27 Search Results for "Rubinfeld, Ronitt"

Document
DOI: 10.4230/LIPIcs.ESA.2024.89
Locally Computing Edge Orientations

Authors: Slobodan Mitrović, Ronitt Rubinfeld, and Mihir Singhal

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

Abstract
We consider the question of orienting the edges in a graph G such that every vertex has bounded out-degree. For graphs of arboricity α, there is an orientation in which every vertex has out-degree at most α and, moreover, the best possible maximum out-degree of an orientation is at least α - 1. We are thus interested in algorithms that can achieve a maximum out-degree of close to α. A widely studied approach for this problem in the distributed algorithms setting is a "peeling algorithm" that provides an orientation with maximum out-degree α(2+ε) in a logarithmic number of iterations. We consider this problem in the local computation algorithm (LCA) model, which quickly answers queries of the form "What is the orientation of edge (u,v)?" by probing the input graph. When the peeling algorithm is executed in the LCA setting by applying standard techniques, e.g., the Parnas-Ron paradigm, it requires Ω(n) probes per query on an n-vertex graph. In the case where G has unbounded degree, we show that any LCA that orients its edges to yield maximum out-degree r must use Ω(√ n/r) probes to G per query in the worst case, even if G is known to be a forest (that is, α = 1). We also show several algorithms with sublinear probe complexity when G has unbounded degree. When G is a tree such that the maximum degree Δ of G is bounded, we demonstrate an algorithm that uses Δ n^{1-log_Δ r + o(1)} probes to G per query. To obtain this result, we develop an edge-coloring approach that ultimately yields a graph-shattering-like result. We also use this shattering-like approach to demonstrate an LCA which 4-colors any tree using sublinear probes per query.
Cite as

Slobodan Mitrović, Ronitt Rubinfeld, and Mihir Singhal. Locally Computing Edge Orientations. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 89:1-89:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{mitrovic_et_al:LIPIcs.ESA.2024.89,
  author =	{Mitrovi\'{c}, Slobodan and Rubinfeld, Ronitt and Singhal, Mihir},
  title =	{{Locally Computing Edge Orientations}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{89:1--89:17},
  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.2024.89},
  URN =		{urn:nbn:de:0030-drops-211603},
  doi =		{10.4230/LIPIcs.ESA.2024.89},
  annote =	{Keywords: local computation algorithms, edge orientation, tree coloring}
}
Document
DOI: 10.4230/DagRep.13.2.33
From Big Data Theory to Big Data Practice (Dagstuhl Seminar 23071)

Authors: Martin Farach-Colton, Fabian Daniel Kuhn, Ronitt Rubinfeld, and Przemysław Uznański

Published in: Dagstuhl Reports, Volume 13, Issue 2 (2023)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 23071 "From Big Data Theory to Big Data Practice". Some recent advances in the theory of algorithms for big data - sublinear/local algorithms, streaming algorithms and external memory algorithms - have translated into impressive improvements in practice, whereas others have remained stubbornly resistant to useful implementations. This seminar aimed to glean lessons for those aspect of these algorithms that have led to practical implementation to see if the lessons learned can both improve the implementations of other theoretical ideas and to help guide the next generation of theoretical advances.
Cite as

Martin Farach-Colton, Fabian Daniel Kuhn, Ronitt Rubinfeld, and Przemysław Uznański. From Big Data Theory to Big Data Practice (Dagstuhl Seminar 23071). In Dagstuhl Reports, Volume 13, Issue 2, pp. 33-46, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{farachcolton_et_al:DagRep.13.2.33,
  author =	{Farach-Colton, Martin and Kuhn, Fabian Daniel and Rubinfeld, Ronitt and Uzna\'{n}ski, Przemys{\l}aw},
  title =	{{From Big Data Theory to Big Data Practice (Dagstuhl Seminar 23071)}},
  pages =	{33--46},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2023},
  volume =	{13},
  number =	{2},
  editor =	{Farach-Colton, Martin and Kuhn, Fabian Daniel and Rubinfeld, Ronitt and Uzna\'{n}ski, Przemys{\l}aw},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.13.2.33},
  URN =		{urn:nbn:de:0030-drops-191809},
  doi =		{10.4230/DagRep.13.2.33},
  annote =	{Keywords: external memory, local algorithms, sublinear algorithms}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.45
New Partitioning Techniques and Faster Algorithms for Approximate Interval Scheduling

Authors: Spencer Compton, Slobodan Mitrović, and Ronitt Rubinfeld

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

Abstract
Interval scheduling is a basic problem in the theory of algorithms and a classical task in combinatorial optimization. We develop a set of techniques for partitioning and grouping jobs based on their starting and ending times, that enable us to view an instance of interval scheduling on many jobs as a union of multiple interval scheduling instances, each containing only a few jobs. Instantiating these techniques in dynamic and local settings of computation leads to several new results. For (1+ε)-approximation of job scheduling of n jobs on a single machine, we develop a fully dynamic algorithm with O((log n)/ε) update and O(log n) query worst-case time. Further, we design a local computation algorithm that uses only O((log N)/ε) queries when all jobs are length at least 1 and have starting/ending times within [0,N]. Our techniques are also applicable in a setting where jobs have rewards/weights. For this case we design a fully dynamic deterministic algorithm whose worst-case update and query time are poly(log n,1/ε). Equivalently, this is the first algorithm that maintains a (1+ε)-approximation of the maximum independent set of a collection of weighted intervals in poly(log n,1/ε) time updates/queries. This is an exponential improvement in 1/ε over the running time of a randomized algorithm of Henzinger, Neumann, and Wiese [SoCG, 2020], while also removing all dependence on the values of the jobs' starting/ending times and rewards, as well as removing the need for any randomness. We also extend our approaches for interval scheduling on a single machine to examine the setting with M machines.
Cite as

Spencer Compton, Slobodan Mitrović, and Ronitt Rubinfeld. New Partitioning Techniques and Faster Algorithms for Approximate Interval Scheduling. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 45:1-45:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{compton_et_al:LIPIcs.ICALP.2023.45,
  author =	{Compton, Spencer and Mitrovi\'{c}, Slobodan and Rubinfeld, Ronitt},
  title =	{{New Partitioning Techniques and Faster Algorithms for Approximate Interval Scheduling}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{45:1--45:16},
  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.2023.45},
  URN =		{urn:nbn:de:0030-drops-180978},
  doi =		{10.4230/LIPIcs.ICALP.2023.45},
  annote =	{Keywords: interval scheduling, dynamic algorithms, local computation algorithms}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.39
Massively Parallel Algorithms for Small Subgraph Counting

Authors: Amartya Shankha Biswas, Talya Eden, Quanquan C. Liu, Ronitt Rubinfeld, and Slobodan Mitrović

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

Abstract
Over the last two decades, frameworks for distributed-memory parallel computation, such as MapReduce, Hadoop, Spark and Dryad, have gained significant popularity with the growing prevalence of large network datasets. The Massively Parallel Computation (MPC) model is the de-facto standard for studying graph algorithms in these frameworks theoretically. Subgraph counting is one such fundamental problem in analyzing massive graphs, with the main algorithmic challenges centering on designing methods which are both scalable and accurate. Given a graph G = (V, E) with n vertices, m edges and T triangles, our first result is an algorithm that outputs a (1+ε)-approximation to T, with asymptotically optimal round and total space complexity provided any S ≥ max{(√ m, n²/m)} space per machine and assuming T = Ω(√{m/n}). Our result gives a quadratic improvement on the bound on T over previous works. We also provide a simple extension of our result to counting any subgraph of k size for constant k ≥ 1. Our second result is an O_δ(log log n)-round algorithm for exactly counting the number of triangles, whose total space usage is parametrized by the arboricity α of the input graph. We extend this result to exactly counting k-cliques for any constant k. Finally, we prove that a recent result of Bera, Pashanasangi and Seshadhri (ITCS 2020) for exactly counting all subgraphs of size at most 5 can be implemented in the MPC model in Õ_δ(√{log n}) rounds, O(n^δ) space per machine and O(mα³) total space. In addition to our theoretical results, we simulate our triangle counting algorithms in real-world graphs obtained from the Stanford Network Analysis Project (SNAP) database. Our results show that both our approximate and exact counting algorithms exhibit improvements in terms of round complexity and approximation ratio, respectively, compared to two previous widely used algorithms for these problems.
Cite as

Amartya Shankha Biswas, Talya Eden, Quanquan C. Liu, Ronitt Rubinfeld, and Slobodan Mitrović. Massively Parallel Algorithms for Small Subgraph Counting. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 39:1-39:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{biswas_et_al:LIPIcs.APPROX/RANDOM.2022.39,
  author =	{Biswas, Amartya Shankha and Eden, Talya and Liu, Quanquan C. and Rubinfeld, Ronitt and Mitrovi\'{c}, Slobodan},
  title =	{{Massively Parallel Algorithms for Small Subgraph Counting}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{39:1--39:28},
  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.2022.39},
  URN =		{urn:nbn:de:0030-drops-171619},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.39},
  annote =	{Keywords: triangle counting, massively parallel computation, clique counting, approximation algorithms, subgraph counting}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.24
Local Access to Random Walks

Authors: Amartya Shankha Biswas, Edward Pyne, and Ronitt Rubinfeld

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

Abstract
For a graph G on n vertices, naively sampling the position of a random walk of at time t requires work Ω(t). We desire local access algorithms supporting position_G(t) queries, which return the position of a random walk from some fixed start vertex s at time t, where the joint distribution of returned positions is 1/poly(n) close to those of a uniformly random walk in 𝓁₁ distance. We first give an algorithm for local access to random walks on a given undirected d-regular graph with Õ(1/(1-λ)√n) runtime per query, where λ is the second-largest eigenvalue of the random walk matrix of the graph in absolute value. Since random d-regular graphs G(n,d) are expanders with high probability, this gives an Õ(√n) algorithm for a graph drawn from G(n,d) whp, which improves on the naive method for small numbers of queries. We then prove that no algorithm with subconstant error given probe access to an input d-regular graph can have runtime better than Ω(√n/log(n)) per query in expectation when the input graph is drawn from G(n,d), obtaining a nearly matching lower bound. We further show an Ω(n^{1/4}) runtime per query lower bound even with an oblivious adversary (i.e. when the query sequence is fixed in advance). We then show that for families of graphs with additional group theoretic structure, dramatically better results can be achieved. We give local access to walks on small-degree abelian Cayley graphs, including cycles and hypercubes, with runtime polylog(n) per query. This also allows for efficient local access to walks on polylog degree expanders. We show that our techniques apply to graphs with high degree by extending or results to graphs constructed using the tensor product (giving fast local access to walks on degree n^ε graphs for any ε ∈ (0,1]) and Cartesian product.
Cite as

Amartya Shankha Biswas, Edward Pyne, and Ronitt Rubinfeld. Local Access to Random Walks. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 24:1-24:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{biswas_et_al:LIPIcs.ITCS.2022.24,
  author =	{Biswas, Amartya Shankha and Pyne, Edward and Rubinfeld, Ronitt},
  title =	{{Local Access to Random Walks}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{24:1--24:22},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.24},
  URN =		{urn:nbn:de:0030-drops-156209},
  doi =		{10.4230/LIPIcs.ITCS.2022.24},
  annote =	{Keywords: sublinear time algorithms, random generation, local computation}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2021.51
Sampling Multiple Edges Efficiently

Authors: Talya Eden, Saleet Mossel, and Ronitt Rubinfeld

Published in: LIPIcs, Volume 207, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)

Abstract
We present a sublinear time algorithm that allows one to sample multiple edges from a distribution that is pointwise ε-close to the uniform distribution, in an amortized-efficient fashion. We consider the adjacency list query model, where access to a graph G is given via degree and neighbor queries. The problem of sampling a single edge in this model has been raised by Eden and Rosenbaum (SOSA 18). Let n and m denote the number of vertices and edges of G, respectively. Eden and Rosenbaum provided upper and lower bounds of Θ^*(n/√ m) for sampling a single edge in general graphs (where O^*(⋅) suppresses poly(1/ε) and poly(log n) dependencies). We ask whether the query complexity lower bound for sampling a single edge can be circumvented when multiple samples are required. That is, can we get an improved amortized per-sample cost if we allow a preprocessing phase? We answer in the affirmative. We present an algorithm that, if one knows the number of required samples q in advance, has an overall cost that is sublinear in q, namely, O^*(√ q ⋅(n/√ m)), which is strictly preferable to O^*(q⋅ (n/√ m)) cost resulting from q invocations of the algorithm by Eden and Rosenbaum. Subsequent to a preliminary version of this work, Tětek and Thorup (arXiv, preprint) proved that this bound is essentially optimal.
Cite as

Talya Eden, Saleet Mossel, and Ronitt Rubinfeld. Sampling Multiple Edges Efficiently. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 51:1-51:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{eden_et_al:LIPIcs.APPROX/RANDOM.2021.51,
  author =	{Eden, Talya and Mossel, Saleet and Rubinfeld, Ronitt},
  title =	{{Sampling Multiple Edges Efficiently}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)},
  pages =	{51:1--51:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-207-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{207},
  editor =	{Wootters, Mary and Sanit\`{a}, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2021.51},
  URN =		{urn:nbn:de:0030-drops-147441},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2021.51},
  annote =	{Keywords: Sampling edges, graph algorithm, sublinear algorithms}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2021.55
Towards a Decomposition-Optimal Algorithm for Counting and Sampling Arbitrary Motifs in Sublinear Time

Authors: Amartya Shankha Biswas, Talya Eden, and Ronitt Rubinfeld

Published in: LIPIcs, Volume 207, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)

Abstract
We consider the problem of sampling and approximately counting an arbitrary given motif H in a graph G, where access to G is given via queries: degree, neighbor, and pair, as well as uniform edge sample queries. Previous algorithms for these tasks were based on a decomposition of H into a collection of odd cycles and stars, denoted D^*(H) = {O_{k₁},...,O_{k_q}, S_{p₁},...,S_{p_𝓁}}. These algorithms were shown to be optimal for the case where H is a clique or an odd-length cycle, but no other lower bounds were known. We present a new algorithm for sampling arbitrary motifs which, up to poly(log n) factors, is always at least as good, and for most graphs G is strictly better. The main ingredient leading to this improvement is an improved uniform algorithm for sampling stars, which might be of independent interest, as it allows to sample vertices according to the p-th moment of the degree distribution. Finally, we prove that this algorithm is decomposition-optimal for decompositions that contain at least one odd cycle. These are the first lower bounds for motifs H with a nontrivial decomposition, i.e., motifs that have more than a single component in their decomposition.
Cite as

Amartya Shankha Biswas, Talya Eden, and Ronitt Rubinfeld. Towards a Decomposition-Optimal Algorithm for Counting and Sampling Arbitrary Motifs in Sublinear Time. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 55:1-55:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{biswas_et_al:LIPIcs.APPROX/RANDOM.2021.55,
  author =	{Biswas, Amartya Shankha and Eden, Talya and Rubinfeld, Ronitt},
  title =	{{Towards a Decomposition-Optimal Algorithm for Counting and Sampling Arbitrary Motifs in Sublinear Time}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)},
  pages =	{55:1--55:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-207-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{207},
  editor =	{Wootters, Mary and Sanit\`{a}, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2021.55},
  URN =		{urn:nbn:de:0030-drops-147480},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2021.55},
  annote =	{Keywords: Sublinear time algorithms, Graph algorithms, Sampling subgraphs, Approximate counting}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2020.27
Almost Optimal Distribution-Free Sample-Based Testing of k-Modality

Authors: Dana Ron and Asaf Rosin

Published in: LIPIcs, Volume 176, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)

Abstract
For an integer k ≥ 0, a sequence σ = σ₁,… ,σ_n over a fully ordered set is k-modal, if there exist indices 1 = a₀ < a₁ < … < a_{k+1} = n such that for each i, the subsequence σ_{a_i},… ,σ_{a_{i+1}} is either monotonically non-decreasing or monotonically non-increasing. The property of k-modality is a natural extension of monotonicity, which has been studied extensively in the area of property testing. We study one-sided error property testing of k-modality in the distribution-free sample-based model. We prove an upper bound of O({√{kn}log k}/ε) on the sample complexity, and an almost matching lower bound of Ω(√{kn}/ε). When the underlying distribution is uniform, we obtain a completely tight bound of Θ(√{kn/ε}), which generalizes what is known for sample-based testing of monotonicity under the uniform distribution.
Cite as

Dana Ron and Asaf Rosin. Almost Optimal Distribution-Free Sample-Based Testing of k-Modality. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 27:1-27:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{ron_et_al:LIPIcs.APPROX/RANDOM.2020.27,
  author =	{Ron, Dana and Rosin, Asaf},
  title =	{{Almost Optimal Distribution-Free Sample-Based Testing of k-Modality}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
  pages =	{27:1--27:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-164-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{176},
  editor =	{Byrka, Jaros{\l}aw and Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2020.27},
  URN =		{urn:nbn:de:0030-drops-126307},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2020.27},
  annote =	{Keywords: Sample-based property testing, Distribution-free property testing, k-modality}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.98
Property Testing of LP-Type Problems

Authors: Rogers Epstein and Sandeep Silwal

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
Given query access to a set of constraints S, we wish to quickly check if some objective function φ subject to these constraints is at most a given value k. We approach this problem using the framework of property testing where our goal is to distinguish the case φ(S) ≤ k from the case that at least an ε fraction of the constraints in S need to be removed for φ(S) ≤ k to hold. We restrict our attention to the case where (S,φ) are LP-Type problems which is a rich family of combinatorial optimization problems with an inherent geometric structure. By utilizing a simple sampling procedure which has been used previously to study these problems, we are able to create property testers for any LP-Type problem whose query complexities are independent of the number of constraints. To the best of our knowledge, this is the first work that connects the area of LP-Type problems and property testing in a systematic way. Among our results are property testers for a variety of LP-Type problems that are new and also problems that have been studied previously such as a tight upper bound on the query complexity of testing clusterability with one cluster considered by Alon, Dar, Parnas, and Ron (FOCS 2000). We also supply a corresponding tight lower bound for this problem and other LP-Type problems using geometric constructions.
Cite as

Rogers Epstein and Sandeep Silwal. Property Testing of LP-Type Problems. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 98:1-98:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{epstein_et_al:LIPIcs.ICALP.2020.98,
  author =	{Epstein, Rogers and Silwal, Sandeep},
  title =	{{Property Testing of LP-Type Problems}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{98:1--98:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.98},
  URN =		{urn:nbn:de:0030-drops-125056},
  doi =		{10.4230/LIPIcs.ICALP.2020.98},
  annote =	{Keywords: property pesting, LP-Type problems, random sampling}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.27
Local Access to Huge Random Objects Through Partial Sampling

Authors: Amartya Shankha Biswas, Ronitt Rubinfeld, and Anak Yodpinyanee

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
Consider an algorithm performing a computation on a huge random object (for example a random graph or a "long" random walk). Is it necessary to generate the entire object prior to the computation, or is it possible to provide query access to the object and sample it incrementally "on-the-fly" (as requested by the algorithm)? Such an implementation should emulate the random object by answering queries in a manner consistent with an instance of the random object sampled from the true distribution (or close to it). This paradigm is useful when the algorithm is sub-linear and thus, sampling the entire object up front would ruin its efficiency. Our first set of results focus on undirected graphs with independent edge probabilities, i.e. each edge is chosen as an independent Bernoulli random variable. We provide a general implementation for this model under certain assumptions. Then, we use this to obtain the first efficient local implementations for the Erdös-Rényi G(n,p) model for all values of p, and the Stochastic Block model. As in previous local-access implementations for random graphs, we support Vertex-Pair and Next-Neighbor queries. In addition, we introduce a new Random-Neighbor query. Next, we give the first local-access implementation for All-Neighbors queries in the (sparse and directed) Kleinberg’s Small-World model. Our implementations require no pre-processing time, and answer each query using O(poly(log n)) time, random bits, and additional space. Next, we show how to implement random Catalan objects, specifically focusing on Dyck paths (balanced random walks on the integer line that are always non-negative). Here, we support Height queries to find the location of the walk, and First-Return queries to find the time when the walk returns to a specified location. This in turn can be used to implement Next-Neighbor queries on random rooted ordered trees, and Matching-Bracket queries on random well bracketed expressions (the Dyck language). Finally, we introduce two features to define a new model that: (1) allows multiple independent (and even simultaneous) instantiations of the same implementation, to be consistent with each other without the need for communication, (2) allows us to generate a richer class of random objects that do not have a succinct description. Specifically, we study uniformly random valid q-colorings of an input graph G with maximum degree Δ. This is in contrast to prior work in the area, where the relevant random objects are defined as a distribution with O(1) parameters (for example, n and p in the G(n,p) model). The distribution over valid colorings is instead specified via a "huge" input (the underlying graph G), that is far too large to be read by a sub-linear time algorithm. Instead, our implementation accesses G through local neighborhood probes, and is able to answer queries to the color of any given vertex in sub-linear time for q ≥ 9Δ, in a manner that is consistent with a specific random valid coloring of G. Furthermore, the implementation is memory-less, and can maintain consistency with non-communicating copies of itself.
Cite as

Amartya Shankha Biswas, Ronitt Rubinfeld, and Anak Yodpinyanee. Local Access to Huge Random Objects Through Partial Sampling. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 27:1-27:65, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{biswas_et_al:LIPIcs.ITCS.2020.27,
  author =	{Biswas, Amartya Shankha and Rubinfeld, Ronitt and Yodpinyanee, Anak},
  title =	{{Local Access to Huge Random Objects Through Partial Sampling}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{27:1--27:65},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.27},
  URN =		{urn:nbn:de:0030-drops-117126},
  doi =		{10.4230/LIPIcs.ITCS.2020.27},
  annote =	{Keywords: sublinear time algorithms, random generation, local computation}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.28
Monotone Probability Distributions over the Boolean Cube Can Be Learned with Sublinear Samples

Authors: Ronitt Rubinfeld and Arsen Vasilyan

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
A probability distribution over the Boolean cube is monotone if flipping the value of a coordinate from zero to one can only increase the probability of an element. Given samples of an unknown monotone distribution over the Boolean cube, we give (to our knowledge) the first algorithm that learns an approximation of the distribution in statistical distance using a number of samples that is sublinear in the domain. To do this, we develop a structural lemma describing monotone probability distributions. The structural lemma has further implications to the sample complexity of basic testing tasks for analyzing monotone probability distributions over the Boolean cube: We use it to give nontrivial upper bounds on the tasks of estimating the distance of a monotone distribution to uniform and of estimating the support size of a monotone distribution. In the setting of monotone probability distributions over the Boolean cube, our algorithms are the first to have sample complexity lower than known lower bounds for the same testing tasks on arbitrary (not necessarily monotone) probability distributions. One further consequence of our learning algorithm is an improved sample complexity for the task of testing whether a distribution on the Boolean cube is monotone.
Cite as

Ronitt Rubinfeld and Arsen Vasilyan. Monotone Probability Distributions over the Boolean Cube Can Be Learned with Sublinear Samples. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 28:1-28:34, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{rubinfeld_et_al:LIPIcs.ITCS.2020.28,
  author =	{Rubinfeld, Ronitt and Vasilyan, Arsen},
  title =	{{Monotone Probability Distributions over the Boolean Cube Can Be Learned with Sublinear Samples}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{28:1--28:34},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.28},
  URN =		{urn:nbn:de:0030-drops-117138},
  doi =		{10.4230/LIPIcs.ITCS.2020.28},
  annote =	{Keywords: Learning distributions, monotone probability distributions, estimating support size}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.69
Testing Properties of Multiple Distributions with Few Samples

Authors: Maryam Aliakbarpour and Sandeep Silwal

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
We propose a new setting for testing properties of distributions while receiving samples from several distributions, but few samples per distribution. Given samples from s distributions, p_1, p_2, …, p_s, we design testers for the following problems: (1) Uniformity Testing: Testing whether all the p_i’s are uniform or ε-far from being uniform in ℓ_1-distance (2) Identity Testing: Testing whether all the p_i’s are equal to an explicitly given distribution q or ε-far from q in ℓ_1-distance, and (3) Closeness Testing: Testing whether all the p_i’s are equal to a distribution q which we have sample access to, or ε-far from q in ℓ_1-distance. By assuming an additional natural condition about the source distributions, we provide sample optimal testers for all of these problems.
Cite as

Maryam Aliakbarpour and Sandeep Silwal. Testing Properties of Multiple Distributions with Few Samples. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 69:1-69:41, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{aliakbarpour_et_al:LIPIcs.ITCS.2020.69,
  author =	{Aliakbarpour, Maryam and Silwal, Sandeep},
  title =	{{Testing Properties of Multiple Distributions with Few Samples}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{69:1--69:41},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.69},
  URN =		{urn:nbn:de:0030-drops-117545},
  doi =		{10.4230/LIPIcs.ITCS.2020.69},
  annote =	{Keywords: Hypothesis Testing, Property Testing, Distribution Testing, Identity Testing, Closeness Testing, Multiple Sources}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2019.52
Approximating the Noise Sensitivity of a Monotone Boolean Function

Authors: Ronitt Rubinfeld and Arsen Vasilyan

Published in: LIPIcs, Volume 145, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)

Abstract
The noise sensitivity of a Boolean function f: {0,1}^n - > {0,1} is one of its fundamental properties. For noise parameter delta, the noise sensitivity is denoted as NS_{delta}[f]. This quantity is defined as follows: First, pick x = (x_1,...,x_n) uniformly at random from {0,1}^n, then pick z by flipping each x_i independently with probability delta. NS_{delta}[f] is defined to equal Pr [f(x) != f(z)]. Much of the existing literature on noise sensitivity explores the following two directions: (1) Showing that functions with low noise-sensitivity are structured in certain ways. (2) Mathematically showing that certain classes of functions have low noise sensitivity. Combined, these two research directions show that certain classes of functions have low noise sensitivity and therefore have useful structure. The fundamental importance of noise sensitivity, together with this wealth of structural results, motivates the algorithmic question of approximating NS_{delta}[f] given an oracle access to the function f. We show that the standard sampling approach is essentially optimal for general Boolean functions. Therefore, we focus on estimating the noise sensitivity of monotone functions, which form an important subclass of Boolean functions, since many functions of interest are either monotone or can be simply transformed into a monotone function (for example the class of unate functions consists of all the functions that can be made monotone by reorienting some of their coordinates [O'Donnell, 2014]). Specifically, we study the algorithmic problem of approximating NS_{delta}[f] for monotone f, given the promise that NS_{delta}[f] >= 1/n^{C} for constant C, and for delta in the range 1/n <= delta <= 1/2. For such f and delta, we give a randomized algorithm performing O((min(1,sqrt{n} delta log^{1.5} n))/(NS_{delta}[f]) poly (1/epsilon)) queries and approximating NS_{delta}[f] to within a multiplicative factor of (1 +/- epsilon). Given the same constraints on f and delta, we also prove a lower bound of Omega((min(1,sqrt{n} delta))/(NS_{delta}[f] * n^{xi})) on the query complexity of any algorithm that approximates NS_{delta}[f] to within any constant factor, where xi can be any positive constant. Thus, our algorithm’s query complexity is close to optimal in terms of its dependence on n. We introduce a novel descending-ascending view of noise sensitivity, and use it as a central tool for the analysis of our algorithm. To prove lower bounds on query complexity, we develop a technique that reduces computational questions about query complexity to combinatorial questions about the existence of "thin" functions with certain properties. The existence of such "thin" functions is proved using the probabilistic method. These techniques also yield new lower bounds on the query complexity of approximating other fundamental properties of Boolean functions: the total influence and the bias.
Cite as

Ronitt Rubinfeld and Arsen Vasilyan. Approximating the Noise Sensitivity of a Monotone Boolean Function. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 52:1-52:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{rubinfeld_et_al:LIPIcs.APPROX-RANDOM.2019.52,
  author =	{Rubinfeld, Ronitt and Vasilyan, Arsen},
  title =	{{Approximating the Noise Sensitivity of a Monotone Boolean Function}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{52:1--52:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-125-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{145},
  editor =	{Achlioptas, Dimitris and V\'{e}gh, L\'{a}szl\'{o} A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2019.52},
  URN =		{urn:nbn:de:0030-drops-112672},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.52},
  annote =	{Keywords: Monotone Boolean functions, noise sensitivity, influence}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2019.58
Local Computation Algorithms for Spanners

Authors: Merav Parter, Ronitt Rubinfeld, Ali Vakilian, and Anak Yodpinyanee

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

Abstract
A graph spanner is a fundamental graph structure that faithfully preserves the pairwise distances in the input graph up to a small multiplicative stretch. The common objective in the computation of spanners is to achieve the best-known existential size-stretch trade-off efficiently. Classical models and algorithmic analysis of graph spanners essentially assume that the algorithm can read the input graph, construct the desired spanner, and write the answer to the output tape. However, when considering massive graphs containing millions or even billions of nodes not only the input graph, but also the output spanner might be too large for a single processor to store. To tackle this challenge, we initiate the study of local computation algorithms (LCAs) for graph spanners in general graphs, where the algorithm should locally decide whether a given edge (u,v) in E belongs to the output (sparse) spanner or not. Such LCAs give the user the "illusion" that a specific sparse spanner for the graph is maintained, without ever fully computing it. We present several results for this setting, including: - For general n-vertex graphs and for parameter r in {2,3}, there exists an LCA for (2r-1)-spanners with O~(n^{1+1/r}) edges and sublinear probe complexity of O~(n^{1-1/2r}). These size/stretch trade-offs are best possible (up to polylogarithmic factors). - For every k >= 1 and n-vertex graph with maximum degree Delta, there exists an LCA for O(k^2) spanners with O~(n^{1+1/k}) edges, probe complexity of O~(Delta^4 n^{2/3}), and random seed of size polylog(n). This improves upon, and extends the work of [Lenzen-Levi, ICALP'18]. We also complement these constructions by providing a polynomial lower bound on the probe complexity of LCAs for graph spanners that holds even for the simpler task of computing a sparse connected subgraph with o(m) edges. To the best of our knowledge, our results on 3 and 5-spanners are the first LCAs with sublinear (in Delta) probe-complexity for Delta = n^{Omega(1)}.
Cite as

Merav Parter, Ronitt Rubinfeld, Ali Vakilian, and Anak Yodpinyanee. Local Computation Algorithms for Spanners. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 58:1-58:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{parter_et_al:LIPIcs.ITCS.2019.58,
  author =	{Parter, Merav and Rubinfeld, Ronitt and Vakilian, Ali and Yodpinyanee, Anak},
  title =	{{Local Computation Algorithms for Spanners}},
  booktitle =	{10th Innovations in Theoretical Computer Science Conference (ITCS 2019)},
  pages =	{58:1--58:21},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2019.58},
  URN =		{urn:nbn:de:0030-drops-101510},
  doi =		{10.4230/LIPIcs.ITCS.2019.58},
  annote =	{Keywords: Local Computation Algorithms, Sub-linear Algorithms, Graph Spanners}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2017.12
Fractional Set Cover in the Streaming Model

Authors: Piotr Indyk, Sepideh Mahabadi, Ronitt Rubinfeld, Jonathan Ullman, Ali Vakilian, and Anak Yodpinyanee

Published in: LIPIcs, Volume 81, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)

Abstract
We study the Fractional Set Cover problem in the streaming model. That is, we consider the relaxation of the set cover problem over a universe of n elements and a collection of m sets, where each set can be picked fractionally, with a value in [0,1]. We present a randomized (1+a)-approximation algorithm that makes p passes over the data, and uses O(polylog(m,n,1/a) (mn^(O(1/(pa)))+n)) memory space. The algorithm works in both the set arrival and the edge arrival models. To the best of our knowledge, this is the first streaming result for the fractional set cover problem. We obtain our results by employing the multiplicative weights update framework in the streaming settings.
Cite as

Piotr Indyk, Sepideh Mahabadi, Ronitt Rubinfeld, Jonathan Ullman, Ali Vakilian, and Anak Yodpinyanee. Fractional Set Cover in the Streaming Model. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 81, pp. 12:1-12:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{indyk_et_al:LIPIcs.APPROX-RANDOM.2017.12,
  author =	{Indyk, Piotr and Mahabadi, Sepideh and Rubinfeld, Ronitt and Ullman, Jonathan and Vakilian, Ali and Yodpinyanee, Anak},
  title =	{{Fractional Set Cover in the Streaming Model}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
  pages =	{12:1--12:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-044-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{81},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} D. P. and Williamson, David P. and Vempala, Santosh S.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2017.12},
  URN =		{urn:nbn:de:0030-drops-75613},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.12},
  annote =	{Keywords: Streaming Algorithms, Fractional Set Cover, LP relaxation, Multiplicative Weight Update}
}
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