arXiv - CS - Data Structures and Algorithms最新文献_第10页

Finding a Shortest $M$-link Path in a Monge Directed Acyclic Graph 在蒙日有向无环图中寻找最短 $M$ 链接路径

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-08-01 DOI: arxiv-2408.00227

Joy Z. Wan

引用次数: 0

An Invertible State Space for Process Trees 进程树的可逆状态空间

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-07-31 DOI: arxiv-2407.21468

Gero Kolhof, Sebastiaan J. van Zelst

引用次数: 0

Simpler Optimal Sorting from a Directed Acyclic Graph 从有向无环图进行更简单的优化排序

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-07-31 DOI: arxiv-2407.21591

Ivor van der Hoog, Eva Rotenberg, Daniel Rutschmann

{"title":"Simpler Optimal Sorting from a Directed Acyclic Graph","authors":"Ivor van der Hoog, Eva Rotenberg, Daniel Rutschmann","doi":"arxiv-2407.21591","DOIUrl":"https://doi.org/arxiv-2407.21591","url":null,"abstract":"Fredman proposed in 1976 the following algorithmic problem: Given are a\u0000ground set $X$, some partial order $P$ over $X$, and some comparison oracle\u0000$O_L$ that specifies a linear order $L$ over $X$ that extends $P$. A query to\u0000$O_L$ has as input distinct $x, x' in X$ and outputs whether $x <_L x'$ or\u0000vice versa. If we denote by $e(P)$ the number of linear extensions of $P$, then\u0000$log e(P)$ is a worst-case lower bound on the number of queries needed to\u0000output the sorted order of $X$. Fredman did not specify in what form the partial order is given. Haeupler,\u0000Hlad'ik, Iacono, Rozhon, Tarjan, and Tv{e}tek ('24) propose to assume as\u0000input a directed acyclic graph, $G$, with $m$ edges and $n=|X|$ vertices.\u0000Denote by $P_G$ the partial order induced by $G$. Algorithmic performance is\u0000measured in running time and the number of queries used, where they use\u0000$Theta(m + n + log e(P_G))$ time and $Theta(log e(P_G))$ queries to output\u0000$X$ in its sorted order. Their algorithm is worst-case optimal in terms of\u0000running time and queries, both. Their algorithm combines topological sorting\u0000with heapsort, and uses sophisticated data structures (including a recent type\u0000of heap with a working-set bound). Their analysis relies upon sophisticated\u0000counting arguments using entropy, recursively defined sets defined over the run\u0000of their algorithm, and vertices in the graph that they identify as bottlenecks\u0000for sorting. In this paper, we do away with sophistication. We show that when the input is\u0000a directed acyclic graph then the problem admits a simple solution using\u0000$Theta(m + n + log e(P_G))$ time and $Theta(log e(P_G))$ queries.\u0000Especially our proofs are much simpler as we avoid the usage of advanced\u0000charging arguments and data structures, and instead rely upon two brief\u0000observations.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"150 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141867316","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

Maintaining $k$-MinHash Signatures over Fully-Dynamic Data Streams with Recovery 在全动态数据流上维护具有恢复功能的 $k$-MinHash 签名

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-07-31 DOI: arxiv-2407.21614

Andrea Clementi, Luciano Gualà, Luca Pepè Sciarria, Alessandro Straziota

{"title":"Maintaining $k$-MinHash Signatures over Fully-Dynamic Data Streams with Recovery","authors":"Andrea Clementi, Luciano Gualà, Luca Pepè Sciarria, Alessandro Straziota","doi":"arxiv-2407.21614","DOIUrl":"https://doi.org/arxiv-2407.21614","url":null,"abstract":"We consider the task of performing Jaccard similarity queries over a large\u0000collection of items that are dynamically updated according to a streaming input\u0000model. An item here is a subset of a large universe $U$ of elements. A\u0000well-studied approach to address this important problem in data mining is to\u0000design fast-similarity data sketches. In this paper, we focus on global\u0000solutions for this problem, i.e., a single data structure which is able to\u0000answer both Similarity Estimation and All-Candidate Pairs queries, while also\u0000dynamically managing an arbitrary, online sequence of element insertions and\u0000deletions received in input. We introduce and provide an in-depth analysis of a dynamic, buffered version\u0000of the well-known $k$-MinHash sketch. This buffered version better manages\u0000critical update operations thus significantly reducing the number of times the\u0000sketch needs to be rebuilt from scratch using expensive recovery queries. We\u0000prove that the buffered $k$-MinHash uses $O(k log |U|)$ memory words per\u0000subset and that its amortized update time per insertion/deletion is $O(k log\u0000|U|)$ with high probability. Moreover, our data structure can return the\u0000$k$-MinHash signature of any subset in $O(k)$ time, and this signature is\u0000exactly the same signature that would be computed from scratch (and thus the\u0000quality of the signature is the same as the one guaranteed by the static\u0000$k$-MinHash). Analytical and experimental comparisons with the other, state-of-the-art\u0000global solutions for this problem given in [Bury et al.,WSDM'18] show that the\u0000buffered $k$-MinHash turns out to be competitive in a wide and relevant range\u0000of the online input parameters.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"209 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141867317","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

Robust Restaking Networks 稳健的重置网络

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-07-31 DOI: arxiv-2407.21785

Naveen Durvasula, Tim Roughgarden

引用次数: 0

Random-Order Interval Selection 随机顺序区间选择

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-07-30 DOI: arxiv-2407.20941

Allan Borodin, Christodoulos Karavasilis

{"title":"Random-Order Interval Selection","authors":"Allan Borodin, Christodoulos Karavasilis","doi":"arxiv-2407.20941","DOIUrl":"https://doi.org/arxiv-2407.20941","url":null,"abstract":"In the problem of online unweighted interval selection, the objective is to\u0000maximize the number of non-conflicting intervals accepted by the algorithm. In\u0000the conventional online model of irrevocable decisions, there is an Omega(n)\u0000lower bound on the competitive ratio, even for randomized algorithms [Bachmann\u0000et al. 2013]. In a line of work that allows for revocable acceptances, [Faigle\u0000and Nawijn 1995] gave a greedy 1-competitive (i.e. optimal) algorithm in the\u0000real-time model, where intervals arrive in order of non-decreasing starting\u0000times. The natural extension of their algorithm in the adversarial (any-order)\u0000model is 2k-competitive [Borodin and Karavasilis 2023], when there are at most\u0000k different interval lengths, and that is optimal for all deterministic, and\u0000memoryless randomized algorithms. We study this problem in the random-order\u0000model, where the adversary chooses the instance, but the online sequence is a\u0000uniformly random permutation of the items. We consider the same algorithm that\u0000is optimal in the cases of the real-time and any-order models, and give an\u0000upper bound of 2.5 on the competitive ratio under random-order arrivals. We also show how to utilize random-order arrivals to extract a random bit\u0000with a worst case bias of 2/3, when there are at least two distinct item types.\u0000We use this bit to derandomize the barely random algorithm of [Fung et al.\u00002014] and get a deterministic 3-competitive algorithm for single-length\u0000interval selection with arbitrary weights.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141867324","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

Settling the Pass Complexity of Approximate Matchings in Dynamic Graph Streams 解决动态图流中近似匹配的传递复杂性问题

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-07-30 DOI: arxiv-2407.21005

Sepehr Assadi, Soheil Behnezhad, Christian Konrad, Kheeran K. Naidu, Janani Sundaresan

{"title":"Settling the Pass Complexity of Approximate Matchings in Dynamic Graph Streams","authors":"Sepehr Assadi, Soheil Behnezhad, Christian Konrad, Kheeran K. Naidu, Janani Sundaresan","doi":"arxiv-2407.21005","DOIUrl":"https://doi.org/arxiv-2407.21005","url":null,"abstract":"A semi-streaming algorithm in dynamic graph streams processes any $n$-vertex\u0000graph by making one or multiple passes over a stream of insertions and\u0000deletions to edges of the graph and using $O(n cdot mbox{polylog}(n))$ space.\u0000Semi-streaming algorithms for dynamic streams were first obtained in the\u0000seminal work of Ahn, Guha, and McGregor in 2012, alongside the introduction of\u0000the graph sketching technique, which remains the de facto way of designing\u0000algorithms in this model and a highly popular technique for designing graph\u0000algorithms in general. We settle the pass complexity of approximating maximum matchings in dynamic\u0000streams via semi-streaming algorithms by improving the state-of-the-art in both\u0000upper and lower bounds. We present a randomized sketching based semi-streaming algorithm for\u0000$O(1)$-approximation of maximum matching in dynamic streams using\u0000$O(loglog{n})$ passes. The approximation ratio of this algorithm can be\u0000improved to $(1+epsilon)$ for any fixed $epsilon > 0$ even on weighted graphs\u0000using standard techniques. This exponentially improves upon several\u0000$O(log{n})$ pass algorithms developed for this problem since the introduction\u0000of the dynamic graph streaming model. In addition, we prove that any semi-streaming algorithm (not only sketching\u0000based) for $O(1)$-approximation of maximum matching in dynamic streams requires\u0000$Omega(loglog{n})$ passes. This presents the first multi-pass lower bound\u0000for this problem, which is already also optimal, settling a longstanding open\u0000question in this area.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"210 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141867225","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 Static and Dynamic Approximation Algorithms for Geometric Optimization Problems: Piercing, Independent Set, Vertex Cover, and Matching 几何优化问题的快速静态和动态逼近算法：穿孔、独立集、顶点覆盖和匹配

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-07-30 DOI: arxiv-2407.20659

Sujoy Bhore, Timothy M. Chan

{"title":"Fast Static and Dynamic Approximation Algorithms for Geometric Optimization Problems: Piercing, Independent Set, Vertex Cover, and Matching","authors":"Sujoy Bhore, Timothy M. Chan","doi":"arxiv-2407.20659","DOIUrl":"https://doi.org/arxiv-2407.20659","url":null,"abstract":"We develop simple and general techniques to obtain faster (near-linear time)\u0000static approximation algorithms, as well as efficient dynamic data structures,\u0000for four fundamental geometric optimization problems: minimum piercing set\u0000(MPS), maximum independent set (MIS), minimum vertex cover (MVC), and\u0000maximum-cardinality matching (MCM). Highlights of our results include the\u0000following: * For $n$ axis-aligned boxes in any constant dimension $d$, we give an\u0000$O(log log n)$-approximation algorithm for MPS that runs in $O(n^{1+delta})$\u0000time for an arbitrarily small constant $delta>0$. This significantly improves\u0000the previous $O(loglog n)$-approximation algorithm by Agarwal, Har-Peled,\u0000Raychaudhury, and Sintos (SODA~2024), which ran in $O(n^{d/2}mathop{rm\u0000polylog} n)$ time. * Furthermore, we show that our algorithm can be made fully dynamic with\u0000$O(n^{delta})$ amortized update time. Previously, Agarwal et al.~(SODA~2024)\u0000obtained dynamic results only in $mathbb{R}^2$ and achieved only\u0000$O(sqrt{n}mathop{rm polylog} n)$ amortized expected update time. * For $n$ axis-aligned rectangles in $mathbb{R}^2$, we give an\u0000$O(1)$-approximation algorithm for MIS that runs in $O(n^{1+delta})$ time. Our\u0000result significantly improves the running time of the celebrated algorithm by\u0000Mitchell (FOCS~2021) (which was about $O(n^{21})$), and answers one of his open\u0000questions. Our algorithm can also be made fully dynamic with $O(n^{delta})$\u0000amortized update time. * For $n$ (unweighted or weighted) fat objects in any constant dimension, we\u0000give a dynamic $O(1)$-approximation algorithm for MIS with $O(n^{delta})$\u0000amortized update time. * For disks in $mathbb{R}^2$ or hypercubes in any constant dimension, we\u0000give the first fully dynamic $(1+varepsilon)$-approximation algorithms for MVC\u0000and MCM with $O(mathop{rm polylog}n)$ amortized update time.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"282 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141867320","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

Randomized Rounding Approaches to Online Allocation, Sequencing, and Matching 在线分配、排序和匹配的随机轮循方法

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-07-29 DOI: arxiv-2407.20419

Will Ma

{"title":"Randomized Rounding Approaches to Online Allocation, Sequencing, and Matching","authors":"Will Ma","doi":"arxiv-2407.20419","DOIUrl":"https://doi.org/arxiv-2407.20419","url":null,"abstract":"Randomized rounding is a technique that was originally used to approximate\u0000hard offline discrete optimization problems from a mathematical programming\u0000relaxation. Since then it has also been used to approximately solve sequential\u0000stochastic optimization problems, overcoming the curse of dimensionality. To\u0000elaborate, one first writes a tractable linear programming relaxation that\u0000prescribes probabilities with which actions should be taken. Rounding then\u0000designs a (randomized) online policy that approximately preserves all of these\u0000probabilities, with the challenge being that the online policy faces hard\u0000constraints, whereas the prescribed probabilities only have to satisfy these\u0000constraints in expectation. Moreover, unlike classical randomized rounding for\u0000offline problems, the online policy's actions unfold sequentially over time,\u0000interspersed by uncontrollable stochastic realizations that affect the\u0000feasibility of future actions. This tutorial provides an introduction for using\u0000randomized rounding to design online policies, through four self-contained\u0000examples representing fundamental problems in the area: online contention\u0000resolution, stochastic probing, stochastic knapsack, and stochastic matching.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141867321","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

Engineering an Efficient Approximate DNF-Counter 设计高效的近似 DNF 计数器

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-07-29 DOI: arxiv-2407.19946

Mate Soos, Uddalok Sarkar, Divesh Aggarwal, Sourav Chakraborty, Kuldeep S. Meel, Maciej Obremski

引用次数: 0