12 Search Results for "Touitou, Noam"

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
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.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.2025.70
Colorful Vertex Recoloring of Bipartite Graphs

Authors: Boaz Patt-Shamir, Adi Rosén, and Seeun William Umboh

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

Abstract
We consider the problem of vertex recoloring: we are given n vertices with their initial coloring, and edges arrive in an online fashion. The algorithm is required to maintain a valid coloring by means of vertex recoloring, where recoloring a vertex incurs a cost. The problem abstracts a scenario of job placement in machines (possibly in the cloud), where vertices represent jobs, colors represent machines, and edges represent "anti affinity" (disengagement) constraints. Online coloring in this setting is a hard problem, and only a few cases were analyzed. One family of instances which is fairly well-understood is bipartite graphs, i.e., instances in which two colors are sufficient to satisfy all constraints. In this case it is known that the competitive ratio of vertex recoloring is Θ(log n). In this paper we propose a generalization of the problem, which allows using additional colors (possibly at a higher cost), to improve overall performance. Concretely, we analyze the simple case of bipartite graphs of bounded largest bond (a bond of a connected graph is an edge-cut that partitions the graph into two connected components). From the upper bound perspective, we propose two algorithms. One algorithm exhibits a trade-off for the uniform-cost case: given Ω(logβ) ≤ c ≤ O(log n) colors, the algorithm guarantees that its cost is at most O((log n)/c) times the optimal offline cost for two colors, where n is the number of vertices and β is the size of the largest bond of the graph. The other algorithm is designed for the case where the additional colors come at a higher cost, D > 1: given Δ additional colors, where Δ is the maximum degree in the graph, the algorithm guarantees a competitive ratio of O(log D). From the lower bounds viewpoint, we show that if the cost of the extra colors is D > 1, no algorithm (even randomized) can achieve a competitive ratio of o(log D). We also show that in the case of general bipartite graphs (i.e., of unbounded bond size), any deterministic online algorithm has competitive ratio Ω(min(D,log n)).
Cite as

Boaz Patt-Shamir, Adi Rosén, and Seeun William Umboh. Colorful Vertex Recoloring of Bipartite Graphs. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 70:1-70:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{pattshamir_et_al:LIPIcs.STACS.2025.70,
  author =	{Patt-Shamir, Boaz and Ros\'{e}n, Adi and Umboh, Seeun William},
  title =	{{Colorful Vertex Recoloring of Bipartite Graphs}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{70:1--70:19},
  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.2025.70},
  URN =		{urn:nbn:de:0030-drops-228955},
  doi =		{10.4230/LIPIcs.STACS.2025.70},
  annote =	{Keywords: online algorithms, competitive analysis, resource augmentation, graph coloring}
}
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.
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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
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.12
Universal Optimization for Non-Clairvoyant Subadditive Joint Replenishment

Authors: Tomer Ezra, Stefano Leonardi, Michał Pawłowski, Matteo Russo, and Seeun William Umboh

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
The online joint replenishment problem (JRP) is a fundamental problem in the area of online problems with delay. Over the last decade, several works have studied generalizations of JRP with different cost functions for servicing requests. Most prior works on JRP and its generalizations have focused on the clairvoyant setting. Recently, Touitou [Noam Touitou, 2023] developed a non-clairvoyant framework that provided an O(√{n log n}) upper bound for a wide class of generalized JRP, where n is the number of request types. We advance the study of non-clairvoyant algorithms by providing a simpler, modular framework that matches the competitive ratio established by Touitou for the same class of generalized JRP. Our key insight is to leverage universal algorithms for Set Cover to approximate arbitrary monotone subadditive functions using a simple class of functions termed disjoint. This allows us to reduce the problem to several independent instances of the TCP Acknowledgement problem, for which a simple 2-competitive non-clairvoyant algorithm is known. The modularity of our framework is a major advantage as it allows us to tailor the reduction to specific problems and obtain better competitive ratios. In particular, we obtain tight O(√n)-competitive algorithms for two significant problems: Multi-Level Aggregation and Weighted Symmetric Subadditive Joint Replenishment. We also show that, in contrast, Touitou’s algorithm is Ω(√{n log n})-competitive for both of these problems.
Cite as

Tomer Ezra, Stefano Leonardi, Michał Pawłowski, Matteo Russo, and Seeun William Umboh. Universal Optimization for Non-Clairvoyant Subadditive Joint Replenishment. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 12:1-12:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ezra_et_al:LIPIcs.APPROX/RANDOM.2024.12,
  author =	{Ezra, Tomer and Leonardi, Stefano and Paw{\l}owski, Micha{\l} and Russo, Matteo and Umboh, Seeun William},
  title =	{{Universal Optimization for Non-Clairvoyant Subadditive Joint Replenishment}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{12:1--12:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.12},
  URN =		{urn:nbn:de:0030-drops-210050},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.12},
  annote =	{Keywords: Set Cover, Joint Replenishment, TCP-Acknowledgment, Subadditive Function Approximation, Multi-Level Aggregation}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.105
Frameworks for Nonclairvoyant Network Design with Deadlines or Delay

Authors: Noam Touitou

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
Clairvoyant network design with deadlines or delay has been studied extensively, culminating in an O(log n)-competitive general framework, where n is the number of possible request types (Azar and Touitou, FOCS 2020). In the nonclairvoyant setting, the problem becomes much harder, as Ω(√n) lower bounds are known for certain problems (Azar et al., STOC 2017). However, no frameworks are known for the nonclairvoyant setting, and previous work focuses only on specific problems, e.g., multilevel aggregation (Le et al., SODA 2023). In this paper, we present the first nonclairvoyant frameworks for network design with deadlines or delay. These frameworks are nearly optimal: their competitive ratio is Õ(√n), which matches known lower bounds up to logarithmic factors.
Cite as

Noam Touitou. Frameworks for Nonclairvoyant Network Design with Deadlines or Delay. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 105:1-105:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{touitou:LIPIcs.ICALP.2023.105,
  author =	{Touitou, Noam},
  title =	{{Frameworks for Nonclairvoyant Network Design with Deadlines or Delay}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{105:1--105:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel 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.2023.105},
  URN =		{urn:nbn:de:0030-drops-181578},
  doi =		{10.4230/LIPIcs.ICALP.2023.105},
  annote =	{Keywords: Online, Deadlines, Delay, Network Design, Nonclairvoyant}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.16
Distortion-Oblivious Algorithms for Scheduling on Multiple Machines

Authors: Yossi Azar, Eldad Peretz, and Noam Touitou

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
We consider the classic online problem of scheduling on multiple machines to minimize total flow time and total stretch where the input consists of estimates on the processing time provided for each job once released. The performance of such algorithms should depend on μ, the error in the estimates of the processing time for that instance (such an algorithm is called a distortion oblivious algorithm). Previously, a distortion oblivious algorithm to minimize flow time was provided only for a single machine. In this paper we extend the work to multiple machines and also consider the total stretch objective. In particular, we design a non-migrative distortion oblivious algorithm to minimize total flow time with a competitive ratio of O(μ log P), where P is the ratio between the maximum to minimum processing time. We show that with immediate-dispatching one cannot achieve a competitive ratio which is a function of μ and P; moreover, a competitive ratio which is sub-polynomial in the number of jobs is also impossible. We also present the first distortion-oblivious algorithm for minimizing the stretch time, both on a single and on multiple machines. The competitive ratio of these algorithms are O(μ²) which is optimal as we also prove a matching Ω(μ²) lower bound.
Cite as

Yossi Azar, Eldad Peretz, and Noam Touitou. Distortion-Oblivious Algorithms for Scheduling on Multiple Machines. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{azar_et_al:LIPIcs.ISAAC.2022.16,
  author =	{Azar, Yossi and Peretz, Eldad and Touitou, Noam},
  title =	{{Distortion-Oblivious Algorithms for Scheduling on Multiple Machines}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.16},
  URN =		{urn:nbn:de:0030-drops-173010},
  doi =		{10.4230/LIPIcs.ISAAC.2022.16},
  annote =	{Keywords: Online, Scheduling, Predictions, Stretch, Flow Time}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.13
Competitive Vertex Recoloring

Authors: Yossi Azar, Chay Machluf, Boaz Patt-Shamir, and Noam Touitou

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
Motivated by placement of jobs in physical machines, we introduce and analyze the problem of online recoloring, or online disengagement. In this problem, we are given a set of n weighted vertices and a k-coloring of the vertices (vertices represent jobs, and colors represent physical machines). Edges, representing conflicts between jobs, are inserted in an online fashion. After every edge insertion, the algorithm must output a proper k-coloring of the vertices. The cost of a recoloring is the sum of weights of vertices whose color changed. Our aim is to minimize the competitive ratio of the algorithm, i.e., the ratio between the cost paid by the online algorithm and the cost paid by an optimal, offline algorithm. We consider a couple of polynomially-solvable coloring variants. Specifically, for 2-coloring bipartite graphs we present an O(log n)-competitive deterministic algorithm and an Ω(log n) lower bound on the competitive ratio of randomized algorithms. For (Δ+1)-coloring, we present tight bounds of Θ(Δ) and Θ(logΔ) on the competitive ratios of deterministic and randomized algorithms, respectively (where Δ denotes the maximum degree). We also consider a dynamic case which allows edge deletions as well as insertions. All our algorithms are applicable to the case where vertices are weighted and the cost of recoloring a vertex is its weight. All our lower bounds hold even in the unweighted case.
Cite as

Yossi Azar, Chay Machluf, Boaz Patt-Shamir, and Noam Touitou. Competitive Vertex Recoloring. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 13:1-13:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{azar_et_al:LIPIcs.ICALP.2022.13,
  author =	{Azar, Yossi and Machluf, Chay and Patt-Shamir, Boaz and Touitou, Noam},
  title =	{{Competitive Vertex Recoloring}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{13:1--13:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.13},
  URN =		{urn:nbn:de:0030-drops-163542},
  doi =		{10.4230/LIPIcs.ICALP.2022.13},
  annote =	{Keywords: coloring with recourse, anti-affinity constraints}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2021.53
Nearly-Tight Lower Bounds for Set Cover and Network Design with Deadlines/Delay

Authors: Noam Touitou

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

Abstract
In network design problems with deadlines/delay, an algorithm must make transmissions over time to satisfy connectivity requests on a graph. To satisfy a request, a transmission must be made that provides the desired connectivity. In the deadline case, this transmission must occur inside a time window associated with the request. In the delay case, the transmission should be as soon as possible after the request’s release, to avoid delay cost. In FOCS 2020, frameworks were given which reduce a network design problem with deadlines/delay to its classic, offline variant, while incurring an additional competitiveness loss factor of O(log n), where n is the number of vertices in the graph. Trying to improve upon this loss factor is thus a natural research direction. The frameworks of FOCS 2020 also apply to set cover with deadlines/delay, in which requests arrive on the elements of a universe over time, and the algorithm must transmit sets to serve them. In this problem, a universe of sets and elements is given, requests arrive on elements over time, and the algorithm must transmit sets to serve them. In this paper, we give nearly tight lower bounds for set cover with deadlines/delay. These lower bounds imply nearly-tight lower bounds of Ω(log n / log log n) for a few network design problems, such as node-weighted Steiner forest and directed Steiner tree. Our results imply that the frameworks in FOCS 2020 are essentially optimal, and improve quadratically over the best previously-known lower bounds.
Cite as

Noam Touitou. Nearly-Tight Lower Bounds for Set Cover and Network Design with Deadlines/Delay. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 53:1-53:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{touitou:LIPIcs.ISAAC.2021.53,
  author =	{Touitou, Noam},
  title =	{{Nearly-Tight Lower Bounds for Set Cover and Network Design with Deadlines/Delay}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{53:1--53:16},
  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.2021.53},
  URN =		{urn:nbn:de:0030-drops-154865},
  doi =		{10.4230/LIPIcs.ISAAC.2021.53},
  annote =	{Keywords: Network Design, Deadlines, Delay, Online, Set Cover}
}
Document
DOI: 10.4230/LIPIcs.ESA.2020.8
Set Cover with Delay - Clairvoyance Is Not Required

Authors: Yossi Azar, Ashish Chiplunkar, Shay Kutten, and Noam Touitou

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

Abstract
In most online problems with delay, clairvoyance (i.e. knowing the future delay of a request upon its arrival) is required for polylogarithmic competitiveness. In this paper, we show that this is not the case for set cover with delay (SCD) - specifically, we present the first non-clairvoyant algorithm, which is O(log n log m)-competitive, where n is the number of elements and m is the number of sets. This matches the best known result for the classic online set cover (a special case of non-clairvoyant SCD). Moreover, clairvoyance does not allow for significant improvement - we present lower bounds of Ω(√{log n}) and Ω(√{log m}) for SCD which apply for the clairvoyant case. In addition, the competitiveness of our algorithm does not depend on the number of requests. Such a guarantee on the size of the universe alone was not previously known even for the clairvoyant case - the only previously-known algorithm (due to Carrasco et al.) is clairvoyant, with competitiveness that grows with the number of requests. For the special case of vertex cover with delay, we show a simpler, deterministic algorithm which is 3-competitive (and also non-clairvoyant).
Cite as

Yossi Azar, Ashish Chiplunkar, Shay Kutten, and Noam Touitou. Set Cover with Delay - Clairvoyance Is Not Required. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 8:1-8:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{azar_et_al:LIPIcs.ESA.2020.8,
  author =	{Azar, Yossi and Chiplunkar, Ashish and Kutten, Shay and Touitou, Noam},
  title =	{{Set Cover with Delay - Clairvoyance Is Not Required}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{8:1--8:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.8},
  URN =		{urn:nbn:de:0030-drops-128749},
  doi =		{10.4230/LIPIcs.ESA.2020.8},
  annote =	{Keywords: Set Cover, Delay, Clairvoyant}
}
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