27 Search Results for "Stanford, David A."

Document
DOI: 10.4230/LIPIcs.ITCS.2024.79
Near-Linear Time and Fixed-Parameter Tractable Algorithms for Tensor Decompositions

Authors: Arvind V. Mahankali, David P. Woodruff, and Ziyu Zhang

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

Abstract
We study low rank approximation of tensors, focusing on the Tensor Train and Tucker decompositions, as well as approximations with tree tensor networks and general tensor networks. As suggested by hardness results also shown in this work, obtaining (1+ε)-approximation algorithms for rank k tensor train and Tucker decompositions efficiently may be computationally hard for these problems. Therefore, we propose different algorithms that respectively satisfy some of the objectives above while violating some others within a bound, known as bicriteria algorithms. On the one hand, for rank-k tensor train decomposition for tensors with q modes, we give a (1 + ε)-approximation algorithm with a small bicriteria rank (O(qk/ε) up to logarithmic factors) and O(q ⋅ nnz(A)) running time, up to lower order terms. Here nnz(A) denotes the number of non-zero entries in the input tensor A. We also show how to convert the algorithm of [Huber et al., 2017] into a relative error approximation algorithm, but their algorithm necessarily has a running time of O(qr² ⋅ nnz(A)) + n ⋅ poly(qk/ε) when converted to a (1 + ε)-approximation algorithm with bicriteria rank r. Thus, the running time of our algorithm is better by at least a k² factor. To the best of our knowledge, our work is the first to achieve a near-input-sparsity time relative error approximation algorithm for tensor train decomposition. Our key technique is a method for efficiently obtaining subspace embeddings for a matrix which is the flattening of a Tensor Train of q tensors - the number of rows in the subspace embeddings is polynomial in q, thus avoiding the curse of dimensionality. We extend our algorithm to tree tensor networks and tensor networks on arbitrary graphs. Another way of coping with intractability is by looking at fixed-parameter tractable (FPT) algorithms. We give FPT algorithms for the tensor train, Tucker, and Canonical Polyadic (CP) decompositions, which are simpler than the FPT algorithms of [Song et al., 2019], since our algorithms do not make use of polynomial system solvers. Our technique of using an exponential number of Gaussian subspace embeddings with exactly k rows (and thus exponentially small success probability) may be of independent interest.
Cite as

Arvind V. Mahankali, David P. Woodruff, and Ziyu Zhang. Near-Linear Time and Fixed-Parameter Tractable Algorithms for Tensor Decompositions. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 79:1-79:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{mahankali_et_al:LIPIcs.ITCS.2024.79,
  author =	{Mahankali, Arvind V. and Woodruff, David P. and Zhang, Ziyu},
  title =	{{Near-Linear Time and Fixed-Parameter Tractable Algorithms for Tensor Decompositions}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{79:1--79:23},
  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.2024.79},
  URN =		{urn:nbn:de:0030-drops-196078},
  doi =		{10.4230/LIPIcs.ITCS.2024.79},
  annote =	{Keywords: Low rank approximation, Sketching algorithms, Tensor decomposition}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.93
Beyond Worst-Case Budget-Feasible Mechanism Design

Authors: Aviad Rubinstein and Junyao Zhao

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

Abstract
Motivated by large-market applications such as crowdsourcing, we revisit the problem of budget-feasible mechanism design under a "small-bidder assumption". Anari, Goel, and Nikzad (2018) gave a mechanism that has optimal competitive ratio 1-1/e on worst-case instances. However, we observe that on many realistic instances, their mechanism is significantly outperformed by a simpler open clock auction by Ensthaler and Giebe (2014), although the open clock auction only achieves competitive ratio 1/2 in the worst case. Is there a mechanism that gets the best of both worlds, i.e., a mechanism that is worst-case optimal and performs favorably on realistic instances? To answer this question, we initiate the study of beyond worst-case budget-feasible mechanism design. Our first main result is the design and the analysis of a natural mechanism that gives an affirmative answer to our question above: - We prove that on every instance, our mechanism performs at least as good as all uniform mechanisms, including Anari, Goel, and Nikzad’s and Ensthaler and Giebe’s mechanisms. - Moreover, we empirically evaluate our mechanism on various realistic instances and observe that it beats the worst-case 1-1/e competitive ratio by a large margin and compares favorably to both mechanisms mentioned above. Our second main result is more interesting in theory: We show that in the semi-adversarial model of budget-smoothed analysis, where the adversary designs a single worst-case market for a distribution of budgets, our mechanism is optimal among all (including non-uniform) mechanisms; furthermore our mechanism guarantees a strictly better-than-(1-1/e) expected competitive ratio for any non-trivial budget distribution regardless of the market. (In contrast, given any bounded range of budgets, we can construct a single market where Anari, Goel, and Nikzad’s mechanism achieves only 1-1/e competitive ratio for every budget in this range.) We complement the positive result with a characterization of the worst-case markets for any given budget distribution and prove a fairly robust hardness result that holds against any budget distribution and any mechanism.
Cite as

Aviad Rubinstein and Junyao Zhao. Beyond Worst-Case Budget-Feasible Mechanism Design. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 93:1-93:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{rubinstein_et_al:LIPIcs.ITCS.2023.93,
  author =	{Rubinstein, Aviad and Zhao, Junyao},
  title =	{{Beyond Worst-Case Budget-Feasible Mechanism Design}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{93:1--93:22},
  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.2023.93},
  URN =		{urn:nbn:de:0030-drops-175969},
  doi =		{10.4230/LIPIcs.ITCS.2023.93},
  annote =	{Keywords: Procurement auctions, Mechanism design, Beyond worst-case analysis}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.17
Finding Monotone Patterns in Sublinear Time, Adaptively

Authors: Omri Ben-Eliezer, Shoham Letzter, and Erik Waingarten

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

Abstract
We investigate adaptive sublinear algorithms for finding monotone patterns in sequential data. Given fixed 2 ≤ k ∈ m N and ε > 0, consider the problem of finding a length-k increasing subsequence in a sequence f : [n] → ℝ, provided that f is ε-far from free of such subsequences. It was shown by Ben-Eliezer et al. [FOCS 2019] that the non-adaptive query complexity of the above task is Θ((log n)^⌊log₂ k⌋). In this work, we break the non-adaptive lower bound, presenting an adaptive algorithm for this problem which makes O(log n) queries. This is optimal, matching the classical Ω(log n) adaptive lower bound by Fischer [Inf. Comp. 2004] for monotonicity testing (which corresponds to the case k = 2). Equivalently, our result implies that testing whether a sequence decomposes into k monotone subsequences can be done with O(log n) queries.
Cite as

Omri Ben-Eliezer, Shoham Letzter, and Erik Waingarten. Finding Monotone Patterns in Sublinear Time, Adaptively. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 17:1-17:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{beneliezer_et_al:LIPIcs.ICALP.2022.17,
  author =	{Ben-Eliezer, Omri and Letzter, Shoham and Waingarten, Erik},
  title =	{{Finding Monotone Patterns in Sublinear Time, Adaptively}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{17:1--17:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.17},
  URN =		{urn:nbn:de:0030-drops-163586},
  doi =		{10.4230/LIPIcs.ICALP.2022.17},
  annote =	{Keywords: property testing, monotone patterns, monotone decomposition, adaptivity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.20
Fully-Dynamic Graph Sparsifiers Against an Adaptive Adversary

Authors: Aaron Bernstein, Jan van den Brand, Maximilian Probst Gutenberg, Danupon Nanongkai, Thatchaphol Saranurak, Aaron Sidford, and He Sun

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

Abstract
Designing efficient dynamic graph algorithms against an adaptive adversary is a major goal in the field of dynamic graph algorithms and has witnessed many exciting recent developments in, e.g., dynamic matching (Wajc STOC'20) and decremental shortest paths (Chuzhoy and Khanna STOC'19). Compared to other graph primitives (e.g. spanning trees and matchings), designing such algorithms for graph spanners and (more broadly) graph sparsifiers poses a unique challenge since there is no fast deterministic algorithm known for static computation and the lack of a way to adjust the output slowly (known as "small recourse/replacements"). This paper presents the first non-trivial efficient adaptive algorithms for maintaining many sparsifiers against an adaptive adversary. Specifically, we present algorithms that maintain 1) a polylog(n)-spanner of size Õ(n) in polylog(n) amortized update time, 2) an O(k)-approximate cut sparsifier of size Õ(n) in Õ(n^{1/k}) amortized update time, and 3) a polylog(n)-approximate spectral sparsifier in polylog(n) amortized update time. Our bounds are the first non-trivial ones even when only the recourse is concerned. Our results hold even against a stronger adversary, who can access the random bits previously used by the algorithms and the amortized update time of all algorithms can be made worst-case by paying sub-polynomial factors. Our spanner result resolves an open question by Ahmed et al. (2019) and our results and techniques imply additional improvements over existing results, including (i) answering open questions about decremental single-source shortest paths by Chuzhoy and Khanna (STOC'19) and Gutenberg and Wulff-Nilsen (SODA'20), implying a nearly-quadratic time algorithm for approximating minimum-cost unit-capacity flow and (ii) de-amortizing a result of Abraham et al. (FOCS'16) for dynamic spectral sparsifiers. Our results are based on two novel techniques. The first technique is a generic black-box reduction that allows us to assume that the graph is initially an expander with almost uniform-degree and, more importantly, stays as an almost uniform-degree expander while undergoing only edge deletions. The second technique is called proactive resampling: here we constantly re-sample parts of the input graph so that, independent of an adversary’s computational power, a desired structure of the underlying graph can be always maintained. Despite its simplicity, the analysis of this sampling scheme is far from trivial, because the adversary can potentially create dependencies between the random choices used by the algorithm. We believe these two techniques could be useful for developing other adaptive algorithms.
Cite as

Aaron Bernstein, Jan van den Brand, Maximilian Probst Gutenberg, Danupon Nanongkai, Thatchaphol Saranurak, Aaron Sidford, and He Sun. Fully-Dynamic Graph Sparsifiers Against an Adaptive Adversary. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 20:1-20:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bernstein_et_al:LIPIcs.ICALP.2022.20,
  author =	{Bernstein, Aaron and van den Brand, Jan and Probst Gutenberg, Maximilian and Nanongkai, Danupon and Saranurak, Thatchaphol and Sidford, Aaron and Sun, He},
  title =	{{Fully-Dynamic Graph Sparsifiers Against an Adaptive Adversary}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{20:1--20:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.20},
  URN =		{urn:nbn:de:0030-drops-163611},
  doi =		{10.4230/LIPIcs.ICALP.2022.20},
  annote =	{Keywords: dynamic graph algorithm, adaptive adversary, spanner, sparsifier}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.24
Reconstructing Decision Trees

Authors: Guy Blanc, Jane Lange, and Li-Yang Tan

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

Abstract
We give the first reconstruction algorithm for decision trees: given queries to a function f that is opt-close to a size-s decision tree, our algorithm provides query access to a decision tree T where: - T has size S := s^O((log s)²/ε³); - dist(f,T) ≤ O(opt)+ε; - Every query to T is answered with poly((log s)/ε)⋅ log n queries to f and in poly((log s)/ε)⋅ n log n time. This yields a tolerant tester that distinguishes functions that are close to size-s decision trees from those that are far from size-S decision trees. The polylogarithmic dependence on s in the efficiency of our tester is exponentially smaller than that of existing testers. Since decision tree complexity is well known to be related to numerous other boolean function properties, our results also provide a new algorithm for reconstructing and testing these properties.
Cite as

Guy Blanc, Jane Lange, and Li-Yang Tan. Reconstructing Decision Trees. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 24:1-24:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{blanc_et_al:LIPIcs.ICALP.2022.24,
  author =	{Blanc, Guy and Lange, Jane and Tan, Li-Yang},
  title =	{{Reconstructing Decision Trees}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{24:1--24:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.24},
  URN =		{urn:nbn:de:0030-drops-163653},
  doi =		{10.4230/LIPIcs.ICALP.2022.24},
  annote =	{Keywords: Property reconstruction, property testing, tolerant testing, decision trees}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.38
Polylogarithmic Sketches for Clustering

Authors: Moses Charikar and Erik Waingarten

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

Abstract
Given n points in 𝓁_p^d, we consider the problem of partitioning points into k clusters with associated centers. The cost of a clustering is the sum of p-th powers of distances of points to their cluster centers. For p ∈ [1,2], we design sketches of size poly(log(nd),k,1/ε) such that the cost of the optimal clustering can be estimated to within factor 1+ε, despite the fact that the compressed representation does not contain enough information to recover the cluster centers or the partition into clusters. This leads to a streaming algorithm for estimating the clustering cost with space poly(log(nd),k,1/ε). We also obtain a distributed memory algorithm, where the n points are arbitrarily partitioned amongst m machines, each of which sends information to a central party who then computes an approximation of the clustering cost. Prior to this work, no such streaming or distributed-memory algorithm was known with sublinear dependence on d for p ∈ [1,2).
Cite as

Moses Charikar and Erik Waingarten. Polylogarithmic Sketches for Clustering. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 38:1-38:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{charikar_et_al:LIPIcs.ICALP.2022.38,
  author =	{Charikar, Moses and Waingarten, Erik},
  title =	{{Polylogarithmic Sketches for Clustering}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{38:1--38:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.38},
  URN =		{urn:nbn:de:0030-drops-163793},
  doi =		{10.4230/LIPIcs.ICALP.2022.38},
  annote =	{Keywords: sketching, clustering}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.55
High-Probability List-Recovery, and Applications to Heavy Hitters

Authors: Dean Doron and Mary Wootters

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

Abstract
An error correcting code 𝒞 : Σ^k → Σⁿ is efficiently list-recoverable from input list size 𝓁 if for any sets ℒ₁, …, ℒ_n ⊆ Σ of size at most 𝓁, one can efficiently recover the list ℒ = {x ∈ Σ^k : ∀ j ∈ [n], 𝒞(x)_j ∈ ℒ_j}. While list-recovery has been well-studied in error correcting codes, all known constructions with "efficient" algorithms are not efficient in the parameter 𝓁. In this work, motivated by applications in algorithm design and pseudorandomness, we study list-recovery with the goal of obtaining a good dependence on 𝓁. We make a step towards this goal by obtaining it in the weaker case where we allow a randomized encoding map and a small failure probability, and where the input lists are derived from unions of codewords. As an application of our construction, we give a data structure for the heavy hitters problem in the strict turnstile model that, for some parameter regimes, obtains stronger guarantees than known constructions.
Cite as

Dean Doron and Mary Wootters. High-Probability List-Recovery, and Applications to Heavy Hitters. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 55:1-55:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{doron_et_al:LIPIcs.ICALP.2022.55,
  author =	{Doron, Dean and Wootters, Mary},
  title =	{{High-Probability List-Recovery, and Applications to Heavy Hitters}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{55:1--55:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.55},
  URN =		{urn:nbn:de:0030-drops-163961},
  doi =		{10.4230/LIPIcs.ICALP.2022.55},
  annote =	{Keywords: List recoverable codes, Heavy Hitters, high-dimensional expanders}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.59
Streaming Submodular Maximization Under Matroid Constraints

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

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

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

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

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@InProceedings{feldman_et_al:LIPIcs.ICALP.2022.59,
  author =	{Feldman, Moran and Liu, Paul and Norouzi-Fard, Ashkan and Svensson, Ola and Zenklusen, Rico},
  title =	{{Streaming Submodular Maximization Under Matroid Constraints}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{59:1--59:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.59},
  URN =		{urn:nbn:de:0030-drops-164007},
  doi =		{10.4230/LIPIcs.ICALP.2022.59},
  annote =	{Keywords: Submodular maximization, streaming, matroid, random order}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.77
Regularized Box-Simplex Games and Dynamic Decremental Bipartite Matching

Authors: Arun Jambulapati, Yujia Jin, Aaron Sidford, and Kevin Tian

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

Abstract
Box-simplex games are a family of bilinear minimax objectives which encapsulate graph-structured problems such as maximum flow [Sherman, 2017], optimal transport [Arun Jambulapati et al., 2019], and bipartite matching [Sepehr Assadi et al., 2022]. We develop efficient near-linear time, high-accuracy solvers for regularized variants of these games. Beyond the immediate applications of such solvers for computing Sinkhorn distances, a prominent tool in machine learning, we show that these solvers can be used to obtain improved running times for maintaining a (fractional) ε-approximate maximum matching in a dynamic decremental bipartite graph against an adaptive adversary. We give a generic framework which reduces this dynamic matching problem to solving regularized graph-structured optimization problems to high accuracy. Through our reduction framework, our regularized box-simplex game solver implies a new algorithm for dynamic decremental bipartite matching in total time Õ(m ⋅ ε^{-3}), from an initial graph with m edges and n nodes. We further show how to use recent advances in flow optimization [Chen et al., 2022] to improve our runtime to m^{1 + o(1)} ⋅ ε^{-2}, thereby demonstrating the versatility of our reduction-based approach. These results improve upon the previous best runtime of Õ(m ⋅ ε^{-4}) [Aaron Bernstein et al., 2020] and illustrate the utility of using regularized optimization problem solvers for designing dynamic algorithms.
Cite as

Arun Jambulapati, Yujia Jin, Aaron Sidford, and Kevin Tian. Regularized Box-Simplex Games and Dynamic Decremental Bipartite Matching. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 77:1-77:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{jambulapati_et_al:LIPIcs.ICALP.2022.77,
  author =	{Jambulapati, Arun and Jin, Yujia and Sidford, Aaron and Tian, Kevin},
  title =	{{Regularized Box-Simplex Games and Dynamic Decremental Bipartite Matching}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{77:1--77:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.77},
  URN =		{urn:nbn:de:0030-drops-164181},
  doi =		{10.4230/LIPIcs.ICALP.2022.77},
  annote =	{Keywords: bipartite matching, decremental matching, dynamic algorithms, continuous optimization, box-simplex games, primal-dual method}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.97
The SDP Value of Random 2CSPs

Authors: Amulya Musipatla, Ryan O'Donnell, Tselil Schramm, and Xinyu Wu

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

Abstract
We consider a very wide class of models for sparse random Boolean 2CSPs; equivalently, degree-2 optimization problems over {±1}ⁿ. For each model ℳ, we identify the "high-probability value" s^*_ℳ of the natural SDP relaxation (equivalently, the quantum value). That is, for all ε > 0 we show that the SDP optimum of a random n-variable instance is (when normalized by n) in the range (s^*_ℳ-ε, s^*_ℳ+ε) with high probability. Our class of models includes non-regular CSPs, and ones where the SDP relaxation value is strictly smaller than the spectral relaxation value.
Cite as

Amulya Musipatla, Ryan O'Donnell, Tselil Schramm, and Xinyu Wu. The SDP Value of Random 2CSPs. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 97:1-97:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{musipatla_et_al:LIPIcs.ICALP.2022.97,
  author =	{Musipatla, Amulya and O'Donnell, Ryan and Schramm, Tselil and Wu, Xinyu},
  title =	{{The SDP Value of Random 2CSPs}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{97:1--97:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.97},
  URN =		{urn:nbn:de:0030-drops-164381},
  doi =		{10.4230/LIPIcs.ICALP.2022.97},
  annote =	{Keywords: Random constraint satisfaction problems}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.106
Maximizing Non-Monotone Submodular Functions over Small Subsets: Beyond 1/2-Approximation

Authors: Aviad Rubinstein and Junyao Zhao

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

Abstract
In this work we give two new algorithms that use similar techniques for (non-monotone) submodular function maximization subject to a cardinality constraint. The first is an offline fixed-parameter tractable algorithm that guarantees a 0.539-approximation for all non-negative submodular functions. The second algorithm works in the random-order streaming model. It guarantees a (1/2+c)-approximation for symmetric functions, and we complement it by showing that no space-efficient algorithm can beat 1/2 for asymmetric functions. To the best of our knowledge this is the first provable separation between symmetric and asymmetric submodular function maximization.
Cite as

Aviad Rubinstein and Junyao Zhao. Maximizing Non-Monotone Submodular Functions over Small Subsets: Beyond 1/2-Approximation. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 106:1-106:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{rubinstein_et_al:LIPIcs.ICALP.2022.106,
  author =	{Rubinstein, Aviad and Zhao, Junyao},
  title =	{{Maximizing Non-Monotone Submodular Functions over Small Subsets: Beyond 1/2-Approximation}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{106:1--106:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.106},
  URN =		{urn:nbn:de:0030-drops-164478},
  doi =		{10.4230/LIPIcs.ICALP.2022.106},
  annote =	{Keywords: Submodular optimization, Fixed-parameter tractability, Random-order streaming}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.111
Beating the Folklore Algorithm for Dynamic Matching

Authors: Mohammad Roghani, Amin Saberi, and David Wajc

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

Abstract
The maximum matching problem in dynamic graphs subject to edge updates (insertions and deletions) has received much attention over the last few years; a multitude of approximation/time tradeoffs were obtained, improving upon the folklore algorithm, which maintains a maximal (and hence 2-approximate) matching in O(n) worst-case update time in n-node graphs. We present the first deterministic algorithm which outperforms the folklore algorithm in terms of both approximation ratio and worst-case update time. Specifically, we give a (2-Ω(1))-approximate algorithm with O(m^{3/8}) = O(n^{3/4}) worst-case update time in n-node, m-edge graphs. For sufficiently small constant ε > 0, no deterministic (2+ε)-approximate algorithm with worst-case update time O(n^{0.99}) was known. Our second result is the first deterministic (2+ε)-approximate weighted matching algorithm with O_ε(1)⋅ O(∜{m}) = O_ε(1)⋅ O(√n) worst-case update time. Neither of our results were previously known to be achievable by a randomized algorithm against an adaptive adversary. Our main technical contributions are threefold: first, we characterize the tight cases for kernels, which are the well-studied matching sparsifiers underlying much of the (2+ε)-approximate dynamic matching literature. This characterization, together with multiple ideas - old and new - underlies our result for breaking the approximation barrier of 2. Our second technical contribution is the first example of a dynamic matching algorithm whose running time is improved due to improving the recourse of other dynamic matching algorithms. Finally, we show how to use dynamic bipartite matching algorithms as black-box subroutines for dynamic matching in general graphs without incurring the natural 3/2 factor in the approximation ratio which such approaches naturally incur (reminiscent of the integrality gap of the fractional matching polytope in general graphs).
Cite as

Mohammad Roghani, Amin Saberi, and David Wajc. Beating the Folklore Algorithm for Dynamic Matching. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 111:1-111:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{roghani_et_al:LIPIcs.ITCS.2022.111,
  author =	{Roghani, Mohammad and Saberi, Amin and Wajc, David},
  title =	{{Beating the Folklore Algorithm for Dynamic Matching}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{111:1--111:23},
  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.2022.111},
  URN =		{urn:nbn:de:0030-drops-157077},
  doi =		{10.4230/LIPIcs.ITCS.2022.111},
  annote =	{Keywords: dynamic matching, dynamic graph algorithms, sublinear algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.113
Budget-Smoothed Analysis for Submodular Maximization

Authors: Aviad Rubinstein and Junyao Zhao

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

Abstract
The greedy algorithm for monotone submodular function maximization subject to cardinality constraint is guaranteed to approximate the optimal solution to within a 1-1/e factor. Although it is well known that this guarantee is essentially tight in the worst case - for greedy and in fact any efficient algorithm, experiments show that greedy performs better in practice. We observe that for many applications in practice, the empirical distribution of the budgets (i.e., cardinality constraints) is supported on a wide range, and moreover, all the existing hardness results in theory break under a large perturbation of the budget. To understand the effect of the budget from both algorithmic and hardness perspectives, we introduce a new notion of budget-smoothed analysis. We prove that greedy is optimal for every budget distribution, and we give a characterization for the worst-case submodular functions. Based on these results, we show that on the algorithmic side, under realistic budget distributions, greedy and related algorithms enjoy provably better approximation guarantees, that hold even for worst-case functions, and on the hardness side, there exist hard functions that are fairly robust to all the budget distributions.
Cite as

Aviad Rubinstein and Junyao Zhao. Budget-Smoothed Analysis for Submodular Maximization. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 113:1-113:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{rubinstein_et_al:LIPIcs.ITCS.2022.113,
  author =	{Rubinstein, Aviad and Zhao, Junyao},
  title =	{{Budget-Smoothed Analysis for Submodular Maximization}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{113:1--113:23},
  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.2022.113},
  URN =		{urn:nbn:de:0030-drops-157095},
  doi =		{10.4230/LIPIcs.ITCS.2022.113},
  annote =	{Keywords: Submodular optimization, Beyond worst-case analysis, Greedy algorithms, Hardness of approximation}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.54
Streaming and Small Space Approximation Algorithms for Edit Distance and Longest Common Subsequence

Authors: Kuan Cheng, Alireza Farhadi, MohammadTaghi Hajiaghayi, Zhengzhong Jin, Xin Li, Aviad Rubinstein, Saeed Seddighin, and Yu Zheng

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

Abstract
The edit distance (ED) and longest common subsequence (LCS) are two fundamental problems which quantify how similar two strings are to one another. In this paper, we first consider these problems in the asymmetric streaming model introduced by Andoni, Krauthgamer and Onak [Andoni et al., 2010] (FOCS'10) and Saks and Seshadhri [Saks and Seshadhri, 2013] (SODA'13). In this model we have random access to one string and streaming access the other one. Our main contribution is a constant factor approximation algorithm for ED with memory Õ(n^δ) for any constant δ > 0. In addition to this, we present an upper bound of Õ _ε(√n) on the memory needed to approximate ED or LCS within a factor 1±ε. All our algorithms are deterministic and run in polynomial time in a single pass. We further study small-space approximation algorithms for ED, LCS, and longest increasing sequence (LIS) in the non-streaming setting. Here, we design algorithms that achieve 1 ± ε approximation for all three problems, where ε > 0 can be any constant and even slightly sub-constant. Our algorithms only use poly-logarithmic space while maintaining a polynomial running time. This significantly improves previous results in terms of space complexity, where all known results need to use space at least Ω(√n). Our algorithms make novel use of triangle inequality and carefully designed recursions to save space, which can be of independent interest.
Cite as

Kuan Cheng, Alireza Farhadi, MohammadTaghi Hajiaghayi, Zhengzhong Jin, Xin Li, Aviad Rubinstein, Saeed Seddighin, and Yu Zheng. Streaming and Small Space Approximation Algorithms for Edit Distance and Longest Common Subsequence. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 54:1-54:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{cheng_et_al:LIPIcs.ICALP.2021.54,
  author =	{Cheng, Kuan and Farhadi, Alireza and Hajiaghayi, MohammadTaghi and Jin, Zhengzhong and Li, Xin and Rubinstein, Aviad and Seddighin, Saeed and Zheng, Yu},
  title =	{{Streaming and Small Space Approximation Algorithms for Edit Distance and Longest Common Subsequence}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{54:1--54:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.54},
  URN =		{urn:nbn:de:0030-drops-141236},
  doi =		{10.4230/LIPIcs.ICALP.2021.54},
  annote =	{Keywords: Edit Distance, Longest Common Subsequence, Longest Increasing Subsequence, Space Efficient Algorithm, Approximation Algorithm}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.78
Near-Optimal Schedules for Simultaneous Multicasts

Authors: Bernhard Haeupler, D. Ellis Hershkowitz, and David Wajc

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

Abstract
We study the store-and-forward packet routing problem for simultaneous multicasts, in which multiple packets have to be forwarded along given trees as fast as possible. This is a natural generalization of the seminal work of Leighton, Maggs and Rao, which solved this problem for unicasts, i.e. the case where all trees are paths. They showed the existence of asymptotically optimal O(C + D)-length schedules, where the congestion C is the maximum number of packets sent over an edge and the dilation D is the maximum depth of a tree. This improves over the trivial O(CD) length schedules. We prove a lower bound for multicasts, which shows that there do not always exist schedules of non-trivial length, o(CD). On the positive side, we construct O(C+D+log² n)-length schedules in any n-node network. These schedules are near-optimal, since our lower bound shows that this length cannot be improved to O(C+D) + o(log n).
Cite as

Bernhard Haeupler, D. Ellis Hershkowitz, and David Wajc. Near-Optimal Schedules for Simultaneous Multicasts. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 78:1-78:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{haeupler_et_al:LIPIcs.ICALP.2021.78,
  author =	{Haeupler, Bernhard and Hershkowitz, D. Ellis and Wajc, David},
  title =	{{Near-Optimal Schedules for Simultaneous Multicasts}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{78:1--78:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.78},
  URN =		{urn:nbn:de:0030-drops-141471},
  doi =		{10.4230/LIPIcs.ICALP.2021.78},
  annote =	{Keywords: Packet routing, multicast, scheduling algorithms}
}
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