18 Search Results for "Ros�n, Adi"

Document
DOI: 10.4230/LIPIcs.ITCS.2024.58
An Improved Protocol for ExactlyN with More Than 3 Players

Authors: Lianna Hambardzumyan, Toniann Pitassi, Suhail Sherif, Morgan Shirley, and Adi Shraibman

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract
The ExactlyN problem in the number-on-forehead (NOF) communication setting asks k players, each of whom can see every input but their own, if the k input numbers add up to N. Introduced by Chandra, Furst and Lipton in 1983, ExactlyN is important for its role in understanding the strength of randomness in communication complexity with many players. It is also tightly connected to the field of combinatorics: its k-party NOF communication complexity is related to the size of the largest corner-free subset in [N]^{k-1}. In 2021, Linial and Shraibman gave more efficient protocols for ExactlyN for 3 players. As an immediate consequence, this also gave a new construction of larger corner-free subsets in [N]². Later that year Green gave a further refinement to their argument. These results represent the first improvements to the highest-order term for k = 3 since the famous work of Behrend in 1946. In this paper we give a corresponding improvement to the highest-order term for k > 3, the first since Rankin in 1961. That is, we give a more efficient protocol for ExactlyN as well as larger corner-free sets in higher dimensions. Nearly all previous results in this line of research approached the problem from the combinatorics perspective, implicitly resulting in non-constructive protocols for ExactlyN. Approaching the problem from the communication complexity point of view and constructing explicit protocols for ExactlyN was key to the improvements in the k = 3 setting. As a further contribution we provide explicit protocols for ExactlyN for any number of players which serves as a base for our improvement.
Cite as

Lianna Hambardzumyan, Toniann Pitassi, Suhail Sherif, Morgan Shirley, and Adi Shraibman. An Improved Protocol for ExactlyN with More Than 3 Players. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 58:1-58:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hambardzumyan_et_al:LIPIcs.ITCS.2024.58,
  author =	{Hambardzumyan, Lianna and Pitassi, Toniann and Sherif, Suhail and Shirley, Morgan and Shraibman, Adi},
  title =	{{An Improved Protocol for ExactlyN with More Than 3 Players}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{58:1--58:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.58},
  URN =		{urn:nbn:de:0030-drops-195868},
  doi =		{10.4230/LIPIcs.ITCS.2024.58},
  annote =	{Keywords: Corner-free sets, number-on-forehead communication}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2023.30
Distributed Partial Coloring via Gradual Rounding

Authors: Avinandan Das, Pierre Fraigniaud, and Adi Rosén

Published in: LIPIcs, Volume 286, 27th International Conference on Principles of Distributed Systems (OPODIS 2023)

Abstract
For k ≥ 0, k-partial (k+1)-coloring asks to color the nodes of an n-node graph using a palette of k+1 colors such that every node v has at least min{k,deg(v)} neighbors colored with colors different from its own color. Hence, proper (Δ+1)-coloring is the special case of k-partial (k+1)-coloring when k = Δ. Ghaffari and Kuhn [FOCS 2021] recently proved that there exists a deterministic distributed algorithm that solves proper (Δ+1)-coloring of n-node graphs with maximum degree Δ in O(log n ⋅ log²Δ) rounds under the LOCAL model of distributed computing. This breakthrough result is achieved via an original iterated rounding approach. Using the same technique, Ghaffari and Kuhn also showed that there exists a deterministic algorithm that solves proper O(a)-coloring of n-node graphs with arboricity a in O(log n ⋅ log³a) rounds. It directly follows from this latter result that k-partial O(k)-coloring can be solved deterministically in O(log n ⋅ log³k) rounds. We develop an extension of the Ghaffari and Kuhn algorithm for proper (Δ+1)-coloring, and show that it solves k-partial (k+1)-coloring, thus generalizing their main result. Our algorithm runs in O(log n ⋅ log³k) rounds, like the algorithm that follows from Ghaffari and Kuhn’s algorithm for graphs with bounded arboricity, but uses only k+1 color, i.e., the smallest number c of colors such that every graph has a k-partial c-coloring. Like all the previously mentioned algorithms, our algorithm actually solves the general list-coloring version of the problem. Specifically, every node v receives as input an integer demand d(v) ≤ deg(v), and a list of at least d(v)+1 colors. Every node must then output a color from its list such that the resulting coloring satisfies that every node v has at least d(v) neighbors with colors different from its own. Our algorithm solves this problem in O(log n ⋅ log³k) rounds where k = max_v d(v). Moreover, in the specific case where all lists of colors given to the nodes as input share a common colors c^* known to all nodes, one can save one log k factor. In particular, for standard k-partial (k+1)-coloring, which corresponds to the case where all nodes are given the same list {1,… ,k+1}, one can modify our algorithm so that it runs in O(log n ⋅ log²k) rounds, and thus matches the complexity of Ghaffari and Kuhn’s algorithm for (Δ+1)-coloring for k = Δ.
Cite as

Avinandan Das, Pierre Fraigniaud, and Adi Rosén. Distributed Partial Coloring via Gradual Rounding. In 27th International Conference on Principles of Distributed Systems (OPODIS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 286, pp. 30:1-30:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{das_et_al:LIPIcs.OPODIS.2023.30,
  author =	{Das, Avinandan and Fraigniaud, Pierre and Ros\'{e}n, Adi},
  title =	{{Distributed Partial Coloring via Gradual Rounding}},
  booktitle =	{27th International Conference on Principles of Distributed Systems (OPODIS 2023)},
  pages =	{30:1--30:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-308-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{286},
  editor =	{Bessani, Alysson and D\'{e}fago, Xavier and Nakamura, Junya and Wada, Koichi and Yamauchi, Yukiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2023.30},
  URN =		{urn:nbn:de:0030-drops-195205},
  doi =		{10.4230/LIPIcs.OPODIS.2023.30},
  annote =	{Keywords: Distributed graph coloring, partial coloring, weak coloring}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.89
The Strength of Equality Oracles in Communication

Authors: Toniann Pitassi, Morgan Shirley, and Adi Shraibman

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

Abstract
It is well-known that randomized communication protocols are more powerful than deterministic protocols. In particular the Equality function requires Ω(n) deterministic communication complexity but has efficient randomized protocols. Previous work of Chattopadhyay, Lovett and Vinyals shows that randomized communication is strictly stronger than what can be solved by deterministic protocols equipped with an Equality oracle. Despite this separation, we are far from understanding the exact strength of Equality oracles in the context of communication complexity. In this work we focus on nondeterminisic communication equipped with an Equality oracle, which is a subclass of Merlin-Arthur communication. We show that this inclusion is strict by proving that the previously-studied Integer Inner Product function, which can be efficiently computed even with bounded-error randomness, cannot be computed using sublinear communication in the nondeterministic Equality model. To prove this we give a new matrix-theoretic characterization of the nondeterministic Equality model: specifically, there is a tight connection between this model and a covering number based on the blocky matrices of Hambardzumyan, Hatami, and Hatami, as well as a natural variant of the Gamma-2 factorization norm. Similar equivalences are shown for the unambiguous nondeterministic model with Equality oracles. A bonus result arises from these proofs: for the studied communication models, a single Equality oracle call suffices without loss of generality. Our results allow us to prove a separation between deterministic and unambiguous nondeterminism in the presence of Equality oracles. This stands in contrast to the result of Yannakakis which shows that these models are polynomially-related without oracles. We suggest a number of intriguing open questions along this direction of inquiry, as well as others that arise from our work.
Cite as

Toniann Pitassi, Morgan Shirley, and Adi Shraibman. The Strength of Equality Oracles in Communication. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 89:1-89:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{pitassi_et_al:LIPIcs.ITCS.2023.89,
  author =	{Pitassi, Toniann and Shirley, Morgan and Shraibman, Adi},
  title =	{{The Strength of Equality Oracles in Communication}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{89:1--89:19},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.89},
  URN =		{urn:nbn:de:0030-drops-175927},
  doi =		{10.4230/LIPIcs.ITCS.2023.89},
  annote =	{Keywords: Factorization norm, blocky rank, Merlin-Arthur}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.107
Keep That Card in Mind: Card Guessing with Limited Memory

Authors: Boaz Menuhin and Moni Naor

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
A card guessing game is played between two players, Guesser and Dealer. At the beginning of the game, the Dealer holds a deck of n cards (labeled 1, ..., n). For n turns, the Dealer draws a card from the deck, the Guesser guesses which card was drawn, and then the card is discarded from the deck. The Guesser receives a point for each correctly guessed card. With perfect memory, a Guesser can keep track of all cards that were played so far and pick at random a card that has not appeared so far, yielding in expectation ln n correct guesses, regardless of how the Dealer arranges the deck. With no memory, the best a Guesser can do will result in a single guess in expectation. We consider the case of a memory bounded Guesser that has m < n memory bits. We show that the performance of such a memory bounded Guesser depends much on the behavior of the Dealer. In more detail, we show that there is a gap between the static case, where the Dealer draws cards from a properly shuffled deck or a prearranged one, and the adaptive case, where the Dealer draws cards thoughtfully, in an adversarial manner. Specifically: 1) We show a Guesser with O(log² n) memory bits that scores a near optimal result against any static Dealer. 2) We show that no Guesser with m bits of memory can score better than O(√m) correct guesses against a random Dealer, thus, no Guesser can score better than min {√m, ln n}, i.e., the above Guesser is optimal. 3) We show an efficient adaptive Dealer against which no Guesser with m memory bits can make more than ln m + 2 ln log n + O(1) correct guesses in expectation. These results are (almost) tight, and we prove them using compression arguments that harness the guessing strategy for encoding.
Cite as

Boaz Menuhin and Moni Naor. Keep That Card in Mind: Card Guessing with Limited Memory. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 107:1-107:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{menuhin_et_al:LIPIcs.ITCS.2022.107,
  author =	{Menuhin, Boaz and Naor, Moni},
  title =	{{Keep That Card in Mind: Card Guessing with Limited Memory}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{107:1--107:28},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.107},
  URN =		{urn:nbn:de:0030-drops-157039},
  doi =		{10.4230/LIPIcs.ITCS.2022.107},
  annote =	{Keywords: Adaptivity vs Non-adaptivity, Adversarial Robustness, Card Guessing, Compression Argument, Information Theory, Streaming Algorithms, Two Player Game}
}
Document
DOI: 10.4230/LIPIcs.CCC.2021.2
An Improved Protocol for the Exactly-N Problem

Authors: Nati Linial and Adi Shraibman

Published in: LIPIcs, Volume 200, 36th Computational Complexity Conference (CCC 2021)

Abstract
In the 3-players exactly-N problem the players need to decide whether x+y+z = N for inputs x,y,z and fixed N. This is the first problem considered in the multiplayer Number On the Forehead (NOF) model. Even though this is such a basic problem, no progress has been made on it throughout the years. Only recently have explicit protocols been found for the first time, yet no improvement in complexity has been achieved to date. The present paper offers the first improved protocol for the exactly-N problem. This improved protocol has also interesting consequences in additive combinatorics. As we explain below, it yields a higher lower bound on the possible density of corner-free sets in [N]×[N].
Cite as

Nati Linial and Adi Shraibman. An Improved Protocol for the Exactly-N Problem. In 36th Computational Complexity Conference (CCC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 200, pp. 2:1-2:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{linial_et_al:LIPIcs.CCC.2021.2,
  author =	{Linial, Nati and Shraibman, Adi},
  title =	{{An Improved Protocol for the Exactly-N Problem}},
  booktitle =	{36th Computational Complexity Conference (CCC 2021)},
  pages =	{2:1--2:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-193-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{200},
  editor =	{Kabanets, Valentine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2021.2},
  URN =		{urn:nbn:de:0030-drops-142760},
  doi =		{10.4230/LIPIcs.CCC.2021.2},
  annote =	{Keywords: Communication complexity, Number-On-the-Forehead, Corner-free sets}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2020.5
The ε-t-Net Problem

Authors: Noga Alon, Bruno Jartoux, Chaya Keller, Shakhar Smorodinsky, and Yelena Yuditsky

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

Abstract
We study a natural generalization of the classical ε-net problem (Haussler - Welzl 1987), which we call the ε-t-net problem: Given a hypergraph on n vertices and parameters t and ε ≥ t/n, find a minimum-sized family S of t-element subsets of vertices such that each hyperedge of size at least ε n contains a set in S. When t=1, this corresponds to the ε-net problem. We prove that any sufficiently large hypergraph with VC-dimension d admits an ε-t-net of size O((1+log t)d/ε log 1/ε). For some families of geometrically-defined hypergraphs (such as the dual hypergraph of regions with linear union complexity), we prove the existence of O(1/ε)-sized ε-t-nets. We also present an explicit construction of ε-t-nets (including ε-nets) for hypergraphs with bounded VC-dimension. In comparison to previous constructions for the special case of ε-nets (i.e., for t=1), it does not rely on advanced derandomization techniques. To this end we introduce a variant of the notion of VC-dimension which is of independent interest.
Cite as

Noga Alon, Bruno Jartoux, Chaya Keller, Shakhar Smorodinsky, and Yelena Yuditsky. The ε-t-Net Problem. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 5:1-5:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{alon_et_al:LIPIcs.SoCG.2020.5,
  author =	{Alon, Noga and Jartoux, Bruno and Keller, Chaya and Smorodinsky, Shakhar and Yuditsky, Yelena},
  title =	{{The \epsilon-t-Net Problem}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{5:1--5:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.5},
  URN =		{urn:nbn:de:0030-drops-121639},
  doi =		{10.4230/LIPIcs.SoCG.2020.5},
  annote =	{Keywords: epsilon-nets, geometric hypergraphs, VC-dimension, linear union complexity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2019.54
On the Communication Complexity of High-Dimensional Permutations

Authors: Nati Linial, Toniann Pitassi, and Adi Shraibman

Published in: LIPIcs, Volume 124, 10th Innovations in Theoretical Computer Science Conference (ITCS 2019)

Abstract
We study the multiparty communication complexity of high dimensional permutations in the Number On the Forehead (NOF) model. This model is due to Chandra, Furst and Lipton (CFL) who also gave a nontrivial protocol for the Exactly-n problem where three players receive integer inputs and need to decide if their inputs sum to a given integer n. There is a considerable body of literature dealing with the same problem, where (N,+) is replaced by some other abelian group. Our work can be viewed as a far-reaching extension of this line of research. We show that the known lower bounds for that group-theoretic problem apply to all high dimensional permutations. We introduce new proof techniques that reveal new and unexpected connections between NOF communication complexity of permutations and a variety of well-known problems in combinatorics. We also give a direct algorithmic protocol for Exactly-n. In contrast, all previous constructions relied on large sets of integers without a 3-term arithmetic progression.
Cite as

Nati Linial, Toniann Pitassi, and Adi Shraibman. On the Communication Complexity of High-Dimensional Permutations. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 54:1-54:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{linial_et_al:LIPIcs.ITCS.2019.54,
  author =	{Linial, Nati and Pitassi, Toniann and Shraibman, Adi},
  title =	{{On the Communication Complexity of High-Dimensional Permutations}},
  booktitle =	{10th Innovations in Theoretical Computer Science Conference (ITCS 2019)},
  pages =	{54:1--54:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-095-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{124},
  editor =	{Blum, Avrim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2019.54},
  URN =		{urn:nbn:de:0030-drops-101470},
  doi =		{10.4230/LIPIcs.ITCS.2019.54},
  annote =	{Keywords: High dimensional permutations, Number On the Forehead model, Additive combinatorics}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2019.64
A New Approach to Multi-Party Peer-to-Peer Communication Complexity

Authors: Adi Rosén and Florent Urrutia

Published in: LIPIcs, Volume 124, 10th Innovations in Theoretical Computer Science Conference (ITCS 2019)

Abstract
We introduce new models and new information theoretic measures for the study of communication complexity in the natural peer-to-peer, multi-party, number-in-hand setting. We prove a number of properties of our new models and measures, and then, in order to exemplify their effectiveness, we use them to prove two lower bounds. The more elaborate one is a tight lower bound of Omega(kn) on the multi-party peer-to-peer randomized communication complexity of the k-player, n-bit function Disjointness, Disj_k^n. The other one is a tight lower bound of Omega(kn) on the multi-party peer-to-peer randomized communication complexity of the k-player, n-bit bitwise parity function, Par_k^n. Both lower bounds hold when n=Omega(k). The lower bound for Disj_k^n improves over the lower bound that can be inferred from the result of Braverman et al. (FOCS 2013), which was proved in the coordinator model and can yield a lower bound of Omega(kn/log k) in the peer-to-peer model. To the best of our knowledge, our lower bounds are the first tight (non-trivial) lower bounds on communication complexity in the natural peer-to-peer multi-party setting. In addition to the above results for communication complexity, we also prove, using the same tools, an Omega(n) lower bound on the number of random bits necessary for the (information theoretic) private computation of the function Disj_k^n.
Cite as

Adi Rosén and Florent Urrutia. A New Approach to Multi-Party Peer-to-Peer Communication Complexity. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 64:1-64:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{rosen_et_al:LIPIcs.ITCS.2019.64,
  author =	{Ros\'{e}n, Adi and Urrutia, Florent},
  title =	{{A New Approach to Multi-Party Peer-to-Peer Communication Complexity}},
  booktitle =	{10th Innovations in Theoretical Computer Science Conference (ITCS 2019)},
  pages =	{64:1--64:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-095-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{124},
  editor =	{Blum, Avrim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2019.64},
  URN =		{urn:nbn:de:0030-drops-101576},
  doi =		{10.4230/LIPIcs.ITCS.2019.64},
  annote =	{Keywords: communication complexity, multi-party communication complexity, peer-to-peer communication complexity, information complexity, private computation}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.13
Tight Bounds on Online Checkpointing Algorithms

Authors: Achiya Bar-On, Itai Dinur, Orr Dunkelman, Rani Hod, Nathan Keller, Eyal Ronen, and Adi Shamir

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
The problem of online checkpointing is a classical problem with numerous applications which had been studied in various forms for almost 50 years. In the simplest version of this problem, a user has to maintain k memorized checkpoints during a long computation, where the only allowed operation is to move one of the checkpoints from its old time to the current time, and his goal is to keep the checkpoints as evenly spread out as possible at all times. At ICALP'13 Bringmann et al. studied this problem as a special case of an online/offline optimization problem in which the deviation from uniformity is measured by the natural discrepancy metric of the worst case ratio between real and ideal segment lengths. They showed this discrepancy is smaller than 1.59-o(1) for all k, and smaller than ln4-o(1)~~1.39 for the sparse subset of k's which are powers of 2. In addition, they obtained upper bounds on the achievable discrepancy for some small values of k. In this paper we solve the main problems left open in the ICALP'13 paper by proving that ln4 is a tight upper and lower bound on the asymptotic discrepancy for all large k, and by providing tight upper and lower bounds (in the form of provably optimal checkpointing algorithms, some of which are in fact better than those of Bringmann et al.) for all the small values of k <= 10.
Cite as

Achiya Bar-On, Itai Dinur, Orr Dunkelman, Rani Hod, Nathan Keller, Eyal Ronen, and Adi Shamir. Tight Bounds on Online Checkpointing Algorithms. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 13:1-13:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{baron_et_al:LIPIcs.ICALP.2018.13,
  author =	{Bar-On, Achiya and Dinur, Itai and Dunkelman, Orr and Hod, Rani and Keller, Nathan and Ronen, Eyal and Shamir, Adi},
  title =	{{Tight Bounds on Online Checkpointing Algorithms}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{13:1--13:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.13},
  URN =		{urn:nbn:de:0030-drops-90179},
  doi =		{10.4230/LIPIcs.ICALP.2018.13},
  annote =	{Keywords: checkpoint, checkpointing algorithm, online algorithm, uniform distribution, discrepancy}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.6
Sublinear Random Access Generators for Preferential Attachment Graphs

Authors: Guy Even, Reut Levi, Moti Medina, and Adi Rosén

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

Abstract
We consider the problem of sampling from a distribution on graphs, specifically when the distribution is defined by an evolving graph model, and consider the time, space and randomness complexities of such samplers. In the standard approach, the whole graph is chosen randomly according to the randomized evolving process, stored in full, and then queries on the sampled graph are answered by simply accessing the stored graph. This may require prohibitive amounts of time, space and random bits, especially when only a small number of queries are actually issued. Instead, we propose to generate the graph on-the-fly, in response to queries, and therefore to require amounts of time, space, and random bits which are a function of the actual number of queries. We focus on two random graph models: the Barabási-Albert Preferential Attachment model (BA-graphs) and the random recursive tree model. We give on-the-fly generation algorithms for both models. With probability 1-1/poly(n), each and every query is answered in polylog(n) time, and the increase in space and the number of random bits consumed by any single query are both polylog(n), where n denotes the number of vertices in the graph. Our results show that, although the BA random graph model is defined by a sequential process, efficient random access to the graph's nodes is possible. In addition to the conceptual contribution, efficient on-the-fly generation of random graphs can serve as a tool for the efficient simulation of sublinear algorithms over large BA-graphs, and the efficient estimation of their performance on such graphs.
Cite as

Guy Even, Reut Levi, Moti Medina, and Adi Rosén. Sublinear Random Access Generators for Preferential Attachment Graphs. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 6:1-6:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{even_et_al:LIPIcs.ICALP.2017.6,
  author =	{Even, Guy and Levi, Reut and Medina, Moti and Ros\'{e}n, Adi},
  title =	{{Sublinear Random Access Generators for Preferential Attachment Graphs}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{6:1--6:15},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.6},
  URN =		{urn:nbn:de:0030-drops-74242},
  doi =		{10.4230/LIPIcs.ICALP.2017.6},
  annote =	{Keywords: local computation algorithms, preferential attachment graphs, random recursive trees, sublinear algorithms}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2016.57
Multi-Party Protocols, Information Complexity and Privacy

Authors: Iordanis Kerenidis, Adi Rosén, and Florent Urrutia

Published in: LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)

Abstract
We introduce the new measure of Public Information Complexity (PIC), as a tool for the study of multi-party computation protocols, and of quantities such as their communication complexity, or the amount of randomness they require in the context of information-theoretic private computations. We are able to use this measure directly in the natural asynchronous message-passing peer-to-peer model and show a number of interesting properties and applications of our new notion: the Public Information Complexity is a lower bound on the Communication Complexity and an upper bound on the Information Complexity; the difference between the Public Information Complexity and the Information Complexity provides a lower bound on the amount of randomness used in a protocol; any communication protocol can be compressed to its Public Information Cost; an explicit calculation of the zero-error Public Information Complexity of the k-party, n-bit Parity function, where a player outputs the bit-wise parity of the inputs. The latter result establishes that the amount of randomness needed for a private protocol that computes this function is Omega(n).
Cite as

Iordanis Kerenidis, Adi Rosén, and Florent Urrutia. Multi-Party Protocols, Information Complexity and Privacy. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 57:1-57:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{kerenidis_et_al:LIPIcs.MFCS.2016.57,
  author =	{Kerenidis, Iordanis and Ros\'{e}n, Adi and Urrutia, Florent},
  title =	{{Multi-Party Protocols, Information Complexity and Privacy}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{57:1--57:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.57},
  URN =		{urn:nbn:de:0030-drops-64696},
  doi =		{10.4230/LIPIcs.MFCS.2016.57},
  annote =	{Keywords: multi-party protocols, information theory, communication complexity, multi-party private computation (MPC), randomness}
}
Document
DOI: 10.4230/LIPIcs.ESA.2016.40
A Constant Approximation Algorithm for Scheduling Packets on Line Networks

Authors: Guy Even, Moti Medina, and Adi Rosén

Published in: LIPIcs, Volume 57, 24th Annual European Symposium on Algorithms (ESA 2016)

Abstract
In this paper we improve the approximation ratio for the problem of scheduling packets on line networks with bounded buffers with the aim of maximizing the throughput. Each node in the network has a local buffer of bounded size B, and each edge (or link) can transmit a limited number c of packets in every time unit. The input to the problem consists of a set of packet requests, each defined by a source node, a destination node, and a release time. We denote by n the size of the network. A solution for this problem is a schedule that delivers (some of the) packets to their destinations without violating the capacity constraints of the network (buffers or edges). Our goal is to design an efficient algorithm that computes a schedule that maximizes the number of packets that arrive to their respective destinations. We give a randomized approximation algorithm with constant approximation ratio for the case where the buffer-size to link-capacity ratio, B/c, does not depend on the input size. This improves over the previously best result of O(log^* n) [Räcke and Rosén SPAA 2009]. Our improvement is based on a new combinatorial lemma that we prove, stating, roughly speaking, that if packets are allowed to stay put in buffers only a limited number of time steps, 2d, where d is the longest source-destination distance, then the optimal solution is decreased by only a constant factor. This claim was not previously known in the integral (unsplitable, zero-one) case, and may find additional applications for routing and scheduling algorithms. While we are not able to give the same improvement for the related problem when packets have hard deadlines, our algorithm does support "soft deadlines". That is, if packets have deadlines, we achieve a constant approximation ratio when the produced solution is allowed to miss deadlines by at most log n time units.
Cite as

Guy Even, Moti Medina, and Adi Rosén. A Constant Approximation Algorithm for Scheduling Packets on Line Networks. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 40:1-40:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{even_et_al:LIPIcs.ESA.2016.40,
  author =	{Even, Guy and Medina, Moti and Ros\'{e}n, Adi},
  title =	{{A Constant Approximation Algorithm for Scheduling Packets on Line Networks}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{40:1--40:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Sankowski, Piotr and Zaroliagis, Christos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.40},
  URN =		{urn:nbn:de:0030-drops-63524},
  doi =		{10.4230/LIPIcs.ESA.2016.40},
  annote =	{Keywords: approximation algorithms, linear programming, randomized rounding, packet scheduling, admission control}
}
Document
DOI: 10.4230/LIPIcs.ESA.2016.73
Online Budgeted Maximum Coverage

Authors: Dror Rawitz and Adi Rosén

Published in: LIPIcs, Volume 57, 24th Annual European Symposium on Algorithms (ESA 2016)

Abstract
We study the Online Budgeted Maximum Coverage (OBMC) problem. Subsets of a weighted ground set U arrive one by one, where each set has a cost. The online algorithm has to select a collection of sets, under the constraint that their cost is at most a given budget. Upon arrival of a set the algorithm must decide whether to accept or to reject the arriving set, and it may also drop previously accepted sets (preemption). Rejecting or dropping a set is irrevocable. The goal is to maximize the total weight of the elements covered by the sets in the chosen collection. We present a deterministic 4/(1-r)-competitive algorithm for OBMC, where r is the maximum ratio between the cost of a set and the total budget. Building on that algorithm, we then present a randomized O(1)-competitive algorithm for OBMC. On the other hand, we show that the competitive ratio of any deterministic online algorithm is Omega(1/(sqrt{1-r})). We also give a deterministic O(Delta)-competitive algorithm, where Delta is the maximum weight of a set (given that the minimum element weight is 1), and if the total weight of all elements, w(U), is known in advance, we show that a slight modification of that algorithm is O(min{Delta,sqrt{w(U)}})-competitive. A matching lower bound of Omega(min{Delta,sqrt{w(U)}}) is also given. Previous to the present work, only the unit cost version of OBMC was studied under the online setting, giving a 4-competitive algorithm [Saha, Getoor, 2009]. Finally, our results, including the lower bounds, apply to Removable Online Knapsack which is the preemptive version of the Online Knapsack problem.
Cite as

Dror Rawitz and Adi Rosén. Online Budgeted Maximum Coverage. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 73:1-73:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{rawitz_et_al:LIPIcs.ESA.2016.73,
  author =	{Rawitz, Dror and Ros\'{e}n, Adi},
  title =	{{Online Budgeted Maximum Coverage}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{73:1--73:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Sankowski, Piotr and Zaroliagis, Christos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.73},
  URN =		{urn:nbn:de:0030-drops-64146},
  doi =		{10.4230/LIPIcs.ESA.2016.73},
  annote =	{Keywords: budgeted coverage, maximum coverage, online algorithms, competitive analysis, removable online knapsack}
}
Document
DOI: 10.4230/LIPIcs.STACS.2015.636
Paid Exchanges are Worth the Price

Authors: Alejandro López-Ortiz, Marc P. Renault, and Adi Rosén

Published in: LIPIcs, Volume 30, 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)

Abstract
We consider the list update problem as defined in the seminal work on competitive analysis by Sleator and Tarjan [12]. In this problem, a sequence of requests, consisting of items to access in a linked list, is given. After an item is accessed it can be moved to any position forward in the list at no cost (free exchange), and, at any time, any two adjacent items can be swapped at a cost of 1 (paid exchange). The cost to access an item is its current position in the list. The goal is to dynamically rearrange the list so as to minimize the total cost (accrued from accesses and exchanges) over the request sequence. We show a lower bound of 12/11 on the worst-case ratio between the performance of an (offline) optimal algorithm that can only perform free exchanges and that of an (offline) optimal algorithm that can perform both paid and free exchanges. This answers an outstanding question that has been open since 1996 [10].
Cite as

Alejandro López-Ortiz, Marc P. Renault, and Adi Rosén. Paid Exchanges are Worth the Price. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 636-648, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{lopezortiz_et_al:LIPIcs.STACS.2015.636,
  author =	{L\'{o}pez-Ortiz, Alejandro and Renault, Marc P. and Ros\'{e}n, Adi},
  title =	{{Paid Exchanges are Worth the Price}},
  booktitle =	{32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
  pages =	{636--648},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-78-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{30},
  editor =	{Mayr, Ernst W. and Ollinger, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.636},
  URN =		{urn:nbn:de:0030-drops-49476},
  doi =		{10.4230/LIPIcs.STACS.2015.636},
  annote =	{Keywords: list update problem, online computation, online algorithms, competitive analysis, lower bounds}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2014.34
The Cover Number of a Matrix and its Algorithmic Applications

Authors: Noga Alon, Troy Lee, and Adi Shraibman

Published in: LIPIcs, Volume 28, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)

Abstract
Given a matrix A, we study how many epsilon-cubes are required to cover the convex hull of the columns of A. We show bounds on this cover number in terms of VC dimension and the gamma_2 norm and give algorithms for enumerating elements of a cover. This leads to algorithms for computing approximate Nash equilibria that unify and extend several previous results in the literature. Moreover, our approximation algorithms can be applied quite generally to a family of quadratic optimization problems that also includes finding the k-by-k combinatorial rectangle of a matrix. In particular, for this problem we give the first quasi-polynomial time additive approximation algorithm that works for any matrix A in [0,1]^{m x n}.
Cite as

Noga Alon, Troy Lee, and Adi Shraibman. The Cover Number of a Matrix and its Algorithmic Applications. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 34-47, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{alon_et_al:LIPIcs.APPROX-RANDOM.2014.34,
  author =	{Alon, Noga and Lee, Troy and Shraibman, Adi},
  title =	{{The Cover Number of a Matrix and its Algorithmic Applications}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
  pages =	{34--47},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-74-3},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{28},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} and Devanur, Nikhil R. and Moore, Cristopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2014.34},
  URN =		{urn:nbn:de:0030-drops-46865},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2014.34},
  annote =	{Keywords: Approximation algorithms, Approximate Nash equilibria, Cover number, VC dimension}
}
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