2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)最新文献_第10页

Distributed Local Approximation Algorithms for Maximum Matching in Graphs and Hypergraphs 图和超图中最大匹配的分布式局部逼近算法

2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS) Pub Date : 2018-07-19 DOI: 10.1109/FOCS.2019.00048

David G. Harris

{"title":"Distributed Local Approximation Algorithms for Maximum Matching in Graphs and Hypergraphs","authors":"David G. Harris","doi":"10.1109/FOCS.2019.00048","DOIUrl":"https://doi.org/10.1109/FOCS.2019.00048","url":null,"abstract":"We describe approximation algorithms in Linial's classic LOCAL model of distributed computing to find maximum-weight matchings in a hypergraph of rank r. Our main result is a deterministic algorithm to generate a matching which is an O(r)-approximation to the maximum weight matching, running in Õ(r log Δ + log^2 Δ + log^* n) rounds. (Here, the Õ() notations hides polyloglog Δ and polylog r factors). This is based on a number of new derandomization techniques extending methods of Ghaffari, Harris & Kuhn (2017). The first main application is to nearly-optimal algorithms for the long-studied problem of maximum-weight graph matching. Specifically, we get a (1+ε) approximation algorithm using Õ(log Δ / ε^3 + polylog(1/ε, log log n)) randomized time and Õ(log^2 Δ / ε^4 + log^*n / ε) deterministic time. The second application is a faster algorithm for hypergraph maximal matching, a versatile subroutine introduced in Ghaffari et al. (2017) for a variety of local graph algorithms. This gives an algorithm for (2 Δ - 1) -edge-list coloring in Õ(log^2 Δ log n) rounds deterministically or Õ( (log log n)^3 ) rounds randomly. Another consequence (with additional optimizations) is an algorithm which generates an edge-orientation with out-degree at most ⌈ (1+ε) λ ⌉ for a graph of arboricity λ; for fixed ε this runs in Õ(log^6 n) rounds deterministically or Õ(log^3 n ) rounds randomly.","PeriodicalId":407139,"journal":{"name":"2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125563793","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: 38

Waring Rank, Parameterized and Exact Algorithms 预警秩、参数化和精确算法

2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS) Pub Date : 2018-07-17 DOI: 10.1109/FOCS.2019.00053

Kevin Pratt

引用次数: 13

Beyond the Lovász Local Lemma: Point to Set Correlations and Their Algorithmic Applications 超越Lovász本地引理:指向集合关联及其算法应用

2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS) Pub Date : 2018-05-05 DOI: 10.1109/FOCS.2019.00049

D. Achlioptas, Fotis Iliopoulos, A. Sinclair

{"title":"Beyond the Lovász Local Lemma: Point to Set Correlations and Their Algorithmic Applications","authors":"D. Achlioptas, Fotis Iliopoulos, A. Sinclair","doi":"10.1109/FOCS.2019.00049","DOIUrl":"https://doi.org/10.1109/FOCS.2019.00049","url":null,"abstract":"Following the groundbreaking algorithm of Moser and Tardos for the Lovasz Local Lemma (LLL), there has been a plethora of results analyzing local search algorithms for various constraint satisfaction problems. The algorithms considered fall into two broad categories: resampling algorithms, analyzed via different algorithmic LLL conditions; and backtracking algorithms, analyzed via entropy compression arguments. This paper introduces a new convergence condition that seamlessly handles resampling, backtracking, and hybrid algorithms, i.e., algorithms that perform both resampling and backtracking steps. Unlike previous work on the LLL, our condition replaces the notion of a dependency or causality graph by quantifying point-to-set correlations between bad events. As a result, our condition simultaneously: (i) captures the most general algorithmic LLL condition known as a special case; (ii) significantly simplifies the analysis of entropy compression applications; (iii) relates backtracking algorithms, which are conceptually very different from resampling algorithms, to the LLL; and most importantly (iv) allows for the analysis of hybrid algorithms, which were outside the scope of previous techniques. We give several applications of our condition, including a new hybrid vertex coloring algorithm that extends the recent breakthrough result of Molloy for coloring triangle-free graphs to arbitrary graphs.","PeriodicalId":407139,"journal":{"name":"2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132839195","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: 30

Optimal Document Exchange and New Codes for Insertions and Deletions 最佳文件交换和新代码的插入和删除

2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS) Pub Date : 2018-04-10 DOI: 10.1109/FOCS.2019.00029

Bernhard Haeupler

{"title":"Optimal Document Exchange and New Codes for Insertions and Deletions","authors":"Bernhard Haeupler","doi":"10.1109/FOCS.2019.00029","DOIUrl":"https://doi.org/10.1109/FOCS.2019.00029","url":null,"abstract":"We give the first communication-optimal document exchange protocol. For any n and k < n our randomized scheme takes any n-bit file F and computes a Θ(k log n/k) -bit summary from which one can reconstruct F, with high probability, given a related file F' with edit distance ED(F,F') ≤ k. The size of our summary is information-theoretically order optimal for all values of k, giving a randomized solution to a longstanding open question of [Orlitsky; FOCS'91]. It also is the first non-trivial solution for the interesting setting where a small constant fraction of symbols have been edited, producing an optimal summary of size O(H(δ)n) for k=δ n. This concludes a long series of better-and-better protocols which produce larger summaries for sub-linear values of k and sub-polynomial failure probabilities. In particular, the recent break-through of [Belazzougui, Zhang; FOCS'16] assumes that k < n^ε, produces a summary of size O(klog^2 k + k log n), and succeeds with probability 1-(k log n)^ -O(1). We also give an efficient derandomized document exchange protocol with summary size O(k log^2 n/k). This improves, for any k, over a deterministic document exchange protocol by Belazzougui with summary size O(k^2 + k log^2 n). Our deterministic document exchange directly provides new efficient systematic error correcting codes for insertions and deletions. These (binary) codes correct any δ fraction of adversarial insertions/deletions while having a rate of 1 - O(δ log^2 1/δ) and improve over the codes of Guruswami and Li and Haeupler, Shahrasbi and Vitercik which have rate 1 - Θ (√δ log^O(1) 1/ε).","PeriodicalId":407139,"journal":{"name":"2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124317448","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: 51