Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)最新文献_第5页

Adversarially Robust Streaming via Dense-Sparse Trade-offs 基于密集-稀疏权衡的对抗性鲁棒流

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2021-09-08 DOI: 10.1137/1.9781611977066.15

Omri Ben-Eliezer, T. Eden, Krzysztof Onak

{"title":"Adversarially Robust Streaming via Dense-Sparse Trade-offs","authors":"Omri Ben-Eliezer, T. Eden, Krzysztof Onak","doi":"10.1137/1.9781611977066.15","DOIUrl":"https://doi.org/10.1137/1.9781611977066.15","url":null,"abstract":"A streaming algorithm is adversarially robust if it is guaranteed to perform correctly even in the presence of an adaptive adversary. Recently, several sophisticated frameworks for robustification of classical streaming algorithms have been developed. One of the main open questions in this area is whether efficient adversarially robust algorithms exist for moment estimation problems under the turnstile streaming model, where both insertions and deletions are allowed. So far, the best known space complexity for streams of length $m$, achieved using differential privacy (DP) based techniques, is of order $tilde{O}(m^{1/2})$ for computing a constant-factor approximation with high constant probability. In this work, we propose a new simple approach to tracking moments by alternating between two different regimes: a sparse regime, in which we can explicitly maintain the current frequency vector and use standard sparse recovery techniques, and a dense regime, in which we make use of existing DP-based robustification frameworks. The results obtained using our technique break the previous $m^{1/2}$ barrier for any fixed $p$. More specifically, our space complexity for $F_2$-estimation is $tilde{O}(m^{2/5})$ and for $F_0$-estimation, i.e., counting the number of distinct elements, it is $tilde O(m^{1/3})$. All existing robustness frameworks have their space complexity depend multiplicatively on a parameter $lambda$ called the emph{flip number} of the streaming problem, where $lambda = m$ in turnstile moment estimation. The best known dependence in these frameworks (for constant factor approximation) is of order $tilde{O}(lambda^{1/2})$, and it is known to be tight for certain problems. Again, our approach breaks this barrier, achieving a dependence of order $tilde{O}(lambda^{1/2 - c(p)})$ for $F_p$-estimation, where $c(p)>0$ depends only on $p$.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"121 1","pages":"214-227"},"PeriodicalIF":0.0,"publicationDate":"2021-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85226193","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: 18

An explicit vector algorithm for high-girth MaxCut 高周长MaxCut的显式矢量算法

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2021-08-27 DOI: 10.1137/1.9781611977066.17

Jessica Thompson, Ojas D. Parekh, Kunal Marwaha

引用次数: 4

Faster Exponential Algorithm for Permutation Pattern Matching 排列模式匹配的快速指数算法

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2021-08-25 DOI: 10.1137/1.9781611977066.21

Paweł Gawrychowski, Mateusz Rzepecki

引用次数: 2

Uniformity Testing in the Shuffle Model: Simpler, Better, Faster Shuffle模型中的一致性测试:更简单、更好、更快

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2021-08-20 DOI: 10.1137/1.9781611977066.13

C. Canonne, Hongyi Lyu

引用次数: 4

Maintaining an EDCS in General Graphs: Simpler, Density-Sensitive and with Worst-Case Time Bounds 一般图中EDCS的维护:更简单、密度敏感和具有最坏情况时间边界

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2021-08-19 DOI: 10.1137/1.9781611977066.2

F. Grandoni, Chris Schwiegelshohn, Shay Solomon, Amitai Uzrad

{"title":"Maintaining an EDCS in General Graphs: Simpler, Density-Sensitive and with Worst-Case Time Bounds","authors":"F. Grandoni, Chris Schwiegelshohn, Shay Solomon, Amitai Uzrad","doi":"10.1137/1.9781611977066.2","DOIUrl":"https://doi.org/10.1137/1.9781611977066.2","url":null,"abstract":"In their breakthrough ICALP'15 paper, Bernstein and Stein presented an algorithm for maintaining a $(3/2+epsilon)$-approximate maximum matching in fully dynamic {em bipartite} graphs with a {em worst-case} update time of $O_epsilon(m^{1/4})$; we use the $O_epsilon$ notation to suppress the $epsilon$-dependence. Their main technical contribution was in presenting a new type of bounded-degree subgraph, which they named an {em edge degree constrained subgraph (EDCS)}, which contains a large matching -- of size that is smaller than the maximum matching size of the entire graph by at most a factor of $3/2+epsilon$. They demonstrate that the EDCS can be maintained with a worst-case update time of $O_epsilon(m^{1/4})$, and their main result follows as a direct corollary. In their followup SODA'16 paper, Bernstein and Stein generalized their result for general graphs, achieving the same update time of $O_epsilon(m^{1/4})$, albeit with an amortized rather than worst-case bound. To date, the best {em deterministic} worst-case update time bound for {em any} better-than-2 approximate matching is $O(sqrt{m})$ [Neiman and Solomon, STOC'13], [Gupta and Peng, FOCS'13]; allowing randomization (against an oblivious adversary) one can achieve a much better (still polynomial) update time for approximation slightly below 2 [Behnezhad, Lacki and Mirrokni, SODA'20]. In this work wefootnote{em quasi nanos, gigantium humeris insidentes} simplify the approach of Bernstein and Stein for bipartite graphs, which allows us to generalize it for general graphs while maintaining the same bound of $O_epsilon(m^{1/4})$ on the {em worst-case} update time. Moreover, our approach is {em density-sensitive}: If the {em arboricity} of the dynamic graph is bounded by $alpha$ at all times, then the worst-case update time of the algorithm is $O_epsilon(sqrt{alpha})$.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"os-32 1","pages":"12-23"},"PeriodicalIF":0.0,"publicationDate":"2021-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87413973","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: 21

A Tighter Relation Between Hereditary Discrepancy and Determinant Lower Bound 遗传差异与行列式下界的密切关系

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2021-08-18 DOI: 10.1137/1.9781611977066.24

Haotian Jiang, Victor Reis

引用次数: 2

Derandomization of Cell Sampling 细胞抽样的非随机化

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2021-08-12 DOI: 10.1137/1.9781611977585.ch26

Alexander Golovnev, Tom Gur, Igor Shinkar

引用次数: 0

Topological Art in Simple Galleries 简单画廊中的拓扑艺术

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2021-08-09 DOI: 10.1137/1.9781611977066.8

Daniel Bertschinger, Nicolas El Maalouly, Tillmann Miltzow, P. Schnider, Simon Weber

引用次数: 6

Sinkless Orientation Made Simple 无下沉定向变得简单

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2021-08-05 DOI: 10.1137/1.9781611977585.ch17

A. Balliu, Janne H. Korhonen, F. Kuhn, Henrik Lievonen, D. Olivetti, Shreyas Pai, A. Paz, J. Rybicki, Stefan Schmid, Jan Studen'y, J. Suomela, Jara Uitto

引用次数: 1

The Quantum Union Bound made easy 量子结合界变得容易了

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2021-03-14 DOI: 10.1137/1.9781611977066.25

R. O'Donnell, R. Venkateswaran

引用次数: 6