Workshop on Analytic Algorithmics and Combinatorics最新文献_第3页

The CLT Analogue for Cyclic Urns 循环瓮的CLT模拟物

Workshop on Analytic Algorithmics and Combinatorics Pub Date : 2015-07-29 DOI: 10.1137/1.9781611974324.11

Noëla Müller, Ralph Neininger

引用次数: 6

Prime Factorization of the Kirchhoff Polynomial: Compact Enumeration of Arborescences Kirchhoff多项式的质因数分解:树列的紧枚举

Workshop on Analytic Algorithmics and Combinatorics Pub Date : 2015-07-28 DOI: 10.1137/1.9781611974324.10

Matús Mihalák, P. Uznański, Pencho Yordanov

{"title":"Prime Factorization of the Kirchhoff Polynomial: Compact Enumeration of Arborescences","authors":"Matús Mihalák, P. Uznański, Pencho Yordanov","doi":"10.1137/1.9781611974324.10","DOIUrl":"https://doi.org/10.1137/1.9781611974324.10","url":null,"abstract":"We study the problem of enumerating all rooted directed spanning trees (arborescences) of a directed graph (digraph) $G=(V,E)$ of $n$ vertices. An arborescence $A$ consisting of edges $e_1,ldots,e_{n-1}$ can be represented as a monomial $e_1cdot e_2 cdots e_{n-1}$ in variables $e in E$. All arborescences $mathsf{arb}(G)$ of a digraph then define the Kirchhoff polynomial $sum_{A in mathsf{arb}(G)} prod_{ein A} e$. We show how to compute a compact representation of the Kirchhoff polynomial -- its prime factorization, and how it relates to combinatorial properties of digraphs such as strong connectivity and vertex domination. In particular, we provide digraph decomposition rules that correspond to factorization steps of the polynomial, and also give necessary and sufficient primality conditions of the resulting factors expressed by connectivity properties of the corresponding decomposed components. Thereby, we obtain a linear time algorithm for decomposing a digraph into components corresponding to factors of the initial polynomial, and a guarantee that no finer factorization is possible. The decomposition serves as a starting point for a recursive deletion-contraction algorithm, and also as a preprocessing phase for iterative enumeration algorithms. Both approaches produce a compressed output and retain some structural properties in the resulting polynomial. This proves advantageous in practical applications such as calculating steady states on digraphs governed by Laplacian dynamics, or computing the greatest common divisor of Kirchhoff polynomials. Finally, we initiate the study of a class of digraphs which allow for a practical enumeration of arborescences. Using our decomposition rules we observe that various digraphs from real-world applications fall into this class or are structurally similar to it.","PeriodicalId":340112,"journal":{"name":"Workshop on Analytic Algorithmics and Combinatorics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129937439","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: 8

Graphs with degree constraints 带度约束的图

Workshop on Analytic Algorithmics and Combinatorics Pub Date : 2015-06-09 DOI: 10.1137/1.9781611974324.4

Élie de Panafieu, Lander Ramos

引用次数: 10

On Distributed Cardinality Estimation: Random Arcs Recycled 关于分布式基数估计:随机弧循环

Workshop on Analytic Algorithmics and Combinatorics Pub Date : 2015-01-04 DOI: 10.1137/1.9781611973761.12

Marcin Kardas, Mirosław Kutyłowski, Jakub Lemiesz

引用次数: 2

Cuts in Increasing Trees 砍伐增加的树木

Workshop on Analytic Algorithmics and Combinatorics Pub Date : 2015-01-04 DOI: 10.1137/1.9781611973761.6

O. Bodini, Antoine Genitrini

引用次数: 4

Repeated fringe subtrees in random rooted trees 随机根树中的重复条纹子树

Workshop on Analytic Algorithmics and Combinatorics Pub Date : 2015-01-04 DOI: 10.1137/1.9781611973761.7

D. Ralaivaosaona, S. Wagner

引用次数: 8

Linear-time generation of inhomogeneous random directed walks 非齐次随机有向行走的线性时间生成

Workshop on Analytic Algorithmics and Combinatorics Pub Date : 2015-01-04 DOI: 10.1137/1.9781611973761.5

Frédérique Bassino, A. Sportiello

{"title":"Linear-time generation of inhomogeneous random directed walks","authors":"Frédérique Bassino, A. Sportiello","doi":"10.1137/1.9781611973761.5","DOIUrl":"https://doi.org/10.1137/1.9781611973761.5","url":null,"abstract":"Directed random walks in dimension two describe the diffusion dynamics of particles in a line. Through a well-known bijection, excursions, i.e. walks in the half-plane, describe families of \"simply-generated\" Galton--Watson trees. These random objects can be generated in linear time, through an algorithm due to Devroye, and crucially based on the fact that the steps of the walk form an exchangeable sequence of random variables. \u0000 \u0000We consider here the random generation of a more general family of structures, in which the transition rates, instead of being fixed once and for all, evolve in time (but not in space). Thus, the steps are not exchangeable anymore. \u0000 \u0000On one side, this generalises diffusion into time-dependent diffusion. On the other side, among other things, this allows to consider effects of excluded volume, for Galton--Watson trees arising from exploration processes on finite random graphs, both directed and undirected. In the directed version, a special case concerns partitions of N objects into M blocks (counted by Stirling numbers of the second kind), and rooted K-maps which are accessible from the root, which in turn are related to the uniform generation of random accessible deterministic complete automata. \u0000 \u0000We present an algorithm, based on the block-decomposition of the problem, and a crucial procedure consisting of a generalised Devroye algorithm, for transition rates which are well-approximated by piecewise exponential functions. The achieved (bit-)complexity remains linear.","PeriodicalId":340112,"journal":{"name":"Workshop on Analytic Algorithmics and Combinatorics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131080579","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

Variance of Size in Regular Graph Tries 正则图尝试的大小方差

Workshop on Analytic Algorithmics and Combinatorics Pub Date : 2015-01-04 DOI: 10.1137/1.9781611973761.9

P. Jacquet, A. Magner

引用次数: 2

A Bound for the Diameter of Random Hyperbolic Graphs 随机双曲图直径的一个界

Workshop on Analytic Algorithmics and Combinatorics Pub Date : 2014-08-13 DOI: 10.1137/1.9781611973761.3

Marcos A. Kiwi, D. Mitsche

{"title":"A Bound for the Diameter of Random Hyperbolic Graphs","authors":"Marcos A. Kiwi, D. Mitsche","doi":"10.1137/1.9781611973761.3","DOIUrl":"https://doi.org/10.1137/1.9781611973761.3","url":null,"abstract":"Random hyperbolic graphs were recently introduced by Krioukov et. al. [KPKVB10] as a model for large networks. Gugelmann, Panagiotou, and Peter [GPP12] then initiated the rigorous study of random hyperbolic graphs using the following model: for $alpha> tfrac{1}{2}$, $Cinmathbb{R}$, $ninmathbb{N}$, set $R=2ln n+C$ and build the graph $G=(V,E)$ with $|V|=n$ as follows: For each $vin V$, generate i.i.d. polar coordinates $(r_{v},theta_{v})$ using the joint density function $f(r,theta)$, with $theta_{v}$ chosen uniformly from $[0,2pi)$ and $r_{v}$ with density $f(r)=frac{alphasinh(alpha r)}{cosh(alpha R)-1}$ for $0leq r< R$. Then, join two vertices by an edge, if their hyperbolic distance is at most $R$. We prove that in the range $tfrac{1}{2} < alpha < 1$ a.a.s. for any two vertices of the same component, their graph distance is $O(log^{C_0+1+o(1)}n)$, where $C_0=2/(tfrac{1}{2}-frac{3}{4}alpha+tfrac{alpha^2}{4})$, thus answering a question raised in [GPP12] concerning the diameter of such random graphs. As a corollary from our proof we obtain that the second largest component has size $O(log^{2C_0+1+o(1)}n)$, thus answering a question of Bode, Fountoulakis and M\"{u}ller [BFM13]. We also show that a.a.s. there exist isolated components forming a path of length $Omega(log n)$, thus yielding a lower bound on the size of the second largest component.","PeriodicalId":340112,"journal":{"name":"Workshop on Analytic Algorithmics and Combinatorics","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127971031","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: 39

On the Algorithmic Lovász Local Lemma and Acyclic Edge Coloring 关于算法Lovász局部引理与无环边着色

Workshop on Analytic Algorithmics and Combinatorics Pub Date : 2014-07-21 DOI: 10.1137/1.9781611973761.2

Ioannis Giotis, L. Kirousis, Kostas I. Psaromiligkos, D. Thilikos

引用次数: 29