Combinatorics, Probability and Computing最新文献_第10页

Towards the Kohayakawa–Kreuter conjecture on asymmetric Ramsey properties 关于非对称Ramsey性质的Kohayakawa-Kreuter猜想

Combinatorics, Probability and Computing Pub Date : 2018-08-15 DOI: 10.1017/S0963548320000267

Frank Mousset, R. Nenadov, W. Samotij

引用次数: 21

Analysis of Robin Hood and Other Hashing Algorithms Under the Random Probing Model, With and Without Deletions 随机探测模型下罗宾汉和其他哈希算法的分析，有和没有删除

Combinatorics, Probability and Computing Pub Date : 2018-08-14 DOI: 10.1017/S0963548318000408

P. V. Poblete, Alfredo Viola

{"title":"Analysis of Robin Hood and Other Hashing Algorithms Under the Random Probing Model, With and Without Deletions","authors":"P. V. Poblete, Alfredo Viola","doi":"10.1017/S0963548318000408","DOIUrl":"https://doi.org/10.1017/S0963548318000408","url":null,"abstract":"Thirty years ago, the Robin Hood collision resolution strategy was introduced for open addressing hash tables, and a recurrence equation was found for the distribution of its search cost. Although this recurrence could not be solved analytically, it allowed for numerical computations that, remarkably, suggested that the variance of the search cost approached a value of 1.883 when the table was full. Furthermore, by using a non-standard mean-centred search algorithm, this would imply that searches could be performed in expected constant time even in a full table. In spite of the time elapsed since these observations were made, no progress has been made in proving them. In this paper we introduce a technique to work around the intractability of the recurrence equation by solving instead an associated differential equation. While this does not provide an exact solution, it is sufficiently powerful to prove a bound of π2/3 for the variance, and thus obtain a proof that the variance of Robin Hood is bounded by a small constant for load factors arbitrarily close to 1. As a corollary, this proves that the mean-centred search algorithm runs in expected constant time. We also use this technique to study the performance of Robin Hood hash tables under a long sequence of insertions and deletions, where deletions are implemented by marking elements as deleted. We prove that, in this case, the variance is bounded by 1/(1−α), where α is the load factor. To model the behaviour of these hash tables, we use a unified approach that we apply also to study the First-Come-First-Served and Last-Come-First-Served collision resolution disciplines, both with and without deletions.","PeriodicalId":10503,"journal":{"name":"Combinatorics, Probability and Computing","volume":"17 1","pages":"600 - 617"},"PeriodicalIF":0.0,"publicationDate":"2018-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84417312","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

Limit laws of planar maps with prescribed vertex degrees 给定顶点度数的平面地图的极限定律

Combinatorics, Probability and Computing Pub Date : 2018-08-08 DOI: 10.1017/S0963548318000573

Gwendal Collet, M. Drmota, Lukas Daniel Klausner

引用次数: 5

On a Problem of Danzer 论丹泽的一个问题

Combinatorics, Probability and Computing Pub Date : 2018-08-01 DOI: 10.1017/S0963548318000445

Nabil H. Mustafa, Saurabh Ray

{"title":"On a Problem of Danzer","authors":"Nabil H. Mustafa, Saurabh Ray","doi":"10.1017/S0963548318000445","DOIUrl":"https://doi.org/10.1017/S0963548318000445","url":null,"abstract":"Let C be a bounded convex object in ℝd, and let P be a set of n points lying outside C. Further, let cp, cq be two integers with 1 ⩽ cq ⩽ cp ⩽ n - ⌊d/2⌋, such that every cp + ⌊d/2⌋ points of P contain a subset of size cq + ⌊d/2⌋ whose convex hull is disjoint from C. Then our main theorem states the existence of a partition of P into a small number of subsets, each of whose convex hulls are disjoint from C. Our proof is constructive and implies that such a partition can be computed in polynomial time. In particular, our general theorem implies polynomial bounds for Hadwiger--Debrunner (p, q) numbers for balls in ℝd. For example, it follows from our theorem that when p > q = (1+β)⋅d/2 for β > 0, then any set of balls satisfying the (p, q)-property can be hit by O((1+β)2d2p1+1/β logp) points. This is the first improvement over a nearly 60 year-old exponential bound of roughly O(2d). Our results also complement the results obtained in a recent work of Keller, Smorodinsky and Tardos where, apart from improvements to the bound on HD(p, q) for convex sets in ℝd for various ranges of p and q, a polynomial bound is obtained for regions with low union complexity in the plane.","PeriodicalId":10503,"journal":{"name":"Combinatorics, Probability and Computing","volume":"13 1","pages":"473 - 482"},"PeriodicalIF":0.0,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81727788","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: 3

Monochromatic cycle partitions in random graphs 随机图中的单色循环划分

Combinatorics, Probability and Computing Pub Date : 2018-07-17 DOI: 10.1017/S0963548320000401

R. Lang, A. Lo

引用次数: 8

Counting higher order tangencies for plane curves 计算平面曲线的高阶切线

Combinatorics, Probability and Computing Pub Date : 2018-07-17 DOI: 10.1017/S096354831900035X

Joshua Zahl

引用次数: 1

Minimax functions on Galton–Watson trees 高尔顿-沃森树上的极大极小函数

Combinatorics, Probability and Computing Pub Date : 2018-06-20 DOI: 10.1017/S0963548319000403

James B. Martin, Roman Stasi'nski

{"title":"Minimax functions on Galton–Watson trees","authors":"James B. Martin, Roman Stasi'nski","doi":"10.1017/S0963548319000403","DOIUrl":"https://doi.org/10.1017/S0963548319000403","url":null,"abstract":"Abstract We consider the behaviour of minimax recursions defined on random trees. Such recursions give the value of a general class of two-player combinatorial games. We examine in particular the case where the tree is given by a Galton–Watson branching process, truncated at some depth 2n, and the terminal values of the level 2n nodes are drawn independently from some common distribution. The case of a regular tree was previously considered by Pearl, who showed that as n → ∞ the value of the game converges to a constant, and by Ali Khan, Devroye and Neininger, who obtained a distributional limit under a suitable rescaling. For a general offspring distribution, there is a surprisingly rich variety of behaviour: the (unrescaled) value of the game may converge to a constant, or to a discrete limit with several atoms, or to a continuous distribution. We also give distributional limits under suitable rescalings in various cases. We also address questions of endogeny. Suppose the game is played on a tree with many levels, so that the terminal values are far from the root. To be confident of playing a good first move, do we need to see the whole tree and its terminal values, or can we play close to optimally by inspecting just the first few levels of the tree? The answers again depend in an interesting way on the offspring distribution. We also mention several open questions.","PeriodicalId":10503,"journal":{"name":"Combinatorics, Probability and Computing","volume":"9 1","pages":"455 - 484"},"PeriodicalIF":0.0,"publicationDate":"2018-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87722386","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: 3

The Infinite limit of random permutations avoiding patterns of length three 避免长度为3的模式的随机排列的无限限制

Combinatorics, Probability and Computing Pub Date : 2018-06-20 DOI: 10.1017/S0963548319000270

R. Pinsky

引用次数: 5

Defective and clustered choosability of sparse graphs 稀疏图的缺陷性和聚类选择性

Combinatorics, Probability and Computing Pub Date : 2018-06-19 DOI: 10.1017/S0963548319000063

Kevin Hendrey, D. Wood

{"title":"Defective and clustered choosability of sparse graphs","authors":"Kevin Hendrey, D. Wood","doi":"10.1017/S0963548319000063","DOIUrl":"https://doi.org/10.1017/S0963548319000063","url":null,"abstract":"Abstract An (improper) graph colouring has defect d if each monochromatic subgraph has maximum degree at most d, and has clustering c if each monochromatic component has at most c vertices. This paper studies defective and clustered list-colourings for graphs with given maximum average degree. We prove that every graph with maximum average degree less than (2d+2)/(d+2)k is k-choosable with defect d. This improves upon a similar result by Havet and Sereni (J. Graph Theory, 2006). For clustered choosability of graphs with maximum average degree m, no (1-ɛ)m bound on the number of colours was previously known. The above result with d=1 solves this problem. It implies that every graph with maximum average degree m is $lfloor{frac{3}{4}m+1}rfloor$-choosable with clustering 2. This extends a result of Kopreski and Yu (Discrete Math., 2017) to the setting of choosability. We then prove two results about clustered choosability that explore the trade-off between the number of colours and the clustering. In particular, we prove that every graph with maximum average degree m is $lfloor{frac{7}{10}m+1}rfloor$-choosable with clustering 9, and is $lfloor{frac{2}{3}m+1}rfloor$-choosable with clustering O(m). As an example, the later result implies that every biplanar graph is 8-choosable with bounded clustering. This is the best known result for the clustered version of the earth–moon problem. The results extend to the setting where we only consider the maximum average degree of subgraphs with at least some number of vertices. Several applications are presented.","PeriodicalId":10503,"journal":{"name":"Combinatorics, Probability and Computing","volume":"113 1","pages":"791 - 810"},"PeriodicalIF":0.0,"publicationDate":"2018-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79459314","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: 11

On finite sets of small tripling or small alternation in arbitrary groups 关于任意群中的小三倍或小交替的有限集

Combinatorics, Probability and Computing Pub Date : 2018-06-15 DOI: 10.1017/S0963548320000176

G. Conant

引用次数: 7