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Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)最新文献

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On the Change-Making Problem 关于变革问题
Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2020-01-01 DOI: 10.1137/1.9781611976014.7
Timothy M. Chan, Qizheng He
{"title":"On the Change-Making Problem","authors":"Timothy M. Chan, Qizheng He","doi":"10.1137/1.9781611976014.7","DOIUrl":"https://doi.org/10.1137/1.9781611976014.7","url":null,"abstract":"Given a set of n non-negative integers representing a coin system, the change-making problem seeks the fewest number of coins that sum up to a given value t, where each type of coin can be used an unlimited number of times. This problem is a popular homework exercise in dynamic programming, where the textbook solution runs in O(nt)","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"27 1","pages":"38-42"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82034275","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
Reducing 3SUM to Convolution-3SUM 将3SUM简化为卷积-3SUM
Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2020-01-01 DOI: 10.1137/1.9781611976014.1
Timothy M. Chan, Qizheng He
{"title":"Reducing 3SUM to Convolution-3SUM","authors":"Timothy M. Chan, Qizheng He","doi":"10.1137/1.9781611976014.1","DOIUrl":"https://doi.org/10.1137/1.9781611976014.1","url":null,"abstract":"Given a set S of n numbers, the 3SUM problem asks to determine whether there exist three elements a, b, c ∈ S such that a + b + c = 0. The related Convolution-3SUM problem asks to determine whether there exist a pair of indices i, j such that A[i] + A[j] = A[i + j], where A is a given array of n numbers. When the numbers are integers, a randomized reduction from 3SUM to Convolution-3SUM was given in a seminal paper by Pǎtraşcu [STOC 2010], which was later improved by Kopelowitz, Pettie, and Porat [SODA 2016] with an O(logn) factor slowdown. In this paper, we present a simple deterministic reduction from 3SUM to Convolution-3SUM for integers bounded by U . We also describe additional ideas to obtaining further improved reductions, with only a (log logn) factor slowdown in the randomized case, and a log U factor slowdown in the deterministic case.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"106 1","pages":"1-7"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75731425","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: 14
Simple Label-Correcting Algorithms for Partially Dynamic Approximate Shortest Paths in Directed Graphs 有向图中部分动态近似最短路径的简单标签校正算法
Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2020-01-01 DOI: 10.1137/1.9781611976014.15
Adam Karczmarz, Jakub Lacki
{"title":"Simple Label-Correcting Algorithms for Partially Dynamic Approximate Shortest Paths in Directed Graphs","authors":"Adam Karczmarz, Jakub Lacki","doi":"10.1137/1.9781611976014.15","DOIUrl":"https://doi.org/10.1137/1.9781611976014.15","url":null,"abstract":"","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"10 1","pages":"106-120"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81980987","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: 14
Dynamic Generalized Closest Pair: Revisiting Eppstein's Technique 动态广义最接近对:重访Eppstein技术
Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2020-01-01 DOI: 10.1137/1.9781611976014.6
Timothy M. Chan
{"title":"Dynamic Generalized Closest Pair: Revisiting Eppstein's Technique","authors":"Timothy M. Chan","doi":"10.1137/1.9781611976014.6","DOIUrl":"https://doi.org/10.1137/1.9781611976014.6","url":null,"abstract":"Eppstein (1995) gave a technique to transform any data structure for dynamic nearest neighbor queries into a data structure for dynamic closest pair, for any distance function; the transformation increases the time bound by two logarithmic factors. We present a similar, simple transformation that is just as good, and can avoid the extra logarithmic factors when the query and update time of the given structure exceed n for some constant ε > 0. Consequently, in the case of an arbitrary distance function, we obtain an optimal O(n)-space data structure to maintain the dynamic closest pair of n points in O(n) amortized time plus O(n) distance evaluations per update.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"16 1","pages":"33-37"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78935365","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
Adaptive Discrete Phase Retrieval 自适应离散相位恢复
Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2020-01-01 DOI: 10.1137/1.9781611976014.9
M. Charikar, Xian Wu, Y. Ye
{"title":"Adaptive Discrete Phase Retrieval","authors":"M. Charikar, Xian Wu, Y. Ye","doi":"10.1137/1.9781611976014.9","DOIUrl":"https://doi.org/10.1137/1.9781611976014.9","url":null,"abstract":"","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"53 1","pages":"47-56"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90308919","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
Fast Fourier Sparsity Testing 快速傅里叶稀疏性测试
Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2019-10-13 DOI: 10.1137/1.9781611976014.10
G. Yaroslavtsev, Samson Zhou
{"title":"Fast Fourier Sparsity Testing","authors":"G. Yaroslavtsev, Samson Zhou","doi":"10.1137/1.9781611976014.10","DOIUrl":"https://doi.org/10.1137/1.9781611976014.10","url":null,"abstract":"A function $f : mathbb{F}_2^n to mathbb{R}$ is $s$-sparse if it has at most $s$ non-zero Fourier coefficients. Motivated by applications to fast sparse Fourier transforms over $mathbb{F}_2^n$, we study efficient algorithms for the problem of approximating the $ell_2$-distance from a given function to the closest $s$-sparse function. While previous works (e.g., Gopalan et al. SICOMP 2011) study the problem of distinguishing $s$-sparse functions from those that are far from $s$-sparse under Hamming distance, to the best of our knowledge no prior work has explicitly focused on the more general problem of distance estimation in the $ell_2$ setting, which is particularly well-motivated for noisy Fourier spectra. Given the focus on efficiency, our main result is an algorithm that solves this problem with query complexity $mathcal{O}(s)$ for constant accuracy and error parameters, which is only quadratically worse than applicable lower bounds.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"14 1","pages":"57-68"},"PeriodicalIF":0.0,"publicationDate":"2019-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87583239","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
Multiplicative Rank-1 Approximation using Length-Squared Sampling 使用长度平方抽样的乘法秩-1近似
Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2019-09-01 DOI: 10.1137/1.9781611976014.4
Ragesh Jaiswal, Amit Kumar
{"title":"Multiplicative Rank-1 Approximation using Length-Squared Sampling","authors":"Ragesh Jaiswal, Amit Kumar","doi":"10.1137/1.9781611976014.4","DOIUrl":"https://doi.org/10.1137/1.9781611976014.4","url":null,"abstract":"We show that the span of $Omega(frac{1}{varepsilon^4})$ rows of any matrix $A subset mathbb{R}^{n times d}$ sampled according to the length-squared distribution contains a rank-$1$ matrix $tilde{A}$ such that $||A - tilde{A}||_F^2 leq (1 + varepsilon) cdot ||A - pi_1(A)||_F^2$, where $pi_1(A)$ denotes the best rank-$1$ approximation of $A$ under the Frobenius norm. Length-squared sampling has previously been used in the context of rank-$k$ approximation. However, the approximation obtained was additive in nature. We obtain a multiplicative approximation albeit only for rank-$1$ approximation.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"24 1","pages":"18-23"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84595073","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
Quantum Approximate Counting, Simplified 简化的量子近似计数
Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2019-08-28 DOI: 10.1137/1.9781611976014.5
S. Aaronson, Patrick Rall
{"title":"Quantum Approximate Counting, Simplified","authors":"S. Aaronson, Patrick Rall","doi":"10.1137/1.9781611976014.5","DOIUrl":"https://doi.org/10.1137/1.9781611976014.5","url":null,"abstract":"In 1998, Brassard, Hoyer, Mosca, and Tapp (BHMT) gave a quantum algorithm for approximate counting. Given a list of $N$ items, $K$ of them marked, their algorithm estimates $K$ to within relative error $varepsilon$ by making only $Oleft( frac{1}{varepsilon}sqrt{frac{N}{K}}right) $ queries. Although this speedup is of \"Grover\" type, the BHMT algorithm has the curious feature of relying on the Quantum Fourier Transform (QFT), more commonly associated with Shor's algorithm. Is this necessary? This paper presents a simplified algorithm, which we prove achieves the same query complexity using Grover iterations only. We also generalize this to a QFT-free algorithm for amplitude estimation. Related approaches to approximate counting were sketched previously by Grover, Abrams and Williams, Suzuki et al., and Wie (the latter two as we were writing this paper), but in all cases without rigorous analysis.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"50 1","pages":"24-32"},"PeriodicalIF":0.0,"publicationDate":"2019-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84265377","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: 101
Distributed Backup Placement in One Round and its Applications to Maximum Matching Approximation and Self-Stabilization 一轮分布式备份布置及其在最大匹配逼近和自稳定中的应用
Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2019-08-01 DOI: 10.1137/1.9781611976014.14
Leonid Barenboim, Gal Oren
{"title":"Distributed Backup Placement in One Round and its Applications to Maximum Matching Approximation and Self-Stabilization","authors":"Leonid Barenboim, Gal Oren","doi":"10.1137/1.9781611976014.14","DOIUrl":"https://doi.org/10.1137/1.9781611976014.14","url":null,"abstract":"In the distributed backup-placement problem each node of a network has to select one neighbor, such that the maximum number of nodes that make the same selection is minimized. This is a natural relaxation of the perfect matching problem, in which each node is selected just by one neighbor. Previous (approximate) solutions for backup placement are non-trivial, even for simple graph topologies, such as dense graphs. In this paper we devise an algorithm for dense graph topologies, including unit disk graphs, unit ball graphs, line graphs, graphs with bounded diversity, and many more. Our algorithm requires just one round, and is as simple as the following operation. Consider a circular list of neighborhood IDs, sorted in an ascending order, and select the ID that is next to the selecting vertex ID. Surprisingly, such a simple one-round strategy turns out to be very efficient for backup placement computation in dense networks. Not only that it improves the number of rounds of the solution, but also the approximation ratio is improved by a multiplicative factor of at least $2$. \u0000Our new algorithm has several interesting implications. In particular, it gives rise to a $(2 + epsilon)$-approximation to maximum matching within $O(log^* n)$ rounds in dense networks. The resulting algorithm is very simple as well, in sharp contrast to previous algorithms that compute such a solution within this running time. Moreover, these algorithms are applicable to a narrower graph family than our algorithm. For the same graph family, the best previously-known result has $O(log {Delta} + log^* n)$ running time. Another interesting implication is the possibility to execute our backup placement algorithm as-is in the self-stabilizing setting. This makes it possible to simplify and improve other algorithms for the self-stabilizing setting, by employing helpful properties of backup placement.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"43 1","pages":"99-105"},"PeriodicalIF":0.0,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80642954","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: 7
Isotonic Regression by Dynamic Programming 动态规划的等渗回归
Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2019-01-01 DOI: 10.4230/OASIcs.SOSA.2019.1
G. Rote
{"title":"Isotonic Regression by Dynamic Programming","authors":"G. Rote","doi":"10.4230/OASIcs.SOSA.2019.1","DOIUrl":"https://doi.org/10.4230/OASIcs.SOSA.2019.1","url":null,"abstract":"For a given sequence of numbers, we want to find a monotonically increasing sequence of the same length that best approximates it in the sense of minimizing the weighted sum of absolute values of the differences. A conceptually easy dynamic programming approach leads to an algorithm with running time O(n logn). While other algorithms with the same running time are known, our algorithm is very simple. The only auxiliary data structure that it requires is a priority queue. The approach extends to other error measures. 2012 ACM Subject Classification Human-centered computing → Graph drawings. Mathematics of computing → Graph algorithms","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"474 1","pages":"1:1-1:18"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77763992","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: 8
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