TPA: Fast, Scalable, and Accurate Method for Approximate Random Walk with Restart on Billion Scale Graphs

Given a large graph, how can we determine similarity between nodes in a fast and accurate way? Random walk with restart (RWR) is a popular measure for this purpose and has been exploited in numerous data mining applications including ranking, anomaly detection, link prediction, and community detection. However, previous methods for computing exact RWR require prohibitive storage sizes and computational costs, and alternative methods which avoid such costs by computing approximate RWR have limited accuracy. In this paper, we propose TPA, a fast, scalable, and highly accurate method for computing approximate RWR on large graphs. TPA exploits two important properties in RWR: 1) nodes close to a seed node are likely to be revisited in following steps due to block-wise structure of many real-world graphs, and 2) RWR scores of nodes which reside far from the seed node are proportional to their PageRank scores. Based on these two properties, TPA divides approximate RWR problem into two subproblems called neighbor approximation and stranger approximation. In the neighbor approximation, TPA estimates RWR scores of nodes close to the seed based on scores of few early steps from the seed. In the stranger approximation, TPA estimates RWR scores for nodes far from the seed using their PageRank. The stranger and neighbor approximations are conducted in the preprocessing phase and the online phase, respectively. Through extensive experiments, we show that TPA requires up to 3.5x less time with up to 40x less memory space than other state-of-the-art methods for the preprocessing phase. In the online phase, TPA computes approximate RWR up to 30x faster than existing methods while maintaining high accuracy.Comment: 12pages, 10 figure

RoundTripRank: Graph-based Proximity with Importance and Specificity

Advanced Digital Sciences Center of the University of Illinois at Urbana-Champaign, Agency for Science, Technology and Research of Singapor

Methods to Improve Applicability and Efficiency of Distributed Data-Centric Compute Frameworks

The success of modern applications depends on the insights they collect from their data repositories. Data repositories for such applications currently exceed exabytes and are rapidly increasing in size, as they collect data from varied sources - web applications, mobile phones, sensors and other connected devices. Distributed storage and data-centric compute frameworks have been invented to store and analyze these large datasets. This dissertation focuses on extending the applicability and improving the efficiency of distributed data-centric compute frameworks

Graph Processing on GPU

Ph.DDOCTOR OF PHILOSOPH

큰 그래프 상에서의 개인화된 페이지 랭크에 대한 빠른 계산 기법

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 전기·컴퓨터공학부, 2020. 8. 이상구.Computation of Personalized PageRank (PPR) in graphs is an important function that is widely utilized in myriad application domains such as search, recommendation, and knowledge discovery. Because the computation of PPR is an expensive process, a good number of innovative and efficient algorithms for computing PPR have been developed. However, efficient computation of PPR within very large graphs with over millions of nodes is still an open problem. Moreover, previously proposed algorithms cannot handle updates efficiently, thus, severely limiting their capability of handling dynamic graphs. In this paper, we present a fast converging algorithm that guarantees high and controlled precision. We improve the convergence rate of traditional Power Iteration method by adopting successive over-relaxation, and initial guess revision, a vector reuse strategy. The proposed method vastly improves on the traditional Power Iteration in terms of convergence rate and computation time, while retaining its simplicity and strictness. Since it can reuse the previously computed vectors for refreshing PPR vectors, its update performance is also greatly enhanced. Also, since the algorithm halts as soon as it reaches a given error threshold, we can flexibly control the trade-off between accuracy and time, a feature lacking in both sampling-based approximation methods and fully exact methods. Experiments show that the proposed algorithm is at least 20 times faster than the Power Iteration and outperforms other state-of-the-art algorithms.그래프 내에서 개인화된 페이지랭크 (P ersonalized P age R ank, PPR 를 계산하는 것은 검색 , 추천 , 지식발견 등 여러 분야에서 광범위하게 활용되는 중요한 작업 이다 . 개인화된 페이지랭크를 계산하는 것은 고비용의 과정이 필요하므로 , 개인화된 페이지랭크를 계산하는 효율적이고 혁신적인 방법들이 다수 개발되어왔다 . 그러나 수백만 이상의 노드를 가진 대용량 그래프에 대한 효율적인 계산은 여전히 해결되지 않은 문제이다 . 그에 더하여 , 기존 제시된 알고리듬들은 그래프 갱신을 효율적으로 다루지 못하여 동적으로 변화하는 그래프를 다루는 데에 한계점이 크다 . 본 연구에서는 높은 정밀도를 보장하고 정밀도를 통제 가능한 , 빠르게 수렴하는 개인화된 페이지랭크 계산 알고리듬을 제시한다 . 전통적인 거듭제곱법 (Power 에 축차가속완화법 (Successive Over Relaxation) 과 초기 추측 값 보정법 (Initial Guess 을 활용한 벡터 재사용 전략을 적용하여 수렴 속도를 개선하였다 . 제시된 방법은 기존 거듭제곱법의 장점인 단순성과 엄밀성을 유지 하면서 도 수렴율과 계산속도를 크게 개선 한다 . 또한 개인화된 페이지랭크 벡터의 갱신을 위하여 이전에 계산 되어 저장된 벡터를 재사용하 여 , 갱신 에 드는 시간이 크게 단축된다 . 본 방법은 주어진 오차 한계에 도달하는 즉시 결과값을 산출하므로 정확도와 계산시간을 유연하게 조절할 수 있으며 이는 표본 기반 추정방법이나 정확한 값을 산출하는 역행렬 기반 방법 이 가지지 못한 특성이다 . 실험 결과 , 본 방법은 거듭제곱법에 비하여 20 배 이상 빠르게 수렴한다는 것이 확인되었으며 , 기 제시된 최고 성능 의 알고리 듬 보다 우수한 성능을 보이는 것 또한 확인되었다1 Introduction 1 2 Preliminaries: Personalized PageRank 4 2.1 Random Walk, PageRank, and Personalized PageRank. 5 2.1.1 Basics on Random Walk 5 2.1.2 PageRank. 6 2.1.3 Personalized PageRank 8 2.2 Characteristics of Personalized PageRank. 9 2.3 Applications of Personalized PageRank. 12 2.4 Previous Work on Personalized PageRank Computation. 17 2.4.1 Basic Algorithms 17 2.4.2 Enhanced Power Iteration 18 2.4.3 Bookmark Coloring Algorithm. 20 2.4.4 Dynamic Programming 21 2.4.5 Monte-Carlo Sampling. 22 2.4.6 Enhanced Direct Solving 24 2.5 Summary 26 3 Personalized PageRank Computation with Initial Guess Revision 30 3.1 Initial Guess Revision and Relaxation 30 3.2 Finding Optimal Weight of Successive Over Relaxation for PPR. 34 3.3 Initial Guess Construction Algorithm for Personalized PageRank. 36 4 Fully Personalized PageRank Algorithm with Initial Guess Revision 42 4.1 FPPR with IGR. 42 4.2 Optimization. 49 4.3 Experiments. 52 5 Personalized PageRank Query Processing with Initial Guess Revision 56 5.1 PPR Query Processing with IGR 56 5.2 Optimization. 64 5.3 Experiments. 67 6 Conclusion 74 Bibliography 77 Appendix 88 Abstract (In Korean) 90Docto

Declarative Cleaning, Analysis, and Querying of Graph-structured Data

Much of today's data including social, biological, sensor, computer, and transportation network data is naturally modeled and represented by graphs. Typically, data describing these networks is observational, and thus noisy and incomplete. Therefore, methods for efficiently managing graph-structured data of this nature are needed, especially with the abundance and increasing sizes of such data. In my dissertation, I develop declarative methods to perform cleaning, analysis and querying of graph-structured data efficiently. For declarative cleaning of graph-structured data, I identify a set of primitives to support the extraction and inference of the underlying true network from observational data, and describe a framework that enables a network analyst to easily implement and combine new extraction and cleaning techniques. The task specification language is based on Datalog with a set of extensions designed to enable different graph cleaning primitives. For declarative analysis, I introduce 'ego-centric pattern census queries', a new type of graph analysis query that supports searching for structural patterns in every node's neighborhood and reporting their counts for further analysis. I define an SQL-based declarative language to support this class of queries, and develop a series of efficient query evaluation algorithms for it. Finally, I present an approach for querying large uncertain graphs that supports reasoning about uncertainty of node attributes, uncertainty of edge existence, and a new type of uncertainty, called identity linkage uncertainty, where a group of nodes can potentially refer to the same real-world entity. I define a probabilistic graph model to capture all these types of uncertainties, and to resolve identity linkage merges. I propose 'context-aware path indexing' and 'join-candidate reduction' methods to efficiently enable subgraph matching queries over large uncertain graphs of this type