ACM Transactions on Algorithms最新文献_第9页

Generic Techniques for Building Top-k Structures 构建Top-k结构的通用技术

IF 1.3 3区计算机科学

ACM Transactions on Algorithms Pub Date : 2022-10-10 DOI: https://dl.acm.org/doi/10.1145/3546074

Saladi Rahul, Yufei Tao

{"title":"Generic Techniques for Building Top-k Structures","authors":"Saladi Rahul, Yufei Tao","doi":"https://dl.acm.org/doi/10.1145/3546074","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3546074","url":null,"abstract":"A reporting query returns the objects satisfying a predicate q from an input set. In prioritized reporting, each object carries a real-valued weight (which can be query dependent), and a query returns the objects that satisfy q and have weights at least a threshold τ. A top-k query finds, among all the objects satisfying q, the k ones of the largest weights; a max query is a special instance with k = 1. We want to design data structures of small space to support queries (and possibly updates) efficiently.Previous work has shown that a top-k structure can also support max and prioritized queries with no performance deterioration. This article explores the opposite direction: do prioritized queries, possibly combined with max queries, imply top-k search? Subject to mild conditions, we provide affirmative answers with two reduction techniques. The first converts a prioritized structure into a static top-k structure with the same space complexity and only a logarithmic blowup in query time. If a max structure is available in addition, our second reduction yields a top-k structure with no degradation in expected performance (this holds for the space, query, and update complexities). Our techniques significantly simplify the design of top-k structures because structures for max and prioritized queries are often easier to obtain. We demonstrate this by developing top-k structures for interval stabbing, 3D dominance, halfspace reporting, linear ranking, and L∞ nearest neighbor search in the RAM and the external memory computation models.","PeriodicalId":50922,"journal":{"name":"ACM Transactions on Algorithms","volume":"27 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138516996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Sticky Brownian Rounding and its Applications to Constraint Satisfaction Problems 粘性布朗舍入及其在约束满足问题中的应用

IF 1.3 3区计算机科学

ACM Transactions on Algorithms Pub Date : 2022-10-10 DOI: https://dl.acm.org/doi/10.1145/3459096

Sepehr Abbasi-Zadeh, Nikhil Bansal, Guru Guruganesh, Aleksandar Nikolov, Roy Schwartz, Mohit Singh

{"title":"Sticky Brownian Rounding and its Applications to Constraint Satisfaction Problems","authors":"Sepehr Abbasi-Zadeh, Nikhil Bansal, Guru Guruganesh, Aleksandar Nikolov, Roy Schwartz, Mohit Singh","doi":"https://dl.acm.org/doi/10.1145/3459096","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3459096","url":null,"abstract":"Semidefinite programming is a powerful tool in the design and analysis of approximation algorithms for combinatorial optimization problems. In particular, the random hyperplane rounding method of Goemans and Williamson [31] has been extensively studied for more than two decades, resulting in various extensions to the original technique and beautiful algorithms for a wide range of applications. Despite the fact that this approach yields tight approximation guarantees for some problems, e.g., Max-Cut, for many others, e.g., Max-SAT and Max-DiCut, the tight approximation ratio is still unknown. One of the main reasons for this is the fact that very few techniques for rounding semi-definite relaxations are known. In this work, we present a new general and simple method for rounding semi-definite programs, based on Brownian motion. Our approach is inspired by recent results in algorithmic discrepancy theory. We develop and present tools for analyzing our new rounding algorithms, utilizing mathematical machinery from the theory of Brownian motion, complex analysis, and partial differential equations. Focusing on constraint satisfaction problems, we apply our method to several classical problems, including Max-Cut, Max-2SAT, and Max-DiCut, and derive new algorithms that are competitive with the best known results. To illustrate the versatility and general applicability of our approach, we give new approximation algorithms for the Max-Cut problem with side constraints that crucially utilizes measure concentration results for the Sticky Brownian Motion, a feature missing from hyperplane rounding and its generalizations.","PeriodicalId":50922,"journal":{"name":"ACM Transactions on Algorithms","volume":"2 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494858","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Tolerant Testers of Image Properties 图像特性公差测试仪

IF 1.3 3区计算机科学

ACM Transactions on Algorithms Pub Date : 2022-10-10 DOI: https://dl.acm.org/doi/10.1145/3531527

Piotr Berman, Meiram Murzabulatov, Sofya Raskhodnikova

{"title":"Tolerant Testers of Image Properties","authors":"Piotr Berman, Meiram Murzabulatov, Sofya Raskhodnikova","doi":"https://dl.acm.org/doi/10.1145/3531527","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3531527","url":null,"abstract":"We initiate a systematic study of tolerant testers of image properties or, equivalently, algorithms that approximate the distance from a given image to the desired property. Image processing is a particularly compelling area of applications for sublinear-time algorithms and, specifically, property testing. However, for testing algorithms to reach their full potential in image processing, they have to be tolerant, which allows them to be resilient to noise.We design efficient approximation algorithms for the following fundamental questions: What fraction of pixels have to be changed in an image so it becomes a half-plane? A representation of a convex object? A representation of a connected object? More precisely, our algorithms approximate the distance to three basic properties (being a half-plane, convexity, and connectedness) within a small additive error ε, after reading poly(1/ε) pixels, independent of the image size. We also design an efficient agnostic proper PAC learner of convex sets (continuous and discrete) in two dimensions under the uniform distribution.Our algorithms require very simple access to the input: uniform random samples for the half-plane property and convexity, and samples from uniformly random blocks for connectedness. However, the analysis of the algorithms, especially for convexity, requires many geometric and combinatorial insights. For example, in the analysis of the algorithm for convexity, we define a set of reference polygons Pε such that (1) every convex image has a nearby polygon in Pε and (2) one can use dynamic programming to quickly compute the smallest empirical distance to a polygon in Pε.","PeriodicalId":50922,"journal":{"name":"ACM Transactions on Algorithms","volume":"2 6‐7","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494909","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Exponential Separations in Local Privacy 指数分离在本地隐私

IF 1.3 3区计算机科学

ACM Transactions on Algorithms Pub Date : 2022-10-10 DOI: https://dl.acm.org/doi/10.1145/3459095

Matthew Joseph, Jieming Mao, Aaron Roth

引用次数: 0

Ranked Document Retrieval in External Memory 外部存储器中的排序文档检索

IF 1.3 3区计算机科学

ACM Transactions on Algorithms Pub Date : 2022-09-22 DOI: 10.1145/3559763

R. Shah, Cheng Sheng, Sharma V. Thankachan, J. Vitter

{"title":"Ranked Document Retrieval in External Memory","authors":"R. Shah, Cheng Sheng, Sharma V. Thankachan, J. Vitter","doi":"10.1145/3559763","DOIUrl":"https://doi.org/10.1145/3559763","url":null,"abstract":"The ranked (or top-k) document retrieval problem is defined as follows: preprocess a collection {T1,T2,… ,Td} of d strings (called documents) of total length n into a data structure, such that for any given query (P,k), where P is a string (called pattern) of length p ≥ 1 and k ∈ [1,d] is an integer, the identifiers of those k documents that are most relevant to P can be reported, ideally in the sorted order of their relevance. The seminal work by Hon et al. [FOCS 2009 and Journal of the ACM 2014] presented an O(n)-space (in words) data structure with O(p+k log k) query time. The query time was later improved to O(p+k) [SODA 2012] and further to O(p/ log σn+k) [SIAM Journal on Computing 2017] by Navarro and Nekrich, where σ is the alphabet size. We revisit this problem in the external memory model and present three data structures. The first one takes O(n)-space and answer queries in O(p/B + log B n + k/B+ log * (n/B)) I/Os, where B is the block size. The second one takes O(n log * (n/B)) space and answer queries in optimal O(p/B + log B n + k/B) I/Os. In both cases, the answers are reported in the unsorted order of relevance. To handle sorted top-k document retrieval, we present an O(n log (d/B)) space data structure with optimal query cost.","PeriodicalId":50922,"journal":{"name":"ACM Transactions on Algorithms","volume":"19 1","pages":"1 - 12"},"PeriodicalIF":1.3,"publicationDate":"2022-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43217564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Cubic Algorithm for Computing the Hermite Normal Form of a Nonsingular Integer Matrix 计算非奇异整矩阵Hermite范式的三次算法

IF 1.3 3区计算机科学

ACM Transactions on Algorithms Pub Date : 2022-09-21 DOI: 10.1145/3617996

Stavros Birmpilis, G. Labahn, A. Storjohann

引用次数: 0

A Polynomial-Time Algorithm for 1/3-Approximate Nash Equilibria in Bimatrix Games 双矩阵对策中1/3-近似纳什均衡的多项式时间算法

IF 1.3 3区计算机科学

ACM Transactions on Algorithms Pub Date : 2022-04-25 DOI: 10.1145/3606697

Argyrios Deligkas, M. Fasoulakis, E. Markakis

引用次数: 9

A PTAS for Capacitated Vehicle Routing on Trees 树上电容车辆路径的PTAS

IF 1.3 3区计算机科学

ACM Transactions on Algorithms Pub Date : 2021-11-05 DOI: 10.1145/3575799

Claire Mathieu, Hang Zhou

引用次数: 14

Hopcroft’s Problem, Log-Star Shaving, 2D Fractional Cascading, and Decision Trees Hopcroft问题，Log-Star剃须，2D分数级联和决策树

IF 1.3 3区计算机科学

ACM Transactions on Algorithms Pub Date : 2021-11-05 DOI: 10.1137/1.9781611977073.10

Timothy M. Chan, D. Zheng

{"title":"Hopcroft’s Problem, Log-Star Shaving, 2D Fractional Cascading, and Decision Trees","authors":"Timothy M. Chan, D. Zheng","doi":"10.1137/1.9781611977073.10","DOIUrl":"https://doi.org/10.1137/1.9781611977073.10","url":null,"abstract":"We revisit Hopcroft’s problem and related fundamental problems about geometric range searching. Given n points and n lines in the plane, we show how to count the number of point-line incidence pairs or the number of point-above-line pairs in O(n4/3) time, which matches the conjectured lower bound and improves the best previous time bound of (n^{4/3}2^{O(log ^*n)} ) obtained almost 30 years ago by Matoušek. We describe two interesting and different ways to achieve the result: the first is randomized and uses a new 2D version of fractional cascading for arrangements of lines; the second is deterministic and uses decision trees in a manner inspired by the sorting technique of Fredman (1976). The second approach extends to any constant dimension. Many consequences follow from these new ideas: for example, we obtain an O(n4/3)-time algorithm for line segment intersection counting in the plane, O(n4/3)-time randomized algorithms for distance selection in the plane and bichromatic closest pair and Euclidean minimum spanning tree in three or four dimensions, and a randomized data structure for halfplane range counting in the plane with O(n4/3) preprocessing time and space and O(n1/3) query time.","PeriodicalId":50922,"journal":{"name":"ACM Transactions on Algorithms","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49116051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 12

An Improved Algorithm for The k-Dyck Edit Distance Problem k-Dyck编辑距离问题的一种改进算法

IF 1.3 3区计算机科学

ACM Transactions on Algorithms Pub Date : 2021-11-03 DOI: 10.1137/1.9781611977073.144

Dvir Fried, Shay Golan, T. Kociumaka, T. Kopelowitz, E. Porat, Tatiana Starikovskaya

引用次数: 7