tailieunhanh - Managing and Mining Graph Data part 43

Managing and Mining Graph Data part 43 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 Sumy on Streaming Algorithms for Massive Graphs 4007 of 1110 graph G V. E is an additive a p -spanner of G if lor every pair of vertices u v E Vi dista u v a dista u v p. We clcscri be rhe algorithm of 21 and iic subroutine in the following fashion. r c describe fit list lire distributed veasioa of die algorithm and then its adaptation to rhe streaming moslcl. As observed ir 121 leaving space complexity arldCi ir is easy to see lirai. many lis lrii iie d algorithms with time complexity T translate _li ree 11 i to atrcaining algorithms that use T patseSt I Or example a trraigntforward streaming adaptation of a synchronous distributed algorithm for aonsiaucting a Bl S iroci would tie the following in each pass over the input rtreenii IỈt s tree grows one more level. An exploration of d levels would retiult. in d parses over the input itrcimii On die thcr hand there are cases in rviiich tha rtinni ng time of a synchronous algorithm may not translate directly to number of passet of lliti dreaming adaf laiion. In the example of the BFS trite. if two BFS trees ate being constructed in parallel some edges may Inc explored bar both construe tionSr casuiling in congestion that may increase running time of the . tilv l algorahni. ilciI for a streaming algorithm IxiuIi explorations oil rhe same edge can he done using only one pass over the stream. AAOx - loiiorv the notations used in 21 . Let diam G denote tile diameter of the graph Gi toi diam G maxu v vdista u v i Given a subset V c Vi slcnotc by Ea V tire net of edges in G Muced by V i toi Ea V u w I u w E E and u w E V . Let G V V Ea V i Denote by Tfc v V the k-neighborhood ol vcrtcx V in the graph G V i toi Tk v V u I u E V and dist V EG y k i The diamctcrof a subset V c Vi denoted by diam V i is the maximin 11 pairwise distance in G between a pair of vertioea from V . Foe a collection E of subsets V c Vi let diam E maxy eE diam V . The spanner contlruclion ulilL-cs graph covers. l or a graph