如果图G有一个生成的欧拉子图,则称G是超欧拉图.用α′(G)表示G中最大独立的边的数目.本文证明了:若G是一个2-边连通简单图且α′(G)≤2,则G要么是可折叠图,要么存在G的某个连通子图H,使得对某个正整数t≥2,约化图G/H是K_(2.t.)推广了[L...如果图G有一个生成的欧拉子图,则称G是超欧拉图.用α′(G)表示G中最大独立的边的数目.本文证明了:若G是一个2-边连通简单图且α′(G)≤2,则G要么是可折叠图,要么存在G的某个连通子图H,使得对某个正整数t≥2,约化图G/H是K_(2.t.)推广了[Lai H J,Yan H.Supereulerian graphs and matchings.Appl.Math.Lett.,2011,24:1867-1869]中的一个主要结果.并且证明了上述文献中提出的一个猜想:3一边连通且α′(G)≤5的简单图是超欧拉图当且仅当它不可收缩成Petersen图.展开更多
Recently, topic models such as Latent Dirichlet Allocation(LDA) have been widely used in large-scale web mining. Many large-scale LDA training systems have been developed, which usually prefer a customized design from...Recently, topic models such as Latent Dirichlet Allocation(LDA) have been widely used in large-scale web mining. Many large-scale LDA training systems have been developed, which usually prefer a customized design from top to bottom with sophisticated synchronization support. We propose an LDA training system named ZenLDA, which follows a generalized design for the distributed data-parallel platform. The novelty of ZenLDA consists of three main aspects:(1) it converts the commonly used serial Collapsed Gibbs Sampling(CGS) inference algorithm to a Monte-Carlo Collapsed Bayesian(MCCB) estimation method, which is embarrassingly parallel;(2)it decomposes the LDA inference formula into parts that can be sampled more efficiently to reduce computation complexity;(3) it proposes a distributed LDA training framework, which represents the corpus as a directed graph with the parameters annotated as corresponding vertices and implements ZenLDA and other well-known inference methods based on Spark. Experimental results indicate that MCCB converges with accuracy similar to that of CGS, while running much faster. On top of MCCB, the ZenLDA formula decomposition achieved the fastest speed among other well-known inference methods. ZenLDA also showed good scalability when dealing with large-scale topic models on the data-parallel platform. Overall, ZenLDA could achieve comparable and even better computing performance with state-of-the-art dedicated systems.展开更多
文摘如果图G有一个生成的欧拉子图,则称G是超欧拉图.用α′(G)表示G中最大独立的边的数目.本文证明了:若G是一个2-边连通简单图且α′(G)≤2,则G要么是可折叠图,要么存在G的某个连通子图H,使得对某个正整数t≥2,约化图G/H是K_(2.t.)推广了[Lai H J,Yan H.Supereulerian graphs and matchings.Appl.Math.Lett.,2011,24:1867-1869]中的一个主要结果.并且证明了上述文献中提出的一个猜想:3一边连通且α′(G)≤5的简单图是超欧拉图当且仅当它不可收缩成Petersen图.
基金partially supported by the National Natural Science Foundation of China(No.61572250)the Science and Technology Program of Jiangsu Province(No.BE2017155)
文摘Recently, topic models such as Latent Dirichlet Allocation(LDA) have been widely used in large-scale web mining. Many large-scale LDA training systems have been developed, which usually prefer a customized design from top to bottom with sophisticated synchronization support. We propose an LDA training system named ZenLDA, which follows a generalized design for the distributed data-parallel platform. The novelty of ZenLDA consists of three main aspects:(1) it converts the commonly used serial Collapsed Gibbs Sampling(CGS) inference algorithm to a Monte-Carlo Collapsed Bayesian(MCCB) estimation method, which is embarrassingly parallel;(2)it decomposes the LDA inference formula into parts that can be sampled more efficiently to reduce computation complexity;(3) it proposes a distributed LDA training framework, which represents the corpus as a directed graph with the parameters annotated as corresponding vertices and implements ZenLDA and other well-known inference methods based on Spark. Experimental results indicate that MCCB converges with accuracy similar to that of CGS, while running much faster. On top of MCCB, the ZenLDA formula decomposition achieved the fastest speed among other well-known inference methods. ZenLDA also showed good scalability when dealing with large-scale topic models on the data-parallel platform. Overall, ZenLDA could achieve comparable and even better computing performance with state-of-the-art dedicated systems.
