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

Revisiting Garg's 2-Approximation Algorithm for the k-MST Problem in Graphs 图中k-MST问题的Garg 2-逼近算法重述

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2023-06-02 DOI: 10.1137/1.9781611977585.ch6

Emmett Breen, Renee Mirka, Zichen Wang, David P. Williamson

引用次数: 1

Min-Max Optimization Made Simple: Approximating the Proximal Point Method via Contraction Maps 简化最小-最大优化:通过收缩映射逼近近点方法

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2023-01-10 DOI: 10.48550/arXiv.2301.03931

V. Cevher, G. Piliouras, Ryann Sim, Stratis Skoulakis

引用次数: 4

Simpler and faster algorithms for detours in planar digraphs 平面有向图中绕行的更简单、更快的算法

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2023-01-06 DOI: 10.48550/arXiv.2301.02421

Meike Hatzel, Konrad Majewski, Michal Pilipczuk, Marek Sokolowski

{"title":"Simpler and faster algorithms for detours in planar digraphs","authors":"Meike Hatzel, Konrad Majewski, Michal Pilipczuk, Marek Sokolowski","doi":"10.48550/arXiv.2301.02421","DOIUrl":"https://doi.org/10.48550/arXiv.2301.02421","url":null,"abstract":"In the directed detour problem one is given a digraph $G$ and a pair of vertices $s$ and~$t$, and the task is to decide whether there is a directed simple path from $s$ to $t$ in $G$ whose length is larger than $mathsf{dist}_{G}(s,t)$. The more general parameterized variant, directed long detour, asks for a simple $s$-to-$t$ path of length at least $mathsf{dist}_{G}(s,t)+k$, for a given parameter $k$. Surprisingly, it is still unknown whether directed detour is polynomial-time solvable on general digraphs. However, for planar digraphs, Wu and Wang~[Networks, '15] proposed an $mathcal{O}(n^3)$-time algorithm for directed detour, while Fomin et al.~[STACS 2022] gave a $2^{mathcal{O}(k)}cdot n^{mathcal{O}(1)}$-time fpt algorithm for directed long detour. The algorithm of Wu and Wang relies on a nontrivial analysis of how short detours may look like in a plane embedding, while the algorithm of Fomin et al.~is based on a reduction to the ${S}$-disjoint paths problem on planar digraphs. This latter problem is solvable in polynomial time using the algebraic machinery of Schrijver~[SIAM~J.~Comp.,~'94], but the degree of the obtained polynomial factor is huge. In this paper we propose two simple algorithms: we show how to solve, in planar digraphs, directed detour in time $mathcal{O}(n^2)$ and directed long detour in time $2^{mathcal{O}(k)}cdot n^4 log n$. In both cases, the idea is to reduce to the $2$-disjoint paths problem in a planar digraph, and to observe that the obtained instances of this problem have a certain topological structure that makes them amenable to a direct greedy strategy.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"80 1","pages":"156-165"},"PeriodicalIF":0.0,"publicationDate":"2023-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80387200","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

A Simple Optimal Algorithm for the 2-Arm Bandit Problem 双臂强盗问题的一种简单优化算法

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2023-01-01 DOI: 10.1137/1.9781611977585.ch33

Maxime Larcher, Robert Meier, A. Steger

引用次数: 0

A Simple Algorithm for Submodular Minimum Linear Ordering 一种简单的次模最小线性排序算法

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2023-01-01 DOI: 10.1137/1.9781611977585.ch3

Dor Katzelnick, Roy Schwartz

引用次数: 0

Proximity Search in the Greedy Tree 贪婪树中的邻近搜索

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2023-01-01 DOI: 10.1137/1.9781611977585.ch29

Oliver A. Chubet, Parth Parikh, Don Sheehy, S. Sheth

引用次数: 0

On the Fine-Grained Complexity of Approximating k-Center in Sparse Graphs 稀疏图中k-中心逼近的细粒度复杂度

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2023-01-01 DOI: 10.1137/1.9781611977585.ch14

Amir Abboud, Vincent Cohen-Addad, Euiwoong Lee, Pasin Manurangsi

引用次数: 2

An Improved Online Reduction from PAC Learning to Mistake-Bounded Learning 从PAC学习到错误边界学习的改进在线还原

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2023-01-01 DOI: 10.1137/1.9781611977585.ch34

Lucas Gretta, Eric Price

引用次数: 0

Simple Random Order Contention Resolution for Graphic Matroids with Almost no Prior Information 几乎没有先验信息的图形拟阵的简单随机顺序争用解决

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2022-11-28 DOI: 10.48550/arXiv.2211.15146

Richard Santiago, I. Sergeev, R. Zenklusen

{"title":"Simple Random Order Contention Resolution for Graphic Matroids with Almost no Prior Information","authors":"Richard Santiago, I. Sergeev, R. Zenklusen","doi":"10.48550/arXiv.2211.15146","DOIUrl":"https://doi.org/10.48550/arXiv.2211.15146","url":null,"abstract":"Random order online contention resolution schemes (ROCRS) are structured online rounding algorithms with numerous applications and links to other well-known online selection problems, like the matroid secretary conjecture. We are interested in ROCRS subject to a matroid constraint, which is among the most studied constraint families. Previous ROCRS required to know upfront the full fractional point to be rounded as well as the matroid. It is unclear to what extent this is necessary. Fu, Lu, Tang, Turkieltaub, Wu, Wu, and Zhang (SOSA 2022) shed some light on this question by proving that no strong (constant-selectable) online or even offline contention resolution scheme exists if the fractional point is unknown, not even for graphic matroids. In contrast, we show, in a setting with slightly more knowledge and where the fractional point reveals one by one, that there is hope to obtain strong ROCRS by providing a simple constant-selectable ROCRS for graphic matroids that only requires to know the size of the ground set in advance. Moreover, our procedure holds in the more general adversarial order with a sample setting, where, after sampling a random constant fraction of the elements, all remaining (non-sampled) elements may come in adversarial order.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"273 1","pages":"84-95"},"PeriodicalIF":0.0,"publicationDate":"2022-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79969833","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

Optimal resizable arrays 最佳可调整大小数组

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2022-11-20 DOI: 10.48550/arXiv.2211.11009

R. Tarjan, Uri Zwick

{"title":"Optimal resizable arrays","authors":"R. Tarjan, Uri Zwick","doi":"10.48550/arXiv.2211.11009","DOIUrl":"https://doi.org/10.48550/arXiv.2211.11009","url":null,"abstract":"A emph{resizable array} is an array that can emph{grow} and emph{shrink} by the addition or removal of items from its end, or both its ends, while still supporting constant-time emph{access} to each item stored in the array given its emph{index}. Since the size of an array, i.e., the number of items in it, varies over time, space-efficient maintenance of a resizable array requires dynamic memory management. A standard doubling technique allows the maintenance of an array of size~$N$ using only $O(N)$ space, with $O(1)$ amortized time, or even $O(1)$ worst-case time, per operation. Sitarski and Brodnik et al. describe much better solutions that maintain a resizable array of size~$N$ using only $N+O(sqrt{N})$ space, still with $O(1)$ time per operation. Brodnik et al. give a simple proof that this is best possible. We distinguish between the space needed for emph{storing} a resizable array, and accessing its items, and the emph{temporary} space that may be needed while growing or shrinking the array. For every integer $rge 2$, we show that $N+O(N^{1/r})$ space is sufficient for storing and accessing an array of size~$N$, if $N+O(N^{1-1/r})$ space can be used briefly during grow and shrink operations. Accessing an item by index takes $O(1)$ worst-case time while grow and shrink operations take $O(r)$ amortized time. Using an exact analysis of a emph{growth game}, we show that for any data structure from a wide class of data structures that uses only $N+O(N^{1/r})$ space to store the array, the amortized cost of grow is $Omega(r)$, even if only grow and access operations are allowed. The time for grow and shrink operations cannot be made worst-case, unless $r=2$.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"4 1","pages":"285-304"},"PeriodicalIF":0.0,"publicationDate":"2022-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91247570","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