19 Search Results for "Feldman, Moran"

Document
DOI: 10.4230/LIPIcs.ESA.2024.8
Interval Selection in Sliding Windows

Authors: Cezar-Mihail Alexandru and Christian Konrad

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
We initiate the study of the Interval Selection problem in the (streaming) sliding window model of computation. In this problem, an algorithm receives a potentially infinite stream of intervals on the line, and the objective is to maintain at every moment an approximation to a largest possible subset of disjoint intervals among the L most recent intervals, for some integer L. We give the following results: 1) In the unit-length intervals case, we give a 2-approximation sliding window algorithm with space Õ(|OPT|), and we show that any sliding window algorithm that computes a (2-ε)-approximation requires space Ω(L), for any ε > 0. 2) In the arbitrary-length case, we give a (11/3+ε)-approximation sliding window algorithm with space Õ(|OPT|), for any constant ε > 0, which constitutes our main result. We also show that space Ω(L) is needed for algorithms that compute a (2.5-ε)-approximation, for any ε > 0. Our main technical contribution is an improvement over the smooth histogram technique, which consists of running independent copies of a traditional streaming algorithm with different start times. By employing the one-pass 2-approximation streaming algorithm by Cabello and Pérez-Lantero [Theor. Comput. Sci. '17] for Interval Selection on arbitrary-length intervals as the underlying algorithm, the smooth histogram technique immediately yields a (4+ε)-approximation in this setting. Our improvement is obtained by forwarding the structure of the intervals identified in a run to the subsequent run, which constrains the shape of an optimal solution and allows us to target optimal intervals differently.
Cite as

Cezar-Mihail Alexandru and Christian Konrad. Interval Selection in Sliding Windows. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 8:1-8:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{alexandru_et_al:LIPIcs.ESA.2024.8,
  author =	{Alexandru, Cezar-Mihail and Konrad, Christian},
  title =	{{Interval Selection in Sliding Windows}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{8:1--8:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.8},
  URN =		{urn:nbn:de:0030-drops-210795},
  doi =		{10.4230/LIPIcs.ESA.2024.8},
  annote =	{Keywords: Sliding window algorithms, Streaming algorithms, Interval selection}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.40
Improved Algorithms for Maximum Coverage in Dynamic and Random Order Streams

Authors: Amit Chakrabarti, Andrew McGregor, and Anthony Wirth

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
The maximum coverage problem is to select k sets, from a collection of m sets, such that the cardinality of their union, in a universe of size n, is maximized. We consider (1-1/e-ε)-approximation algorithms for this NP-hard problem in three standard data stream models. 1) Dynamic Model. The stream consists of a sequence of sets being inserted and deleted. Our multi-pass algorithm uses ε^{-2} k ⋅ polylog(n,m) space. The best previous result (Assadi and Khanna, SODA 2018) used (n +ε^{-4} k) polylog(n,m) space. While both algorithms use O(ε^{-1} log m) passes, our analysis shows that, when ε ≤ 1/log log m, it is possible to reduce the number of passes by a 1/log log m factor without incurring additional space. 2) Random Order Model. In this model, there are no deletions, and the sets forming the instance are uniformly randomly permuted to form the input stream. We show that a single pass and k polylog(n,m) space suffices for arbitrary small constant ε. The best previous result, by Warneke et al. (ESA 2023), used k² polylog(n,m) space. 3) Insert-Only Model. Lastly, our results, along with numerous previous results, use a sub-sampling technique introduced by McGregor and Vu (ICDT 2017) to sparsify the input instance. We explain how this technique and others used in the paper can be implemented such that the amortized update time of our algorithm is polylogarithmic. This also implies an improvement of the state-of-the-art insert only algorithms in terms of the update time: polylog(m,n) update time suffices, whereas the best previous result by Jaud et al. (SEA 2023) required update time that was linear in k.
Cite as

Amit Chakrabarti, Andrew McGregor, and Anthony Wirth. Improved Algorithms for Maximum Coverage in Dynamic and Random Order Streams. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 40:1-40:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chakrabarti_et_al:LIPIcs.ESA.2024.40,
  author =	{Chakrabarti, Amit and McGregor, Andrew and Wirth, Anthony},
  title =	{{Improved Algorithms for Maximum Coverage in Dynamic and Random Order Streams}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{40:1--40:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.40},
  URN =		{urn:nbn:de:0030-drops-211114},
  doi =		{10.4230/LIPIcs.ESA.2024.40},
  annote =	{Keywords: Data Stream Computation, Maximum Coverage, Submodular Maximization}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.73
Laminar Matroid Secretary: Greedy Strikes Back

Authors: Zhiyi Huang, Zahra Parsaeian, and Zixuan Zhu

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
We show that a simple greedy algorithm is 4.75-competitive for the Laminar Matroid Secretary Problem, improving the 3√3 ≈ 5.196-competitive algorithm based on the forbidden sets technique (Soto, Turkieltaub, and Verdugo, 2018).
Cite as

Zhiyi Huang, Zahra Parsaeian, and Zixuan Zhu. Laminar Matroid Secretary: Greedy Strikes Back. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 73:1-73:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{huang_et_al:LIPIcs.ESA.2024.73,
  author =	{Huang, Zhiyi and Parsaeian, Zahra and Zhu, Zixuan},
  title =	{{Laminar Matroid Secretary: Greedy Strikes Back}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{73:1--73:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.73},
  URN =		{urn:nbn:de:0030-drops-211443},
  doi =		{10.4230/LIPIcs.ESA.2024.73},
  annote =	{Keywords: Matroid Secretary, Greedy Algorithm, Laminar Matroid}
}
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
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.16
Weighted Matching in the Random-Order Streaming and Robust Communication Models

Authors: Diba Hashemi and Weronika Wrzos-Kaminska

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

Abstract
We study the maximum weight matching problem in the random-order semi-streaming model and in the robust communication model. Unlike many other sublinear models, in these two frameworks, there is a large gap between the guarantees of the best known algorithms for the unweighted and weighted versions of the problem. In the random-order semi-streaming setting, the edges of an n-vertex graph arrive in a stream in a random order. The goal is to compute an approximate maximum weight matching with a single pass over the stream using O(npolylog n) space. Our main result is a (2/3-ε)-approximation algorithm for maximum weight matching in random-order streams, using space O(n log n log R), where R is the ratio between the heaviest and the lightest edge in the graph. Our result nearly matches the best known unweighted (2/3+ε₀)-approximation (where ε₀ ∼ 10^{-14} is a small constant) achieved by Assadi and Behnezhad [Assadi and Behnezhad, 2021], and significantly improves upon previous weighted results. Our techniques also extend to the related robust communication model, in which the edges of a graph are partitioned randomly between Alice and Bob. Alice sends a single message of size O(npolylog n) to Bob, who must compute an approximate maximum weight matching. We achieve a (5/6-ε)-approximation using O(n log n log R) words of communication, matching the results of Azarmehr and Behnezhad [Azarmehr and Behnezhad, 2023] for unweighted graphs.
Cite as

Diba Hashemi and Weronika Wrzos-Kaminska. Weighted Matching in the Random-Order Streaming and Robust Communication Models. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 16:1-16:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hashemi_et_al:LIPIcs.APPROX/RANDOM.2024.16,
  author =	{Hashemi, Diba and Wrzos-Kaminska, Weronika},
  title =	{{Weighted Matching in the Random-Order Streaming and Robust Communication Models}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{16:1--16:26},
  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.2024.16},
  URN =		{urn:nbn:de:0030-drops-210097},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.16},
  annote =	{Keywords: Maximum Weight Matching, Streaming, Random-Order Streaming, Robust Communication Complexity}
}
Document
DOI: 10.4230/LIPIcs.ITC.2024.6
Information-Theoretic Single-Server PIR in the Shuffle Model

Authors: Yuval Ishai, Mahimna Kelkar, Daniel Lee, and Yiping Ma

Published in: LIPIcs, Volume 304, 5th Conference on Information-Theoretic Cryptography (ITC 2024)

Abstract
We revisit the problem of private information retrieval (PIR) in the shuffle model, where queries can be made anonymously by multiple clients. We present the first single-server PIR protocol in this model that has sublinear per-client communication and information-theoretic security. Moreover, following one-time preprocessing on the server side, our protocol only requires sublinear per-client computation. Concretely, for every γ > 0, the protocol has O(n^{γ}) communication and computation costs per (stateless) client, with 1/poly(n) statistical security, assuming that a size-n database is simultaneously accessed by poly(n) clients. This should be contrasted with the recent breakthrough result of Lin, Mook, and Wichs (STOC 2023) on doubly efficient PIR in the standard model, which is (inherently) limited to computational security.
Cite as

Yuval Ishai, Mahimna Kelkar, Daniel Lee, and Yiping Ma. Information-Theoretic Single-Server PIR in the Shuffle Model. In 5th Conference on Information-Theoretic Cryptography (ITC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 304, pp. 6:1-6:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ishai_et_al:LIPIcs.ITC.2024.6,
  author =	{Ishai, Yuval and Kelkar, Mahimna and Lee, Daniel and Ma, Yiping},
  title =	{{Information-Theoretic Single-Server PIR in the Shuffle Model}},
  booktitle =	{5th Conference on Information-Theoretic Cryptography (ITC 2024)},
  pages =	{6:1--6:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-333-1},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{304},
  editor =	{Aggarwal, Divesh},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2024.6},
  URN =		{urn:nbn:de:0030-drops-205142},
  doi =		{10.4230/LIPIcs.ITC.2024.6},
  annote =	{Keywords: Private information retrieval, Shuffle model}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.100
Subquadratic Submodular Maximization with a General Matroid Constraint

Authors: Yusuke Kobayashi and Tatsuya Terao

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We consider fast algorithms for monotone submodular maximization with a general matroid constraint. We present a randomized (1 - 1/e - ε)-approximation algorithm that requires Õ_{ε}(√r n) independence oracle and value oracle queries, where n is the number of elements in the matroid and r ≤ n is the rank of the matroid. This improves upon the previously best algorithm by Buchbinder-Feldman-Schwartz [Mathematics of Operations Research 2017] that requires Õ_{ε}(r² + √rn) queries. Our algorithm is based on continuous relaxation, as with other submodular maximization algorithms in the literature. To achieve subquadratic query complexity, we develop a new rounding algorithm, which is our main technical contribution. The rounding algorithm takes as input a point represented as a convex combination of t bases of a matroid and rounds it to an integral solution. Our rounding algorithm requires Õ(r^{3/2} t) independence oracle queries, while the previously best rounding algorithm by Chekuri-Vondrák-Zenklusen [FOCS 2010] requires O(r² t) independence oracle queries. A key idea in our rounding algorithm is to use a directed cycle of arbitrary length in an auxiliary graph, while the algorithm of Chekuri-Vondrák-Zenklusen focused on directed cycles of length two.
Cite as

Yusuke Kobayashi and Tatsuya Terao. Subquadratic Submodular Maximization with a General Matroid Constraint. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 100:1-100:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kobayashi_et_al:LIPIcs.ICALP.2024.100,
  author =	{Kobayashi, Yusuke and Terao, Tatsuya},
  title =	{{Subquadratic Submodular Maximization with a General Matroid Constraint}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{100:1--100:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.100},
  URN =		{urn:nbn:de:0030-drops-202437},
  doi =		{10.4230/LIPIcs.ICALP.2024.100},
  annote =	{Keywords: submodular maximization, matroid constraint, approximation algorithm, rounding algorithm, query complexity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.115
On the Cut-Query Complexity of Approximating Max-Cut

Authors: Orestis Plevrakis, Seyoon Ragavan, and S. Matthew Weinberg

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We consider the problem of query-efficient global max-cut on a weighted undirected graph in the value oracle model examined by [Rubinstein et al., 2018]. Graph algorithms in this cut query model and other query models have recently been studied for various other problems such as min-cut, connectivity, bipartiteness, and triangle detection. Max-cut in the cut query model can also be viewed as a natural special case of submodular function maximization: on query S ⊆ V, the oracle returns the total weight of the cut between S and V\S. Our first main technical result is a lower bound stating that a deterministic algorithm achieving a c-approximation for any c > 1/2 requires Ω(n) queries. This uses an extension of the cut dimension to rule out approximation (prior work of [Graur et al., 2020] introducing the cut dimension only rules out exact solutions). Secondly, we provide a randomized algorithm with Õ(n) queries that finds a c-approximation for any c < 1. We achieve this using a query-efficient sparsifier for undirected weighted graphs (prior work of [Rubinstein et al., 2018] holds only for unweighted graphs). To complement these results, for most constants c ∈ (0,1], we nail down the query complexity of achieving a c-approximation, for both deterministic and randomized algorithms (up to logarithmic factors). Analogously to general submodular function maximization in the same model, we observe a phase transition at c = 1/2: we design a deterministic algorithm for global c-approximate max-cut in O(log n) queries for any c < 1/2, and show that any randomized algorithm requires Ω(n/log n) queries to find a c-approximate max-cut for any c > 1/2. Additionally, we show that any deterministic algorithm requires Ω(n²) queries to find an exact max-cut (enough to learn the entire graph).
Cite as

Orestis Plevrakis, Seyoon Ragavan, and S. Matthew Weinberg. On the Cut-Query Complexity of Approximating Max-Cut. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 115:1-115:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{plevrakis_et_al:LIPIcs.ICALP.2024.115,
  author =	{Plevrakis, Orestis and Ragavan, Seyoon and Weinberg, S. Matthew},
  title =	{{On the Cut-Query Complexity of Approximating Max-Cut}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{115:1--115:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.115},
  URN =		{urn:nbn:de:0030-drops-202587},
  doi =		{10.4230/LIPIcs.ICALP.2024.115},
  annote =	{Keywords: query complexity, maximum cut, approximation algorithms, graph sparsification}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.15
List Update with Delays or Time Windows

Authors: Yossi Azar, Shahar Lewkowicz, and Danny Vainstein

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We address the problem of List Update, which is considered one of the fundamental problems in online algorithms and competitive analysis. In this context, we are presented with a list of elements and receive requests for these elements over time. Our objective is to fulfill these requests, incurring a cost proportional to their position in the list. Additionally, we can swap any two consecutive elements at a cost of 1. The renowned "Move to Front" algorithm, introduced by Sleator and Tarjan, immediately moves any requested element to the front of the list. They demonstrated that this algorithm achieves a competitive ratio of 2. While this bound is impressive, the actual cost of the algorithm’s solution can be excessively high. For example, if we request the last half of the list, the resulting solution cost becomes quadratic in the list’s length. To address this issue, we consider a more generalized problem called List Update with Time Windows. In this variant, each request arrives with a specific deadline by which it must be served, rather than being served immediately. Moreover, we allow the algorithm to process multiple requests simultaneously, accessing the corresponding elements in a single pass. The cost incurred in this case is determined by the position of the furthest element accessed, leading to a significant reduction in the total solution cost. We introduce this problem to explore lower solution costs, but it necessitates the development of new algorithms. For instance, Move-to-Front fails when handling the simple scenario of requesting the last half of the list with overlapping time windows. In our work, we present a natural O(1) competitive algorithm for this problem. While the algorithm itself is intuitive, its analysis is intricate, requiring the use of a novel potential function. Additionally, we delve into a more general problem called List Update with Delays, where the fixed deadlines are replaced with arbitrary delay functions. In this case, the cost includes not only the access and swapping costs, but also penalties for the delays incurred until the requests are served. This problem encompasses a special case known as the prize collecting version, where a request may go unserved up to a given deadline, resulting in a specified penalty. For this more comprehensive problem, we establish an O(1) competitive algorithm. However, the algorithm for the delay version is more complex, and its analysis involves significantly more intricate considerations.
Cite as

Yossi Azar, Shahar Lewkowicz, and Danny Vainstein. List Update with Delays or Time Windows. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 15:1-15:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{azar_et_al:LIPIcs.ICALP.2024.15,
  author =	{Azar, Yossi and Lewkowicz, Shahar and Vainstein, Danny},
  title =	{{List Update with Delays or Time Windows}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{15:1--15:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.15},
  URN =		{urn:nbn:de:0030-drops-201583},
  doi =		{10.4230/LIPIcs.ICALP.2024.15},
  annote =	{Keywords: Online, List Update, Delay, Time Window, Deadline}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.95
An Improved Lower Bound for Matroid Intersection Prophet Inequalities

Authors: Raghuvansh R. Saxena, Santhoshini Velusamy, and S. Matthew Weinberg

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
We consider prophet inequalities subject to feasibility constraints that are the intersection of q matroids. The best-known algorithms achieve a Θ(q)-approximation, even when restricted to instances that are the intersection of q partition matroids, and with i.i.d. Bernoulli random variables [José R. Correa et al., 2022; Moran Feldman et al., 2016; Marek Adamczyk and Michal Wlodarczyk, 2018]. The previous best-known lower bound is Θ(√q) due to a simple construction of [Robert Kleinberg and S. Matthew Weinberg, 2012] (which uses i.i.d. Bernoulli random variables, and writes the construction as the intersection of partition matroids). We establish an improved lower bound of q^{1/2+Ω(1/log log q)} by writing the construction of [Robert Kleinberg and S. Matthew Weinberg, 2012] as the intersection of asymptotically fewer partition matroids. We accomplish this via an improved upper bound on the product dimension of a graph with p^p disjoint cliques of size p, using recent techniques developed in [Noga Alon and Ryan Alweiss, 2020].
Cite as

Raghuvansh R. Saxena, Santhoshini Velusamy, and S. Matthew Weinberg. An Improved Lower Bound for Matroid Intersection Prophet Inequalities. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 95:1-95:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{saxena_et_al:LIPIcs.ITCS.2023.95,
  author =	{Saxena, Raghuvansh R. and Velusamy, Santhoshini and Weinberg, S. Matthew},
  title =	{{An Improved Lower Bound for Matroid Intersection Prophet Inequalities}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{95:1--95:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.95},
  URN =		{urn:nbn:de:0030-drops-175986},
  doi =		{10.4230/LIPIcs.ITCS.2023.95},
  annote =	{Keywords: Prophet Inequalities, Intersection of Matroids}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.41
On Maximizing Sums of Non-Monotone Submodular and Linear Functions

Authors: Benjamin Qi

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

Abstract
We study the problem of Regularized Unconstrained Submodular Maximization (RegularizedUSM) as defined by [Bodek and Feldman '22]. In this problem, we are given query access to a non-negative submodular function f: 2^N → ℝ_{≥ 0} and a linear function 𝓁: 2^N → ℝ over the same ground set N, and the objective is to output a set T ⊆ N approximately maximizing the sum f(T)+𝓁(T). Specifically, an algorithm is said to provide an (α,β)-approximation for RegularizedUSM if it outputs a set T such that E[f(T)+𝓁(T)] ≥ max_{S ⊆ N}[α ⋅ f(S)+β⋅ 𝓁(S)]. We also study the setting where S and T are constrained to be independent in a given matroid, which we refer to as Regularized Constrained Submodular Maximization (RegularizedCSM). The special case of RegularizedCSM with monotone f has been extensively studied [Sviridenko et al. '17, Feldman '18, Harshaw et al. '19]. On the other hand, we are aware of only one prior work that studies RegularizedCSM with non-monotone f [Lu et al. '21], and that work constrains 𝓁 to be non-positive. In this work, we provide improved (α,β)-approximation algorithms for both {RegularizedUSM} and {RegularizedCSM} with non-monotone f. In particular, we are the first to provide nontrivial (α,β)-approximations for RegularizedCSM where the sign of 𝓁 is unconstrained, and the α we obtain for RegularizedUSM improves over [Bodek and Feldman '22] for all β ∈ (0,1). In addition to approximation algorithms, we provide improved inapproximability results for all of the aforementioned cases. In particular, we show that the α our algorithm obtains for {RegularizedCSM} with unconstrained 𝓁 is essentially tight for β ≥ e/(e+1). Using similar ideas, we are also able to show 0.478-inapproximability for maximizing a submodular function where S and T are subject to a cardinality constraint, improving a 0.491-inapproximability result due to [Oveis Gharan and Vondrak '10].
Cite as

Benjamin Qi. On Maximizing Sums of Non-Monotone Submodular and Linear Functions. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 41:1-41:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{qi:LIPIcs.ISAAC.2022.41,
  author =	{Qi, Benjamin},
  title =	{{On Maximizing Sums of Non-Monotone Submodular and Linear Functions}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{41:1--41:16},
  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.2022.41},
  URN =		{urn:nbn:de:0030-drops-173263},
  doi =		{10.4230/LIPIcs.ISAAC.2022.41},
  annote =	{Keywords: submodular maximization, regularization, continuous greedy, inapproximability}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.33
Maximum Matching Sans Maximal Matching: A New Approach for Finding Maximum Matchings in the Data Stream Model

Authors: Moran Feldman and Ariel Szarf

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

Abstract
The problem of finding a maximum size matching in a graph (known as the maximum matching problem) is one of the most classical problems in computer science. Despite a significant body of work dedicated to the study of this problem in the data stream model, the state-of-the-art single-pass semi-streaming algorithm for it is still a simple greedy algorithm that computes a maximal matching, and this way obtains 1/2-approximation. Some previous works described two/three-pass algorithms that improve over this approximation ratio by using their second and third passes to improve the above mentioned maximal matching. One contribution of this paper continues this line of work by presenting new three-pass semi-streaming algorithms that work along these lines and obtain improved approximation ratios of 0.6111 and 0.5694 for triangle-free and general graphs, respectively. Unfortunately, a recent work [Christian Konrad and Kheeran K. Naidu, 2021] shows that the strategy of constructing a maximal matching in the first pass and then improving it in further passes has limitations. Additionally, this technique is unlikely to get us closer to single-pass semi-streaming algorithms obtaining a better than 1/2-approximation. Therefore, it is interesting to come up with algorithms that do something else with their first pass (we term such algorithms non-maximal-matching-first algorithms). No such algorithms are currently known (to the best of our knowledge), and the main contribution of this paper is describing such algorithms that obtain approximation ratios of 0.5384 and 0.5555 in two and three passes, respectively, for general graphs (the result for three passes improves over the previous state-of-the-art, but is worse than the result of this paper mentioned in the previous paragraph for general graphs). The improvements obtained by these results are, unfortunately, numerically not very impressive, but the main importance (in our opinion) of these results is in demonstrating the potential of non-maximal-matching-first algorithms.
Cite as

Moran Feldman and Ariel Szarf. Maximum Matching Sans Maximal Matching: A New Approach for Finding Maximum Matchings in the Data Stream Model. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 33:1-33:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{feldman_et_al:LIPIcs.APPROX/RANDOM.2022.33,
  author =	{Feldman, Moran and Szarf, Ariel},
  title =	{{Maximum Matching Sans Maximal Matching: A New Approach for Finding Maximum Matchings in the Data Stream Model}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{33:1--33:24},
  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.2022.33},
  URN =		{urn:nbn:de:0030-drops-171559},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.33},
  annote =	{Keywords: Maximum matching, semi-streaming algorithms, multi-pass algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.23
Maximizing Sums of Non-Monotone Submodular and Linear Functions: Understanding the Unconstrained Case

Authors: Kobi Bodek and Moran Feldman

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

Abstract
Motivated by practical applications, recent works have considered maximization of sums of a submodular function g and a linear function 𝓁. Almost all such works, to date, studied only the special case of this problem in which g is also guaranteed to be monotone. Therefore, in this paper we systematically study the simplest version of this problem in which g is allowed to be non-monotone, namely the unconstrained variant, which we term Regularized Unconstrained Submodular Maximization (RegularizedUSM). Our main algorithmic result is the first non-trivial guarantee for general RegularizedUSM. For the special case of RegularizedUSM in which the linear function 𝓁 is non-positive, we prove two inapproximability results, showing that the algorithmic result implied for this case by previous works is not far from optimal. Finally, we reanalyze the known Double Greedy algorithm to obtain improved guarantees for the special case of RegularizedUSM in which the linear function 𝓁 is non-negative; and we complement these guarantees by showing that it is not possible to obtain (1/2, 1)-approximation for this case (despite intuitive arguments suggesting that this approximation guarantee is natural).
Cite as

Kobi Bodek and Moran Feldman. Maximizing Sums of Non-Monotone Submodular and Linear Functions: Understanding the Unconstrained Case. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 23:1-23:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bodek_et_al:LIPIcs.ESA.2022.23,
  author =	{Bodek, Kobi and Feldman, Moran},
  title =	{{Maximizing Sums of Non-Monotone Submodular and Linear Functions: Understanding the Unconstrained Case}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{23:1--23:17},
  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.2022.23},
  URN =		{urn:nbn:de:0030-drops-169618},
  doi =		{10.4230/LIPIcs.ESA.2022.23},
  annote =	{Keywords: Unconstrained submodular maximization, regularization, double greedy, non-oblivious local search, inapproximability}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.52
Submodular Maximization Subject to Matroid Intersection on the Fly

Authors: Moran Feldman, Ashkan Norouzi-Fard, Ola Svensson, and Rico Zenklusen

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

Abstract
Despite a surge of interest in submodular maximization in the data stream model, there remain significant gaps in our knowledge about what can be achieved in this setting, especially when dealing with multiple constraints. In this work, we nearly close several basic gaps in submodular maximization subject to k matroid constraints in the data stream model. We present a new hardness result showing that super polynomial memory in k is needed to obtain an o(k/(log k))-approximation. This implies near optimality of prior algorithms. For the same setting, we show that one can nevertheless obtain a constant-factor approximation by maintaining a set of elements whose size is independent of the stream size. Finally, for bipartite matching constraints, a well-known special case of matroid intersection, we present a new technique to obtain hardness bounds that are significantly stronger than those obtained with prior approaches. Prior results left it open whether a 2-approximation may exist in this setting, and only a complexity-theoretic hardness of 1.91 was known. We prove an unconditional hardness of 2.69.
Cite as

Moran Feldman, Ashkan Norouzi-Fard, Ola Svensson, and Rico Zenklusen. Submodular Maximization Subject to Matroid Intersection on the Fly. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 52:1-52:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{feldman_et_al:LIPIcs.ESA.2022.52,
  author =	{Feldman, Moran and Norouzi-Fard, Ashkan and Svensson, Ola and Zenklusen, Rico},
  title =	{{Submodular Maximization Subject to Matroid Intersection on the Fly}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{52:1--52:14},
  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.2022.52},
  URN =		{urn:nbn:de:0030-drops-169902},
  doi =		{10.4230/LIPIcs.ESA.2022.52},
  annote =	{Keywords: Submodular Maximization, Matroid Intersection, Streaming Algorithms}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.59
Streaming Submodular Maximization Under Matroid Constraints

Authors: Moran Feldman, Paul Liu, Ashkan Norouzi-Fard, Ola Svensson, and Rico Zenklusen

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

Abstract
Recent progress in (semi-)streaming algorithms for monotone submodular function maximization has led to tight results for a simple cardinality constraint. However, current techniques fail to give a similar understanding for natural generalizations, including matroid constraints. This paper aims at closing this gap. For a single matroid of rank k (i.e., any solution has cardinality at most k), our main results are: - A single-pass streaming algorithm that uses Õ(k) memory and achieves an approximation guarantee of 0.3178. - A multi-pass streaming algorithm that uses Õ(k) memory and achieves an approximation guarantee of (1-1/e - ε) by taking a constant (depending on ε) number of passes over the stream. This improves on the previously best approximation guarantees of 1/4 and 1/2 for single-pass and multi-pass streaming algorithms, respectively. In fact, our multi-pass streaming algorithm is tight in that any algorithm with a better guarantee than 1/2 must make several passes through the stream and any algorithm that beats our guarantee of 1-1/e must make linearly many passes (as well as an exponential number of value oracle queries). Moreover, we show how the approach we use for multi-pass streaming can be further strengthened if the elements of the stream arrive in uniformly random order, implying an improved result for p-matchoid constraints.
Cite as

Moran Feldman, Paul Liu, Ashkan Norouzi-Fard, Ola Svensson, and Rico Zenklusen. Streaming Submodular Maximization Under Matroid Constraints. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 59:1-59:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{feldman_et_al:LIPIcs.ICALP.2022.59,
  author =	{Feldman, Moran and Liu, Paul and Norouzi-Fard, Ashkan and Svensson, Ola and Zenklusen, Rico},
  title =	{{Streaming Submodular Maximization Under Matroid Constraints}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{59:1--59:20},
  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.2022.59},
  URN =		{urn:nbn:de:0030-drops-164007},
  doi =		{10.4230/LIPIcs.ICALP.2022.59},
  annote =	{Keywords: Submodular maximization, streaming, matroid, random order}
}
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