TAILIEUCHUNG - Managing and Mining Graph Data part 42

Managing and Mining Graph Data part 42 is a comprehensive survey book in graph data analytics. It contains extensive surveys on important graph topics such as graph languages, indexing, clustering, data generation, pattern mining, classification, keyword search, pattern matching, and privacy. It also studies a number of domain-specific scenarios such as stream mining, web graphs, social networks, chemical and biological data. The chapters are written by leading researchers, and provide a broad perspective of the area. This is the first comprehensive survey book in the emerging topic of graph data processing. . | A Survey on Streaming Algorithms for Massive Graphs 397 Other variants of streaming model also exist. For example the W-stream model 115 allows the algorithm to write to annotate the stream during each pass. Thest annotations can titan be utiilizcd Ings i-l lc algorithm in the successive paascSi Another variant 1 augments the streaming model by adding a sorting primisive. X Statistics and Counting Triangles In this sectinni we describe it silt ot problems that involve graphs but essentially curt be reduced to prohicms whose input is an array presented as a stream nf the array clcmcntn gor an a sequence of increments to the el-ements i Foe example the array a 2 1 3 can be given as a stream a 1 1 a 3 1 a 3 1 a 2 1 a 1 1 a 3 1 . Assuming nil tits entries of lite array lake vains 0 al. the beginning of the stream aftes the operations tn the dream. we obtain the array a. There are many streaming algorithms t tal. com vu les. for this array statistics such aa ircquascy moments 3 24 31 heavy letters 13 10 and construct succinct csala atrustures that suapoct queries such as range queries 38 These algoaithmc can he directly applied once graph problem is reduced to the coarcsponding paobtem of an array. We consider thesi prohiemo inaolving line degree of the graph nodes. For an undirected graph the degree ot tr rode is ths number of edges incident so the node. One may view Shat these is a virtual array D associated with each graph tuch that D z is the degree of the nodCi tn rhe streaming scttlac. a stream of edges lransiatac to updates to the array D. For example the stream 1 2 4 8 2 7 . means rhe operation sequence D 1 1 D 2 1 D 4 1 D 8 1 D 2 1 D 7 1 . . The degree array can he extended to directed graph rvhoaa we may have one out-degree array and one intdcgrcc array. Thu t acquiacy moment problem is io compute the k-th moment fk ZXi D z fc af tint node degrees the heavy hitte ttroblem is to report after seeing the graph streauSi ihtt nodes having .

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