Top PPR Topk Personalized Page Rank Queries with

Top. PPR: Top-k Personalized Page. Rank Queries with Precision Guarantees on Large Graphs Zhewei Wei, Xiaodong He, Xiaokui Xiao, Sibo Wang, Shuo Shang and Ji-Rong Wen Contact: zhewei@ruc. edu. cn

Personalized Page. Rank (PPR) 9 10 2 8 1 11 3 s 6 5 7 � 12

Top-k PPR queries 0. 04 9 0. 10 2 0. 13 1 3 8 0. 13 6 5 7 � 0. 05 12 0. 08 s Node 4 0. 03 10 11 0. 04 Node 1 Node 2 Node 3 Node s Node 5 Node 6 Node 7 Node 8 Node 9 Node 10 Node 11 Node 12 0. 13 0. 10 0. 13 0. 22 0. 13 0. 05 0. 08 0. 04 0. 03 0. 04 0. 02 Top-5

Applications � Personalized Web Search § [Haveliwala et al. WWW’ 2002] � Graph Clustering § [FOCS’ 2006] § [Hao et al. KDD’ 2017] � Recommendation § Twitter “Who-to-Follow” § [Gupta et a. , KDD’ 2013] § Linked. In “People You May Know” § Pinterest “Related Pins” § [David C et al. WWW 2017] § Tencent: “King of Glory”

Existing works on Top-k PPR Queries � Drawbacks § Requires preprocessing and large index § Unable to run on dynamic graphs § or unable to return exact top-k node set § or offers slow query time on large graphs

Our Method: Top. PPR �

Top. PPR algorithm � Combining three existing techniques in a nontrivial way. s t Forward search Random walk sampling Backward Search [Andersen et al. WAW 07] [Andersen et al. FOCS 06] [Fogaras et al. IM 05]

Top. PPR algorithm � Major Challenge: How to efficiently perform backward search on all nodes? s V

Top. PPR algorithm � Only perform (deeper) backward search on nodes that we are not sure about Top-k set Vk s Candidate set C Confidence bounds computed by Empirical Bernstein Inequality Non-top-k set

Experiments �

Exact Top-k PPR queries

Approximate Top-k PPR queries FORA+: Best indexbased algorithm

Conclusion �Top. PPR: offers theoretical guarantee on the precision of the result �Computes exact and approximate top-k PPR queries w. h. p. § Without preprocessing or indexing �Superior performance on real world graphs.

Thank you!