首页 > 最新文献

Workshop on Analytic Algorithmics and Combinatorics最新文献

英文 中文
Fast Algorithm for Optimal Compression of Graphs 图的快速优化压缩算法
Pub Date : 2010-01-16 DOI: 10.1137/1.9781611973006.5
Yongwook Choi
We consider the problem of finding optimal description for general unlabeled graphs. Given a probability distribution on labeled graphs, we introduced in [4] a structural entropy as a lower bound for the lossless compression of such graphs. Specifically, we proved that the structural entropy for the Erdos--Renyi random graph, in which edges are added with probability p, is (n2)h(p) − n log n + O(n), where n is the number of vertices and h(p) = −p log p − (1 − p) log(1−p) is the entropy rate of a conventional memoryless binary source. In this paper, we prove the asymptotic equipartition property for such graphs. Then, we propose a faster compression algorithm that asymptotically achieves the structural entropy up to the first two leading terms with high probability. Our algorithm runs in O(n + e) time on average where e is the number of edges. To prove its asymptotic optimality, we introduce binary trees that one can classify as in-between tries and digital search trees. We use analytic techniques such as generating functions, Mellin transform, and poissonization to establish our findings. Our experimental results confirm theoretical results and show the usefulness of our algorithm for real-world graphs such as the Internet, biological networks, and social networks.
研究一般无标记图的最优描述问题。给定标记图上的概率分布,我们在[4]中引入了结构熵作为对此类图进行无损压缩的下界。具体来说,我们证明了Erdos- Renyi随机图的结构熵为(n2)h(p)−n log n + O(n),其中n为顶点数,h(p) =−p log p−(1−p) log(1−p)是传统无记忆二进制源的熵率。本文证明了这类图的渐近均分性质。然后,我们提出了一种更快的压缩算法,该算法可以高概率地渐近达到前两项的结构熵。我们的算法平均运行时间为O(n + e)这里e是边的个数。为了证明其渐近最优性,我们引入了二叉树,可以将其分类为中间尝试和数字搜索树。我们使用生成函数、Mellin变换和泊松化等分析技术来建立我们的发现。我们的实验结果证实了理论结果,并显示了我们的算法对现实世界的图形(如互联网、生物网络和社交网络)的有用性。
{"title":"Fast Algorithm for Optimal Compression of Graphs","authors":"Yongwook Choi","doi":"10.1137/1.9781611973006.5","DOIUrl":"https://doi.org/10.1137/1.9781611973006.5","url":null,"abstract":"We consider the problem of finding optimal description for general unlabeled graphs. Given a probability distribution on labeled graphs, we introduced in [4] a structural entropy as a lower bound for the lossless compression of such graphs. Specifically, we proved that the structural entropy for the Erdos--Renyi random graph, in which edges are added with probability p, is (n2)h(p) − n log n + O(n), where n is the number of vertices and h(p) = −p log p − (1 − p) log(1−p) is the entropy rate of a conventional memoryless binary source. In this paper, we prove the asymptotic equipartition property for such graphs. Then, we propose a faster compression algorithm that asymptotically achieves the structural entropy up to the first two leading terms with high probability. Our algorithm runs in O(n + e) time on average where e is the number of edges. To prove its asymptotic optimality, we introduce binary trees that one can classify as in-between tries and digital search trees. We use analytic techniques such as generating functions, Mellin transform, and poissonization to establish our findings. Our experimental results confirm theoretical results and show the usefulness of our algorithm for real-world graphs such as the Internet, biological networks, and social networks.","PeriodicalId":340112,"journal":{"name":"Workshop on Analytic Algorithmics and Combinatorics","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115323959","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
On Two Distributions of Subgroups of Free Groups 关于自由群的两个子群的分布
Pub Date : 2010-01-16 DOI: 10.1137/1.9781611973006.11
Frédérique Bassino, A. Martino, C. Nicaud, E. Ventura, P. Weil
We study and compare two natural distributions of finitely generated subgroups of free groups. One is based on the random generation of tuples of reduced words; that is the one classically used by group theorists. The other relies on Stallings' graphical representation of subgroups and in spite of its naturality, it was only recently considered. The combinatorial structures underlying both distributions are studied in this paper with methods of analytic combinatorics. We use these methods to point out the differences between these distributions. It is particularly interesting that certain important properties of subgroups that are generic in one distribution, turn out to be negligible in the other.
我们研究并比较了自由群的有限生成子群的两个自然分布。一种是基于约简词元组的随机生成;这是群论学家经常使用的。另一种依赖于斯托林斯对子群体的图形表示,尽管它很自然,但直到最近才被考虑。本文用解析组合学的方法研究了这两种分布的组合结构。我们使用这些方法来指出这些分布之间的差异。特别有趣的是,子群的某些重要性质在一个分布中是一般的,在另一个分布中却可以忽略不计。
{"title":"On Two Distributions of Subgroups of Free Groups","authors":"Frédérique Bassino, A. Martino, C. Nicaud, E. Ventura, P. Weil","doi":"10.1137/1.9781611973006.11","DOIUrl":"https://doi.org/10.1137/1.9781611973006.11","url":null,"abstract":"We study and compare two natural distributions of finitely generated subgroups of free groups. One is based on the random generation of tuples of reduced words; that is the one classically used by group theorists. The other relies on Stallings' graphical representation of subgroups and in spite of its naturality, it was only recently considered. The combinatorial structures underlying both distributions are studied in this paper with methods of analytic combinatorics. We use these methods to point out the differences between these distributions. It is particularly interesting that certain important properties of subgroups that are generic in one distribution, turn out to be negligible in the other.","PeriodicalId":340112,"journal":{"name":"Workshop on Analytic Algorithmics and Combinatorics","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116645778","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
The Subset Partial Order: Computing and Combinatorics 子集偏序:计算与组合
Pub Date : 2010-01-16 DOI: 10.1137/1.9781611973006.4
Amr Elmasry
Given a family F of k sets with cardinalities s1, s2, . . ., sk and N = [EQUATION], we show that the size of the partial order graph induced by the subset relation (called the subset graph) is [EQUATION], where B = log (N/ log2 N). This implies a simpler proof to the O(N2/ log2 N) bound concluded in [2]. We also give an algorithm that computes the subset graph for any family of sets F. Our algorithm requires O(nk2/ log k) time and space on a pointer machine, where n is the number of domain elements. When F is dense, i.e. N = Θ(nk), the algorithm requires O(N2/ log2 N) time and space. We give a construction for a dense family whose subset graph is of size Θ(N2/ log2 N), indicating the optimality of our algorithm for dense families. The subset graph can be dynamically maintained when F undergoes set insertion and deletion in O(nk/ log k) time per update (that is sub-linear in N for the case of dense families). If we assume words of b ≤ k bits, allow bits to be packed in words, and use bitwise operations, the above running time and space requirements can be reduced by a factor of b log (k/b + 1)/ log k and b2 log (k/b + 1)/ log k respectively.
给定一个集族F (k),其基数为s1, s2,…,sk, N = [EQUATION],我们证明了由子集关系(称为子集图)引起的偏序图的大小为[EQUATION],其中B = log (N/ log2n)。这意味着对[2]中得出的O(N2/ log2n)界的一个更简单的证明。我们还给出了一种计算任意集合f的子集图的算法。我们的算法在指针机上需要O(nk2/ log k)的时间和空间,其中n是域元素的数量。当F密度较大,即N = Θ(nk)时,算法需要O(N2/ log2n)的时间和空间。我们给出了一个密集族的子集图的大小为Θ(N2/ log2n)的构造,表明了我们的算法对于密集族的最优性。当F在每次更新的O(nk/ log k)时间内进行集的插入和删除时,可以动态维护子集图(对于密集族,这在N中是次线性的)。如果我们假设b个字≤k位,允许以字的形式封装位,并使用按位运算,则上述运行时间和空间需求可以分别减少b log (k/b + 1)/ log k和b2 log (k/b + 1)/ log k。
{"title":"The Subset Partial Order: Computing and Combinatorics","authors":"Amr Elmasry","doi":"10.1137/1.9781611973006.4","DOIUrl":"https://doi.org/10.1137/1.9781611973006.4","url":null,"abstract":"Given a family F of k sets with cardinalities s1, s2, . . ., sk and N = [EQUATION], we show that the size of the partial order graph induced by the subset relation (called the subset graph) is [EQUATION], where B = log (N/ log2 N). This implies a simpler proof to the O(N2/ log2 N) bound concluded in [2]. \u0000 \u0000We also give an algorithm that computes the subset graph for any family of sets F. Our algorithm requires O(nk2/ log k) time and space on a pointer machine, where n is the number of domain elements. When F is dense, i.e. N = Θ(nk), the algorithm requires O(N2/ log2 N) time and space. We give a construction for a dense family whose subset graph is of size Θ(N2/ log2 N), indicating the optimality of our algorithm for dense families. The subset graph can be dynamically maintained when F undergoes set insertion and deletion in O(nk/ log k) time per update (that is sub-linear in N for the case of dense families). If we assume words of b ≤ k bits, allow bits to be packed in words, and use bitwise operations, the above running time and space requirements can be reduced by a factor of b log (k/b + 1)/ log k and b2 log (k/b + 1)/ log k respectively.","PeriodicalId":340112,"journal":{"name":"Workshop on Analytic Algorithmics and Combinatorics","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125961289","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: 5
Preference-constrained Oriented Matching 偏好约束的定向匹配
Pub Date : 2010-01-16 DOI: 10.1137/1.9781611973006.9
L. Fleischer, Zoya Svitkina
We introduce and study a combinatorial problem called preference-constrained oriented matching. This problem is defined on a directed graph in which each node has preferences over its out-neighbors, and the goal is to find a maximum-size matching on this graph that satisfies a certain preference constraint. One of our main results is a structural theorem showing that if the given graph is complete, then for any preference ordering there always exists a feasible matching that covers a constant fraction of the nodes. This result allows us to correct an error in a proof by Azar, Jain, and Mirrokni [1], establishing a lower bound on the price of anarchy in coordination mechanisms for scheduling. We also show that the preference-constrained oriented matching problem is APX-hard and give a constant-factor approximation algorithm for it.
我们引入并研究了一个组合问题——偏好约束导向匹配。这个问题是在一个有向图上定义的,其中每个节点对其外部邻居都有偏好,目标是在这个图上找到满足某个偏好约束的最大尺寸匹配。我们的主要结果之一是一个结构定理,表明如果给定的图是完全的,那么对于任何偏好排序,总是存在一个覆盖恒定部分节点的可行匹配。这个结果允许我们纠正Azar, Jain和mirrorkni[1]证明中的一个错误,建立了调度协调机制中无政府状态代价的下界。我们还证明了偏好约束的定向匹配问题是apx困难的,并给出了该问题的常因子逼近算法。
{"title":"Preference-constrained Oriented Matching","authors":"L. Fleischer, Zoya Svitkina","doi":"10.1137/1.9781611973006.9","DOIUrl":"https://doi.org/10.1137/1.9781611973006.9","url":null,"abstract":"We introduce and study a combinatorial problem called preference-constrained oriented matching. This problem is defined on a directed graph in which each node has preferences over its out-neighbors, and the goal is to find a maximum-size matching on this graph that satisfies a certain preference constraint. One of our main results is a structural theorem showing that if the given graph is complete, then for any preference ordering there always exists a feasible matching that covers a constant fraction of the nodes. This result allows us to correct an error in a proof by Azar, Jain, and Mirrokni [1], establishing a lower bound on the price of anarchy in coordination mechanisms for scheduling. We also show that the preference-constrained oriented matching problem is APX-hard and give a constant-factor approximation algorithm for it.","PeriodicalId":340112,"journal":{"name":"Workshop on Analytic Algorithmics and Combinatorics","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126466924","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: 14
Bivariate Asymptotics for Striped Plane Partitions 条纹平面分区的双变量渐近性
Pub Date : 2010-01-16 DOI: 10.1137/1.9781611973006.3
D. Panario, L. Richmond, Benjamin Young
We give a new asymptotic formula for a refined enumeration of plane partitions. Specifically: color the parts πi,j of a plane partition π according to the equivalence class of i --- j (mod 2), and keep track of the sums of the 0-colored and 1-colored parts seperately. We find, for large plane partitions, that the difference between these two sums is asymptotically Gaussian (and we compute the mean and standard deviation of the distribution). Our approach is to modify a multivariate technique of Haselgrove and Temperley.
给出了平面分区的精细化枚举的一个新的渐近公式。具体来说:根据i—j (mod 2)的等价类,给平面分区π的π、j部分上色,并分别记录0色部分和1色部分的和。我们发现,对于大的平面分区,这两个和之间的差是渐近的高斯分布(我们计算分布的均值和标准差)。我们的方法是修改Haselgrove和Temperley的多元技术。
{"title":"Bivariate Asymptotics for Striped Plane Partitions","authors":"D. Panario, L. Richmond, Benjamin Young","doi":"10.1137/1.9781611973006.3","DOIUrl":"https://doi.org/10.1137/1.9781611973006.3","url":null,"abstract":"We give a new asymptotic formula for a refined enumeration of plane partitions. Specifically: color the parts πi,j of a plane partition π according to the equivalence class of i --- j (mod 2), and keep track of the sums of the 0-colored and 1-colored parts seperately. We find, for large plane partitions, that the difference between these two sums is asymptotically Gaussian (and we compute the mean and standard deviation of the distribution). Our approach is to modify a multivariate technique of Haselgrove and Temperley.","PeriodicalId":340112,"journal":{"name":"Workshop on Analytic Algorithmics and Combinatorics","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131530298","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
Newton Iteration: From Numerics to Combinatorics, and Back 牛顿迭代:从数值学到组合学再回来
Pub Date : 2010-01-16 DOI: 10.1137/1.9781611973006.6
B. Salvy
The talk will explore a variety of old and recent algorithms whose efficiency boils down to the fast convergence of Newton iteration. Numerically, and close to the root, the number of correct digits is doubled at each iteration. When working with power series, the problem of picking a good initial point disappears and the number of coefficients is doubled at each iteration. This observation, coupled with fast multiplication, leads to fast algorithms in a variety of problems of symbolic computation, ranging from classical results on algebraic series to more recent ones on systems of differential equations.
讲座将探讨各种新旧算法,其效率归结为牛顿迭代的快速收敛。在数值上,在接近根的地方,每次迭代正确数字的数量翻倍。当处理幂级数时,选择一个好的初始点的问题消失了,每次迭代系数的数量增加了一倍。这种观察,加上快速乘法,导致了各种符号计算问题的快速算法,从代数级数的经典结果到最近的微分方程系统的结果。
{"title":"Newton Iteration: From Numerics to Combinatorics, and Back","authors":"B. Salvy","doi":"10.1137/1.9781611973006.6","DOIUrl":"https://doi.org/10.1137/1.9781611973006.6","url":null,"abstract":"The talk will explore a variety of old and recent algorithms whose efficiency boils down to the fast convergence of Newton iteration. Numerically, and close to the root, the number of correct digits is doubled at each iteration. When working with power series, the problem of picking a good initial point disappears and the number of coefficients is doubled at each iteration. This observation, coupled with fast multiplication, leads to fast algorithms in a variety of problems of symbolic computation, ranging from classical results on algebraic series to more recent ones on systems of differential equations.","PeriodicalId":340112,"journal":{"name":"Workshop on Analytic Algorithmics and Combinatorics","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120906148","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
On the Search Path Length of Random Binary Skip Graphs 关于随机二叉跳图的搜索路径长度
Pub Date : 2010-01-16 DOI: 10.1137/1.9781611973006.1
Philippe Duchon, H. Larchevêque
In this paper we consider the skip graph data structure, a load balancing alternative to skip lists, designed to perform better in a distributed environment. We extend previous results of Devroye on skip lists, and prove that the maximum length of a search path in a random binary skip graph of size n is of order log n with high probability.
在本文中,我们考虑跳跃图数据结构,一种负载平衡替代跳跃表,旨在更好地在分布式环境中执行。我们扩展了Devroye先前关于跳跃表的结果,证明了一个大小为n的随机二元跳跃图中搜索路径的最大长度有高概率是log n阶的。
{"title":"On the Search Path Length of Random Binary Skip Graphs","authors":"Philippe Duchon, H. Larchevêque","doi":"10.1137/1.9781611973006.1","DOIUrl":"https://doi.org/10.1137/1.9781611973006.1","url":null,"abstract":"In this paper we consider the skip graph data structure, a load balancing alternative to skip lists, designed to perform better in a distributed environment. We extend previous results of Devroye on skip lists, and prove that the maximum length of a search path in a random binary skip graph of size n is of order log n with high probability.","PeriodicalId":340112,"journal":{"name":"Workshop on Analytic Algorithmics and Combinatorics","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127183620","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
The Connectivity-Profile of Random Increasing k-trees 随机递增k树的连通性
Pub Date : 2009-10-19 DOI: 10.1137/1.9781611973006.13
Alexis Darrasse, Hsien-Kuei Hwang, O. Bodini, Michèle Soria
Random increasing k-trees represent an interesting, useful class of strongly dependent graphs for which analytic-combinatorial tools can be successfully applied. We study in this paper a notion called connectivity-profile and derive asymptotic estimates for it; some interesting consequences will also be given.
随机增加的k树代表了一类有趣的、有用的强相关图,分析组合工具可以成功地应用于这些图。本文研究了一种称为连通性剖面的概念,并给出了它的渐近估计;还将给出一些有趣的结果。
{"title":"The Connectivity-Profile of Random Increasing k-trees","authors":"Alexis Darrasse, Hsien-Kuei Hwang, O. Bodini, Michèle Soria","doi":"10.1137/1.9781611973006.13","DOIUrl":"https://doi.org/10.1137/1.9781611973006.13","url":null,"abstract":"Random increasing k-trees represent an interesting, useful class of strongly dependent graphs for which analytic-combinatorial tools can be successfully applied. We study in this paper a notion called connectivity-profile and derive asymptotic estimates for it; some interesting consequences will also be given.","PeriodicalId":340112,"journal":{"name":"Workshop on Analytic Algorithmics and Combinatorics","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125379689","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: 10
Prediction of Unseen Proportions in Urn Models with Restricted Sampling 限制抽样下瓮模型中未见比例的预测
Pub Date : 2009-01-03 DOI: 10.1137/1.9781611972993.12
M. Lladser
Imagine an urn with colored balls but with an unknown composition i.e. you do not know what are the specific colors in the urn nor their relative proportions. The urn could be composed by infinitely many colors and to learn about its composition you have been sampling balls with replacement from it. In this extended abstract we will construct exact confidence intervals for the proportion in the urn of the so far unobserved colors when there is an upper-bound m for the additional number of samples permitted from the urn. The research is motivated by a variety of situations of practical interest. For instance, the different colors in the urn could represent different solutions to a particular binding site problem in a random RNA pool, or the number of different species of bacteria present in a sample of soil or the gut of a person with a digestive disorder.
想象一个有彩色球的骨灰盒,但成分未知,即你不知道骨灰盒中的具体颜色是什么,也不知道它们的相对比例。这个瓮可以由无限多种颜色组成,为了了解它的成分,你一直在用它的替代品取样球。在这个扩展摘要中,当瓮中允许的额外样本数量有上界m时,我们将为瓮中迄今未观察到的颜色的比例构造精确的置信区间。研究的动机是各种实际兴趣的情况。例如,瓮中的不同颜色可以代表随机RNA池中特定结合位点问题的不同解决方案,或者土壤样本中存在的不同种类细菌的数量,或者患有消化系统疾病的人的肠道。
{"title":"Prediction of Unseen Proportions in Urn Models with Restricted Sampling","authors":"M. Lladser","doi":"10.1137/1.9781611972993.12","DOIUrl":"https://doi.org/10.1137/1.9781611972993.12","url":null,"abstract":"Imagine an urn with colored balls but with an unknown composition i.e. you do not know what are the specific colors in the urn nor their relative proportions. The urn could be composed by infinitely many colors and to learn about its composition you have been sampling balls with replacement from it. In this extended abstract we will construct exact confidence intervals for the proportion in the urn of the so far unobserved colors when there is an upper-bound m for the additional number of samples permitted from the urn. The research is motivated by a variety of situations of practical interest. For instance, the different colors in the urn could represent different solutions to a particular binding site problem in a random RNA pool, or the number of different species of bacteria present in a sample of soil or the gut of a person with a digestive disorder.","PeriodicalId":340112,"journal":{"name":"Workshop on Analytic Algorithmics and Combinatorics","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117228596","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: 5
Average Size of Unstretched Remote-Spanners 未拉伸遥控扳手的平均尺寸
Pub Date : 2009-01-03 DOI: 10.1137/1.9781611972993.4
P. Jacquet, L. Viennot
Motivated by the optimization of link state routing in ad hoc networks, and the concept of multipoint relays, we introduce the notion of remote-spanner. Given an unweighted graph G, a remote spanner is a set of links H such that for any pair of nodes (u, v) there exists a shortest path in G for which all links in the path that are not adjacent to u belong to H. The remote spanner is a kind of minimal topology information beyond its neighborhood that any node would need in order to compute its shortest paths in a distributed way. This can be extended to k-connected graphs by considering minimum length sum over k disjoint paths as distance. In this paper, we give distributed algorithms for computing remote-spanners in order to obtain sparse remote-spanners with various properties. We provide a polynomial distributed algorithm that computes a k-connecting unstretched remote-spanner whose number of edges is at a factor 2(1 + log Δ) from optimal where Δ is the maximum degree of a node. Interestingly, its expected compression ratio in number of edges is O(k/n log n) in Erdos-Renyi graph model and O((k/n)2/3) in the unit disk graph model with a uniform Poisson distribution of nodes.
基于ad hoc网络中链路状态路由的优化和多点中继的概念,我们引入了远程扳手的概念。给定一个未加权图G,远程扳手是一组链路H,使得对于任意一对节点(u, v),在G中存在一条最短路径,该路径中所有不与u相邻的链路都属于H。远程扳手是一种超越其邻域的最小拓扑信息,任何节点为了以分布式方式计算其最短路径都需要这种信息。这可以通过考虑k个不相交路径的最小长度和作为距离来扩展到k连通图。为了得到具有不同性质的稀疏远程扳手,本文给出了计算远程扳手的分布式算法。我们提供了一个多项式分布式算法,该算法计算一个k连接的未拉伸远程扳手,其边数是最优的2倍(1 + log Δ),其中Δ是节点的最大度。有趣的是,其期望边数压缩比在Erdos-Renyi图模型中为O(k/n log n),在节点均匀泊松分布的单元磁盘图模型中为O((k/n)2/3)。
{"title":"Average Size of Unstretched Remote-Spanners","authors":"P. Jacquet, L. Viennot","doi":"10.1137/1.9781611972993.4","DOIUrl":"https://doi.org/10.1137/1.9781611972993.4","url":null,"abstract":"Motivated by the optimization of link state routing in ad hoc networks, and the concept of multipoint relays, we introduce the notion of remote-spanner. Given an unweighted graph G, a remote spanner is a set of links H such that for any pair of nodes (u, v) there exists a shortest path in G for which all links in the path that are not adjacent to u belong to H. The remote spanner is a kind of minimal topology information beyond its neighborhood that any node would need in order to compute its shortest paths in a distributed way. This can be extended to k-connected graphs by considering minimum length sum over k disjoint paths as distance. \u0000 \u0000In this paper, we give distributed algorithms for computing remote-spanners in order to obtain sparse remote-spanners with various properties. We provide a polynomial distributed algorithm that computes a k-connecting unstretched remote-spanner whose number of edges is at a factor 2(1 + log Δ) from optimal where Δ is the maximum degree of a node. Interestingly, its expected compression ratio in number of edges is O(k/n log n) in Erdos-Renyi graph model and O((k/n)2/3) in the unit disk graph model with a uniform Poisson distribution of nodes.","PeriodicalId":340112,"journal":{"name":"Workshop on Analytic Algorithmics and Combinatorics","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115379435","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
期刊
Workshop on Analytic Algorithmics and Combinatorics
全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1