Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)最新文献_第4页

Oblivious Online Contention Resolution Schemes 无关联机争用解决方案

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2021-11-20 DOI: 10.1137/1.9781611977066.20

Hu Fu, P. Lu, Zhihao Gavin Tang, Abner Turkieltaub, Hongxun Wu, Jinzhao Wu, Qianfan Zhang

引用次数: 4

A Simple Approximation Algorithm for Vector Scheduling and Applications to Stochastic Min-Norm Load Balancing 矢量调度的一种简单逼近算法及其在随机最小范数负载均衡中的应用

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2021-11-14 DOI: 10.1137/1.9781611977066.18

Sharat Ibrahimpur, Chaitanya Swamy

引用次数: 1

A Simple Algorithm for Multiple-Source Shortest Paths in Planar Digraphs 平面有向图中多源最短路径的一种简单算法

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2021-11-14 DOI: 10.1137/1.9781611977066.1

Debarati Das, Evangelos Kipouridis, M. Gutenberg, Christian Wulff-Nilsen

引用次数: 1

Tight Bounds for Differentially Private Anonymized Histograms 差分私有匿名直方图的紧边界

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2021-11-05 DOI: 10.1137/1.9781611977066.14

Pasin Manurangsi

引用次数: 4

Deterministic Approximation of Random Walks via Queries in Graphs of Unbounded Size 无界图中随机游走查询的确定性逼近

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2021-11-03 DOI: 10.1137/1.9781611977066.5

Edward Pyne, S. Vadhan

{"title":"Deterministic Approximation of Random Walks via Queries in Graphs of Unbounded Size","authors":"Edward Pyne, S. Vadhan","doi":"10.1137/1.9781611977066.5","DOIUrl":"https://doi.org/10.1137/1.9781611977066.5","url":null,"abstract":"Consider the following computational problem: given a regular digraph G = (V,E), two vertices u, v ∈ V , and a walk length t ∈ N, estimate the probability that a random walk of length t from u ends at v to within ±ε. A randomized algorithm can solve this problem by carrying out O(1/ε) random walks of length t from u and outputting the fraction that end at v. In this paper, we study deterministic algorithms for this problem that are also restricted to carrying out walks of length t from u and seeing which ones end at v. Specifically, if G is d-regular, the algorithm is given oracle access to a function f : [d] → {0, 1} where f(x) is 1 if the walk from u specified by the edge labels in x ends at v. We assume that G is consistently labelled, meaning that the edges of label i for each i ∈ [d] form a permutation on V . We show that there exists a deterministic algorithm that makes poly(dt/ε) nonadaptive queries to f , regardless of the number of vertices in the graph G. Crucially, and in contrast to the randomized algorithm, our algorithm does not simply output the average value of its queries. Indeed, Hoza, Pyne, and Vadhan (ITCS 2021) showed that any deterministic algorithm of the latter form that works for graphs of unbounded size must have query complexity at least exp(Ω̃(log(t) log(1/ε))). In the language of pseudorandomness, our result is a separation between the query complexity of “deterministic samplers” and “deterministic averaging samplers” for the class of “permutation branching programs of unbounded width”. Our separation is stronger than the prior separation of Pyne and Vadhan (CCC 2021), and has a much simpler proof (not using spectral graph theory or the Impagliazzo–Nisan–Wigderson pseudorandom generator). On the other hand, the algorithm of Pyne and Vadhan is explicit and computable in small space, whereas ours is not explicit (unless we assume the existence of an optimal explicit pseudorandom generator for permutation branching programs of bounded width).","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"28 1","pages":"57-67"},"PeriodicalIF":0.0,"publicationDate":"2021-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74897106","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 6

Parameterized Convexity Testing 参数化凸性测试

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2021-10-25 DOI: 10.1137/1.9781611977066.12

A. Lahiri, I. Newman, Nithin M. Varma

引用次数: 0

Voting algorithms for unique games on complete graphs 完全图上唯一游戏的投票算法

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2021-10-22 DOI: 10.1137/1.9781611977585.ch12

Antoine M'eot, A. D. Mesmay, Moritz Mühlenthaler, Alantha Newman

{"title":"Voting algorithms for unique games on complete graphs","authors":"Antoine M'eot, A. D. Mesmay, Moritz Mühlenthaler, Alantha Newman","doi":"10.1137/1.9781611977585.ch12","DOIUrl":"https://doi.org/10.1137/1.9781611977585.ch12","url":null,"abstract":"An approximation algorithm for a constraint satisfaction problem is called robust if it outputs an assignment satisfying a $(1 - f(epsilon))$-fraction of the constraints on any $(1-epsilon)$-satisfiable instance, where the loss function $f$ is such that $f(epsilon) rightarrow 0$ as $epsilon rightarrow 0$. Moreover, the runtime of a robust algorithm should not depend in any way on $epsilon$. In this paper, we present such an algorithm for Min-Unique-Games on complete graphs with $q$ labels. Specifically, the loss function is $f(epsilon) = (epsilon + c_{epsilon} epsilon^2)$, where $c_{epsilon}$ is a constant depending on $epsilon$ such that $lim_{epsilon rightarrow 0} c_{epsilon} = 16$. The runtime of our algorithm is $O(qn^3)$ (with no dependence on $epsilon$) and can run in time $O(qn^2)$ using a randomized implementation with a slightly larger constant $c_{epsilon}$. Our algorithm is combinatorial and uses voting to find an assignment. It can furthermore be used to provide a PTAS for Min-Unique-Games on complete graphs, recovering a result of Karpinski and Schudy with a simpler algorithm and proof. We also prove NP-hardness for Min-Unique-Games on complete graphs and (using a randomized reduction) even in the case where the constraints form a cyclic permutation, which is also known as Min-Linear-Equations-mod-$q$ on complete graphs.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"44 1","pages":"124-136"},"PeriodicalIF":0.0,"publicationDate":"2021-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85535974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Finding Relevant Points for Nearest-Neighbor Classification 寻找最近邻分类的相关点

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2021-10-12 DOI: 10.1137/1.9781611977066.6

D. Eppstein

引用次数: 2

Towards Non-Uniform k-Center with Constant Types of Radii 关于半径为常数型的非均匀k中心问题

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2021-10-06 DOI: 10.1137/1.9781611977066.16

Xinrui Jia, Lars Rohwedder, K. Sheth, O. Svensson

{"title":"Towards Non-Uniform k-Center with Constant Types of Radii","authors":"Xinrui Jia, Lars Rohwedder, K. Sheth, O. Svensson","doi":"10.1137/1.9781611977066.16","DOIUrl":"https://doi.org/10.1137/1.9781611977066.16","url":null,"abstract":"In the Non-Uniform k-Center problem we need to cover a finite metric space using k balls of different radii that can be scaled uniformly. The goal is to minimize the scaling factor. If the number of different radii is unbounded, the problem does not admit a constant-factor approximation algorithm but it has been conjectured that such an algorithm exists if the number of radii is constant. Yet, this is known only for the case of two radii. Our first contribution is a simple black box reduction which shows that if one can handle the variant of t− 1 radii with outliers, then one can also handle t radii. Together with an algorithm by Chakrabarty and Negahbani for two radii with outliers, this immediately implies a constant-factor approximation algorithm for three radii; thus making further progress on the conjecture. Furthermore, using algorithms for the k-center with outliers problem, that is the one radii with outliers case, we also get a simple algorithm for two radii. The algorithm by Chakrabarty and Negahbani uses a top-down approach, starting with the larger radius and then proceeding to the smaller one. Our reduction, on the other hand, looks only at the smallest radius and eliminates it, which suggests that a bottom-up approach is promising. In this spirit, we devise a modification of the Chakrabarty and Negahbani algorithm which runs in a bottom-up fashion, and in this way we recover their result with the advantage of having a simpler analysis. ∗Supported by the Swiss National Science Foundation project 200021-184656 “Randomness in Problem Instances and Randomized Algorithms.”","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"8 1","pages":"228-237"},"PeriodicalIF":0.0,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76326593","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Frequency-Domain Representation of First-Order Methods: A Simple and Robust Framework of Analysis 一阶方法的频域表示:一个简单而稳健的分析框架

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2021-09-10 DOI: 10.1137/1.9781611977066.10

Ioannis Anagnostides, Ioannis Panageas

{"title":"Frequency-Domain Representation of First-Order Methods: A Simple and Robust Framework of Analysis","authors":"Ioannis Anagnostides, Ioannis Panageas","doi":"10.1137/1.9781611977066.10","DOIUrl":"https://doi.org/10.1137/1.9781611977066.10","url":null,"abstract":"Motivated by recent applications in min-max optimization, we employ tools from nonlinear control theory in order to analyze a class of\"historical\"gradient-based methods, for which the next step lies in the span of the previously observed gradients within a time horizon. Specifically, we leverage techniques developed by Hu and Lessard (2017) to build a frequency-domain framework which reduces the analysis of such methods to numerically-solvable algebraic tasks, establishing linear convergence under a class of strongly monotone and co-coercive operators. On the applications' side, we focus on the Optimistic Gradient Descent (OGD) method, which augments the standard Gradient Descent with an additional past-gradient in the optimization step. The proposed framework leads to a simple and sharp analysis of OGD -- and generalizations thereof -- under a much broader regime of parameters. Notably, this characterization directly extends under adversarial noise in the observed value of the gradient. Moreover, our frequency-domain framework provides an exact quantitative comparison between simultaneous and alternating updates of OGD. An interesting byproduct is that OGD -- and variants thereof -- is an instance of PID control, arguably one of the most influential algorithms of the last century; this observation sheds more light to the stabilizing properties of\"optimism\".","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"38 1","pages":"131-160"},"PeriodicalIF":0.0,"publicationDate":"2021-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73528270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4