Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)最新文献_第2页

Tight Bounds for Vertex Connectivity in Dynamic Streams 动态流中顶点连通性的紧边界

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2022-11-09 DOI: 10.48550/arXiv.2211.04685

Sepehr Assadi, Vihan Shah

引用次数: 0

Faster Walsh-Hadamard Transform and Matrix Multiplication over Finite Fields using Lookup Tables 更快的沃尔什-阿达玛变换和矩阵乘法在有限的领域使用查找表

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2022-11-09 DOI: 10.48550/arXiv.2211.04643

Josh Alman

{"title":"Faster Walsh-Hadamard Transform and Matrix Multiplication over Finite Fields using Lookup Tables","authors":"Josh Alman","doi":"10.48550/arXiv.2211.04643","DOIUrl":"https://doi.org/10.48550/arXiv.2211.04643","url":null,"abstract":"We use lookup tables to design faster algorithms for important algebraic problems over finite fields. These faster algorithms, which only use arithmetic operations and lookup table operations, may help to explain the difficulty of determining the complexities of these important problems. Our results over a constant-sized finite field are as follows. The Walsh-Hadamard transform of a vector of length $N$ can be computed using $O(N log N / log log N)$ bit operations. This generalizes to any transform defined as a Kronecker power of a fixed matrix. By comparison, the Fast Walsh-Hadamard transform (similar to the Fast Fourier transform) uses $O(N log N)$ arithmetic operations, which is believed to be optimal up to constant factors. Any algebraic algorithm for multiplying two $N times N$ matrices using $O(N^omega)$ operations can be converted into an algorithm using $O(N^omega / (log N)^{omega/2 - 1})$ bit operations. For example, Strassen's algorithm can be converted into an algorithm using $O(N^{2.81} / (log N)^{0.4})$ bit operations. It remains an open problem with practical implications to determine the smallest constant $c$ such that Strassen's algorithm can be implemented to use $c cdot N^{2.81} + o(N^{2.81})$ arithmetic operations; using a lookup table allows one to save a super-constant factor in bit operations.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"246 1","pages":"137-144"},"PeriodicalIF":0.0,"publicationDate":"2022-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86705348","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: 0

Fully-dynamic-to-incremental reductions with known deletion order (e.g. sliding window) 已知删除顺序的完全动态到增量的缩减(例如滑动窗口)

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2022-11-09 DOI: 10.48550/arXiv.2211.05178

Binghui Peng, A. Rubinstein

{"title":"Fully-dynamic-to-incremental reductions with known deletion order (e.g. sliding window)","authors":"Binghui Peng, A. Rubinstein","doi":"10.48550/arXiv.2211.05178","DOIUrl":"https://doi.org/10.48550/arXiv.2211.05178","url":null,"abstract":"Dynamic algorithms come in three main flavors: $mathit{incremental}$ (insertions-only), $mathit{decremental}$ (deletions-only), or $mathit{fully}$ $mathit{dynamic}$ (both insertions and deletions). Fully dynamic is the holy grail of dynamic algorithm design; it is obviously more general than the other two, but is it strictly harder? Several works managed to reduce fully dynamic to the incremental or decremental models by taking advantage of either specific structure of the incremental/decremental algorithms (e.g. [HK99, HLT01, BKS12, ADKKP16, BS80, OL81, OvL81]), or specific order of insertions/deletions (e.g. [AW14,HKNS15,KPP16]). Our goal in this work is to get a black-box fully-to-incremental reduction that is as general as possible. We find that the following conditions are necessary: $bullet$ The incremental algorithm must have a worst-case (rather than amortized) running time guarantee. $bullet$ The reduction must work in what we call the $mathit{deletions}$-$mathit{look}$-$mathit{ahead}$ $mathit{model}$, where the order of deletions among current elements is known in advance. A notable practical example is the\"sliding window\"(FIFO) order of updates. Under those conditions, we design: $bullet$ A simple, practical, amortized-fully-dynamic to worst-case-incremental reduction with a $log(T)$-factor overhead on the running time, where $T$ is the total number of updates. $bullet$ A theoretical worst-case-fully-dynamic to worst-case-incremental reduction with a $mathsf{polylog}(T)$-factor overhead on the running time.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"42 1","pages":"261-271"},"PeriodicalIF":0.0,"publicationDate":"2022-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82522320","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: 2

Sampling an Edge in Sublinear Time Exactly and Optimally 在亚线性时间内精确和最优地采样边缘

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2022-11-09 DOI: 10.48550/arXiv.2211.04981

T. Eden, Shyam Narayanan, Jakub Tvetek

引用次数: 0

A Local Search-Based Approach for Set Covering 一种基于局部搜索的集合覆盖方法

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2022-11-08 DOI: 10.48550/arXiv.2211.04444

Anupam Gupta, Euiwoong Lee, Jason Li

{"title":"A Local Search-Based Approach for Set Covering","authors":"Anupam Gupta, Euiwoong Lee, Jason Li","doi":"10.48550/arXiv.2211.04444","DOIUrl":"https://doi.org/10.48550/arXiv.2211.04444","url":null,"abstract":"In the Set Cover problem, we are given a set system with each set having a weight, and we want to find a collection of sets that cover the universe, whilst having low total weight. There are several approaches known (based on greedy approaches, relax-and-round, and dual-fitting) that achieve a $H_k approx ln k + O(1)$ approximation for this problem, where the size of each set is bounded by $k$. Moreover, getting a $ln k - O(ln ln k)$ approximation is hard. Where does the truth lie? Can we close the gap between the upper and lower bounds? An improvement would be particularly interesting for small values of $k$, which are often used in reductions between Set Cover and other combinatorial optimization problems. We consider a non-oblivious local-search approach: to the best of our knowledge this gives the first $H_k$-approximation for Set Cover using an approach based on local-search. Our proof fits in one page, and gives a integrality gap result as well. Refining our approach by considering larger moves and an optimized potential function gives an $(H_k - Omega(log^2 k)/k)$-approximation, improving on the previous bound of $(H_k - Omega(1/k^8))$ (emph{R. Hassin and A. Levin, SICOMP '05}) based on a modified greedy algorithm.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"97 1","pages":"1-11"},"PeriodicalIF":0.0,"publicationDate":"2022-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76972287","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: 3

A Simple Combinatorial Algorithm for Robust Matroid Center 鲁棒矩阵中心的一种简单组合算法

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2022-11-07 DOI: 10.48550/arXiv.2211.03601

Georg Anegg, Laura Vargas Koch, R. Zenklusen

引用次数: 0

Simple Set Sketching 简单布景素描

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2022-11-07 DOI: 10.48550/arXiv.2211.03683

Jakob Baek Tejs Houen, R. Pagh, Stefan Walzer

{"title":"Simple Set Sketching","authors":"Jakob Baek Tejs Houen, R. Pagh, Stefan Walzer","doi":"10.48550/arXiv.2211.03683","DOIUrl":"https://doi.org/10.48550/arXiv.2211.03683","url":null,"abstract":"Imagine handling collisions in a hash table by storing, in each cell, the bit-wise exclusive-or of the set of keys hashing there. This appears to be a terrible idea: For $alpha n$ keys and $n$ buckets, where $alpha$ is constant, we expect that a constant fraction of the keys will be unrecoverable due to collisions. We show that if this collision resolution strategy is repeated three times independently the situation reverses: If $alpha$ is below a threshold of $approx 0.81$ then we can recover the set of all inserted keys in linear time with high probability. Even though the description of our data structure is simple, its analysis is nontrivial. Our approach can be seen as a variant of the Invertible Bloom Filter (IBF) of Eppstein and Goodrich. While IBFs involve an explicit checksum per bucket to decide whether the bucket stores a single key, we exploit the idea of quotienting, namely that some bits of the key are implicit in the location where it is stored. We let those serve as an implicit checksum. These bits are not quite enough to ensure that no errors occur and the main technical challenge is to show that decoding can recover from these errors.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"25 1 1","pages":"228-241"},"PeriodicalIF":0.0,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75419019","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

Simplified Prophet Inequalities for Combinatorial Auctions 组合拍卖的简化先知不等式

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2022-11-01 DOI: 10.48550/arXiv.2211.00707

Alexander Braun, Thomas Kesselheim

引用次数: 0

An Optimal Lower Bound for Simplex Range Reporting 单纯形范围报告的最优下界

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2022-10-26 DOI: 10.48550/arXiv.2210.14736

P. Afshani, P. Cheng

{"title":"An Optimal Lower Bound for Simplex Range Reporting","authors":"P. Afshani, P. Cheng","doi":"10.48550/arXiv.2210.14736","DOIUrl":"https://doi.org/10.48550/arXiv.2210.14736","url":null,"abstract":"We give a simplified and improved lower bound for the simplex range reporting problem. We show that given a set $P$ of $n$ points in $mathbb{R}^d$, any data structure that uses $S(n)$ space to answer such queries must have $Q(n)=Omega((n^2/S(n))^{(d-1)/d}+k)$ query time, where $k$ is the output size. For near-linear space data structures, i.e., $S(n)=O(nlog^{O(1)}n)$, this improves the previous lower bounds by Chazelle and Rosenberg [CR96] and Afshani [A12] but perhaps more importantly, it is the first ever tight lower bound for any variant of simplex range searching for $dge 3$ dimensions. We obtain our lower bound by making a simple connection to well-studied problems in incident geometry which allows us to use known constructions in the area. We observe that a small modification of a simple already existing construction can lead to our lower bound. We believe that our proof is accessible to a much wider audience, at least compared to the previous intricate probabilistic proofs based on measure arguments by Chazelle and Rosenberg [CR96] and Afshani [A12]. The lack of tight or almost-tight (up to polylogarithmic factor) lower bounds for near-linear space data structures is a major bottleneck in making progress on problems such as proving lower bounds for multilevel data structures. It is our hope that this new line of attack based on incidence geometry can lead to further progress in this area.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"15 1","pages":"272-277"},"PeriodicalIF":0.0,"publicationDate":"2022-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75242395","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: 2

A Simple Deterministic Distributed Low-Diameter Clustering 一种简单的确定性分布式低直径聚类

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2022-10-21 DOI: 10.48550/arXiv.2210.11784

Václav Rozhoň, Bernhard Haeupler, C. Grunau

引用次数: 0