Proceedings of the 2021 SIAM Conference on Applied and Computational Discrete Algorithms. SIAM Conference on Applied and Computational Discrete Algorithms (2021 : Online)最新文献

Irreducibility of Recombination Markov Chains in the Triangular Lattice 三角格中复合马尔可夫链的不可约性

Proceedings of the 2021 SIAM Conference on Applied and Computational Discrete Algorithms. SIAM Conference on Applied and Computational Discrete Algorithms (2021 : Online) Pub Date : 2023-05-26 DOI: 10.1137/1.9781611977714.9

Sarah Cannon

{"title":"Irreducibility of Recombination Markov Chains in the Triangular Lattice","authors":"Sarah Cannon","doi":"10.1137/1.9781611977714.9","DOIUrl":"https://doi.org/10.1137/1.9781611977714.9","url":null,"abstract":"In the United States, regions are frequently divided into districts for the purpose of electing representatives. How the districts are drawn can affect who's elected, and drawing districts to give an advantage to a certain group is known as gerrymandering. It can be surprisingly difficult to detect gerrymandering, but one algorithmic method is to compare a current districting plan to a large number of randomly sampled plans to see whether it is an outlier. Recombination Markov chains are often used for this random sampling: randomly choose two districts, consider their union, and split this union in a new way. This works well in practice, but the theory behind it remains underdeveloped. For example, it's not known if recombination Markov chains are irreducible, that is, if recombination moves suffice to move from any districting plan to any other. Irreducibility of recombination Markov chains can be formulated as a graph problem: for a graph $G$, is the space of all partitions of $G$ into $k$ connected subgraphs ($k$ districts) connected by recombination moves? We consider three simply connected districts and district sizes $k_1pm 1$ vertices, $k_2pm 1$ vertices, and $k3pm 1$ vertices. We prove for arbitrarily large triangular regions in the triangular lattice, recombination Markov chains are irreducible. This is the first proof of irreducibility under tight district size constraints for recombination Markov chains beyond small or trivial examples.","PeriodicalId":93610,"journal":{"name":"Proceedings of the 2021 SIAM Conference on Applied and Computational Discrete Algorithms. SIAM Conference on Applied and Computational Discrete Algorithms (2021 : Online)","volume":"30 1","pages":"98-109"},"PeriodicalIF":0.0,"publicationDate":"2023-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89687777","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

Engineering Fully Dynamic Δ-Orientation Algorithms 工程完全动态Δ-Orientation算法

Proceedings of the 2021 SIAM Conference on Applied and Computational Discrete Algorithms. SIAM Conference on Applied and Computational Discrete Algorithms (2021 : Online) Pub Date : 2023-01-01 DOI: 10.48550/arXiv.2301.06968

Jannick Borowitz, Ernestine Großmann, Christian Schulz

引用次数: 0

Exponential Convergence of Sinkhorn Under Regularization Scheduling 正则化调度下Sinkhorn的指数收敛性

Proceedings of the 2021 SIAM Conference on Applied and Computational Discrete Algorithms. SIAM Conference on Applied and Computational Discrete Algorithms (2021 : Online) Pub Date : 2022-07-02 DOI: 10.48550/arXiv.2207.00736

Jingbang Chen, Yang P. Liu, Richard Peng, Arvind Ramaswami

引用次数: 1

The Quantile Matching Problem and Point Cloud Registration 分位数匹配问题与点云配准

Proceedings of the 2021 SIAM Conference on Applied and Computational Discrete Algorithms. SIAM Conference on Applied and Computational Discrete Algorithms (2021 : Online) Pub Date : 2021-01-01 DOI: 10.1137/1.9781611976830.2

S. Chrétien, O. Karasan, Ecenur Oguz, M. Pınar

引用次数: 0

On the Difference between Search Space Size and Query Complexity in Contraction Hierarchies 压缩层次结构中搜索空间大小与查询复杂度的差异

Proceedings of the 2021 SIAM Conference on Applied and Computational Discrete Algorithms. SIAM Conference on Applied and Computational Discrete Algorithms (2021 : Online) Pub Date : 2021-01-01 DOI: 10.1137/1.9781611976830.8

Claudius Proissl, Tobias Rupp

引用次数: 0

Improving Tug-of-War sketch using Control-Variates method 用控制变量法改进拔河草图

Proceedings of the 2021 SIAM Conference on Applied and Computational Discrete Algorithms. SIAM Conference on Applied and Computational Discrete Algorithms (2021 : Online) Pub Date : 2021-01-01 DOI: 10.1137/1.9781611976830.7

Rameshwar Pratap, Bhisham Dev Verma, R. Kulkarni

{"title":"Improving Tug-of-War sketch using Control-Variates method","authors":"Rameshwar Pratap, Bhisham Dev Verma, R. Kulkarni","doi":"10.1137/1.9781611976830.7","DOIUrl":"https://doi.org/10.1137/1.9781611976830.7","url":null,"abstract":"Computing space-efficient summary, or textit{a.k.a. sketches}, of large data, is a central problem in the streaming algorithm. Such sketches are used to answer textit{post-hoc} queries in several data analytics tasks. The algorithm for computing sketches typically requires to be fast, accurate, and space-efficient. A fundamental problem in the streaming algorithm framework is that of computing the frequency moments of data streams. The frequency moments of a sequence containing $f_i$ elements of type $i$, are the numbers $mathbf{F}_k=sum_{i=1}^n {f_i}^k,$ where $iin [n]$. This is also called as $ell_k$ norm of the frequency vector $(f_1, f_2, ldots f_n).$ Another important problem is to compute the similarity between two data streams by computing the inner product of the corresponding frequency vectors. The seminal work of Alon, Matias, and Szegedy~cite{AMS}, textit{a.k.a. Tug-of-war} (or AMS) sketch gives a randomized sublinear space (and linear time) algorithm for computing the frequency moments, and the inner product between two frequency vectors corresponding to the data streams. However, the variance of these estimates typically tends to be large. In this work, we focus on minimizing the variance of these estimates. We use the techniques from the classical Control-Variate method~cite{Lavenberg} which is primarily known for variance reduction in Monte-Carlo simulations, and as a result, we are able to obtain significant variance reduction, at the cost of a little computational overhead. We present a theoretical analysis of our proposal and complement it with supporting experiments on synthetic as well as real-world datasets.","PeriodicalId":93610,"journal":{"name":"Proceedings of the 2021 SIAM Conference on Applied and Computational Discrete Algorithms. SIAM Conference on Applied and Computational Discrete Algorithms (2021 : Online)","volume":"19 1","pages":"66-76"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90903070","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

Parameterized algorithms for identifying gene co-expression modules via weighted clique decomposition 基于加权团块分解的参数化基因共表达模块识别算法

Proceedings of the 2021 SIAM Conference on Applied and Computational Discrete Algorithms. SIAM Conference on Applied and Computational Discrete Algorithms (2021 : Online) Pub Date : 2021-01-01 DOI: 10.1137/1.9781611976830.11

Madison Cooley, C. Greene, Davis Issac, M. Pividori, Blair D. Sullivan

引用次数: 4

Efficient signed backward substitution for piecewise affine functions via path problems in a directed acyclic graph 基于有向无环图路径问题的分段仿射函数的有效符号逆向代换

Proceedings of the 2021 SIAM Conference on Applied and Computational Discrete Algorithms. SIAM Conference on Applied and Computational Discrete Algorithms (2021 : Online) Pub Date : 2021-01-01 DOI: 10.1137/1.9781611976830.16

T. Bosse, Ralf Seidler, H. M. Bücker

引用次数: 0

Search and evacuation with a near majority of faulty agents 搜索和疏散几乎都是错误的特工

Proceedings of the 2021 SIAM Conference on Applied and Computational Discrete Algorithms. SIAM Conference on Applied and Computational Discrete Algorithms (2021 : Online) Pub Date : 2021-01-01 DOI: 10.1137/1.9781611976830.20

J. Czyzowicz, R. Killick, E. Kranakis, Grzegorz Stachowiak

引用次数: 4

A Parallel Approximation Algorithm for Maximizing Submodular b-Matching 最大化子模b匹配的并行逼近算法

Proceedings of the 2021 SIAM Conference on Applied and Computational Discrete Algorithms. SIAM Conference on Applied and Computational Discrete Algorithms (2021 : Online) Pub Date : 2021-01-01 DOI: 10.1137/1.9781611976830.5

S. Ferdous, A. Pothen, Arif M. Khan, Ajay Panyala, M. Halappanavar

{"title":"A Parallel Approximation Algorithm for Maximizing Submodular b-Matching","authors":"S. Ferdous, A. Pothen, Arif M. Khan, Ajay Panyala, M. Halappanavar","doi":"10.1137/1.9781611976830.5","DOIUrl":"https://doi.org/10.1137/1.9781611976830.5","url":null,"abstract":"We design new serial and parallel approximation algorithms for computing a maximum weight $b$-matching in an edge-weighted graph with a submodular objective function. This problem is NP-hard; the new algorithms have approximation ratio $1/3$, and are relaxations of the Greedy algorithm that rely only on local information in the graph, making them parallelizable. We have designed and implemented Local Lazy Greedy algorithms for both serial and parallel computers. We have applied the approximate submodular $b$-matching algorithm to assign tasks to processors in the computation of Fock matrices in quantum chemistry on parallel computers. The assignment seeks to reduce the run time by balancing the computational load on the processors and bounding the number of messages that each processor sends. We show that the new assignment of tasks to processors provides a four fold speedup over the currently used assignment in the NWChemEx software on $8000$ processors on the Summit supercomputer at Oak Ridge National Lab.","PeriodicalId":93610,"journal":{"name":"Proceedings of the 2021 SIAM Conference on Applied and Computational Discrete Algorithms. SIAM Conference on Applied and Computational Discrete Algorithms (2021 : Online)","volume":"27 1","pages":"45-56"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80896294","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