Managing and Mining Graph Data part 17 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. . | 1442 MANAGING AND MINING GRAPH DATA for subgraph isomorplúsm. Procedure Search i iterates on he ith node to find fsasible mappings for that node. Procedure Checkfu -. v examines if ui can be mapped to v by conridcring their edges. Line 12 maps u to v. hites 13-16 continue to search lor titre text nodr or ifit is the last node evaluate the graphrwrde predicate. If7 il in trsix. then a feasible mapping V P V G has hfen found and is reportxd time 15 i. Line 16 stops searching immediately if only one mapping is required. The graph pattern and tine graph me represented as a vertex set and an edge set respectively. In addition adjacency tisis of rhe graph pattern are used to support dine 21o dot line 22 edges of graph G can bn r cicntisil in a hashtable where keyr are pairs of the and poiitto. To avoid repeated evaluation of edge dlinc 22 avoihcr hi ti litaitlw cun he uted to store evaluated pairs of edges. The time complexity of Algorithm is O nk where n and k me the tines of graph G and nxaph pattern P respectively. This complexity is a conssc ticncc of luhgraph isomorphism that is known to be NP-hard. In practice tiie running time depvnds on ilic size of the search space. Ait sorv consider pofsfelc wayt to accelerate Algorithm 1 How to reduce fee size of ui for each node ufl How to fliciently rclrlxvc uf 2 How no reduce thl overall search space ui x . x uk 3 How So optimlzc the search order Wa ptesext three techniques . rcrpcctivtiy address the above questions. The firsS prunes each ui inili f lLlaHy and s exri ts f it efficiently through indexmg. The second tcchniquc piuncs the overall search space by comldcring aii nodes in lite pattern simultancoiisiy. The third technique applies idear front traditional query optirmzatioh to find the right search order. Local Pruning and Retrieval of Feasible Mates Node sitribules can tie indexed c t teatiit using traditional index structures such Bit 6-0 81 Tins at lows fof
