, and weights denote respectively the costs of opening airports in the cities and building railways that connect pairs of cities. The parameter $k$ can be thought of as the capacity of an airport. The goal is to construct a minimum cost network of airports and railways connecting the cities, where each connected component in the network spans at most k vertices, contains an open airport, and the network satisfies some additional requirements specific to the problem in the framework. We consider two problems in this framework. In the AR_F problem there are no additional requirements for the network. This problem is related to capacitated facility location. In the AR_P problem, we require each component to be a path with airports at both endpoints. AR_P is a relaxation of the capacitated vehicle routing problem (CVRP). We consider the problems in the two-dimensional Euclidean setting. We show that both AR_F and AR_P are NP-hard, even for uniform vertex weights (i.e., when the cost of building an airport is the same for all cities). On the positive side, we provide polynomial time approximation schemes for AR_F and AR_P when vertex weights are uniform. We also investigate AR_F and AR_P for k = infinity. In this setting we present an exact polynomial time algorithm for AR_F with general vertex costs, which also works for general edge costs. In contrast to AR_F, AR_P remains NP-hard when k = infinity, and we present a polynomial time approximation scheme for general vertex weights. We believe that our PTAS for AR_P with uniform vertex weights and arbitrary k brings us closer towards a PTAS for Euclidean CVRP, for which the main difficulty is to deal with paths of length at most k.
Cite as

Anna Adamaszek, Antonios Antoniadis, and Tobias Mömke. Airports and Railways: Facility Location Meets Network Design. In 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 47, pp. 6:1-6:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{adamaszek_et_al:LIPIcs.STACS.2016.6,
  author =	{Adamaszek, Anna and Antoniadis, Antonios and M\"{o}mke, Tobias},
  title =	{{Airports and Railways: Facility Location Meets Network Design}},
  booktitle =	{33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
  pages =	{6:1--6:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-001-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{47},
  editor =	{Ollinger, Nicolas and Vollmer, Heribert},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2016.6},
  URN =		{urn:nbn:de:0030-drops-57074},
  doi =		{10.4230/LIPIcs.STACS.2016.6},
  annote =	{Keywords: approximation algorithms, geometric approximation, facility location, network design, PTAS}
}
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