On the Distributed Complexity of Large-Scale Graph Computations

Motivated by the increasing need to understand the distributed algorithmic foundations of large-scale graph computations, we study some fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$ machines jointly perform computations on graphs with $n$ nodes (typically, $n \gg k$). The input graph is assumed to be initially randomly partitioned among the $k$ machines, a common implementation in many real-world systems. Communication is point-to-point, and the goal is to minimize the number of communication {\em rounds} of the computation. Our main contribution is the {\em General Lower Bound Theorem}, a theorem that can be used to show non-trivial lower bounds on the round complexity of distributed large-scale data computations. The General Lower Bound Theorem is established via an information-theoretic approach that relates the round complexity to the minimal amount of information required by machines to solve the problem. Our approach is generic and this theorem can be used in a "cookbook" fashion to show distributed lower bounds in the context of several problems, including non-graph problems. We present two applications by showing (almost) tight lower bounds for the round complexity of two fundamental graph problems, namely {\em PageRank computation} and {\em triangle enumeration}. Our approach, as demonstrated in the case of PageRank, can yield tight lower bounds for problems (including, and especially, under a stochastic partition of the input) where communication complexity techniques are not obvious. Our approach, as demonstrated in the case of triangle enumeration, can yield stronger round lower bounds as well as message-round tradeoffs compared to approaches that use communication complexity techniques

Personalized Fuzzy Text Search Using Interest Prediction and Word Vectorization

In this paper we study the personalized text search problem. The keyword based search method in conventional algorithms has a low efficiency in understanding users' intention since the semantic meaning, user profile, user interests are not always considered. Firstly, we propose a novel text search algorithm using a inverse filtering mechanism that is very efficient for label based item search. Secondly, we adopt the Bayesian network to implement the user interest prediction for an improved personalized search. According to user input, it searches the related items using keyword information, predicted user interest. Thirdly, the word vectorization is used to discover potential targets according to the semantic meaning. Experimental results show that the proposed search engine has an improved efficiency and accuracy and it can operate on embedded devices with very limited computational resources

Practice of streaming processing of dynamic graphs: concepts, models, and systems

http://arxiv.org/abs/1912.12740Published versio