Database laboratory Regular Seminar 2013-11-11 TaeHoon Kim

1. Chonbuk National Univ Database Laboratory v.2 TurboGraph: A Fast Parallel Graph Engine Handling Billion-scale Graphs in a Single PCWook-Shin Han, Sangyeon Lee, Kyungyeol ParkJeong-Hoon Lee, Min-Soo Kim, Jinha Kim, Hwanjo YuPOSTECH, DGISTSIGKDD 2013, ACM Database laboratory Regular Seminar 2013-11-11 TaeHoon Kim ACM SIGKDD is conference (Knowledge discovery and data mining)

2. Contents • Introduction • Related Work • Efficient Graph Storage • Disk-Based Parallel Graph Computation • Processing Graph Queries* • Experiments • Conclusion

3. Introduction • Graphs are used to model many real objects • Web graph, chemical compound, biological structure • Very large real graph size • Facebook reached one billion users on Oct. 4, 2012 • Yahoo Web graph consisting of 1.4 billion vertices and 6.6 billion edges • However, if there are a billion vertices in the graph database, the size of the mapping table is too large to fit into memory • For fast graph retrieval on a single commodity PC, graphs must be stored in fast external memory, such as FlashSSDs

4. Introduction • Proposed to handle big graph efficiently • GBase is recent graph engine using MapReduce • If the graph is represented as a compressed matrix-vector, computation solves many representative • However, distributed systems based on MapReduce are generally slow unless there is a sufficient number of machines in a cluster • Distributed system based on the vertexcentric programing model Pregel, GraphLab, PowerGraph has been propossed • However, efficient of graph operations is very difficult • User needs to be skilled at managing and tuning a distributed systems in a cluster, which is a nontrivial job for the ordinary users • Recently, a disk-based graph processing engine on a single PC called GraphChi has been propossed • Exploits the novel concept of parallel sliding windows(PSW)

5. Introduction • Processing PSW of GraphChi • 1)Loading a subgraph 2)updating the vertices and edge 3)writing the updated parts of the subgraph to disk • We observe that PSW incurs four serious problem • 1)In order to start updating vertices/edges in a shard file, their in-edges must be fully loaded in memory • 2)All edges in the shard file source and target vertices are in the same execution interval are processed in sequential order which hinder full parallelism • 3)At each iteration, a significant number of updated edges can be flushed to disk • If the size of graph is very large and/or there exist many iteration, GraphChi involve a significant amount of disk I/Os • 4)Even if a query needs to access a small portion of the data, it reads the whole graph at the first iteration  poor utilization(h/w)

6. Introduction • Inthis paper, TurboGraph provides • First truly parallel graph engine on a single PC • Full parallelism including FlashSSD IO parallelism and multi-core parallelism • Full overlap of CPU processing and I/O processing • We present TurboGraph to process billion-scale graphs very efficiently by using modern hardware on a single PC • We present a novel parallel execution model called pin-and-slide • Implements the column view of the matrix-vector multiplication

7. Related Work • Distributed synchronous approaches • PEGASUS and Gbase • based on MapReduce and support matrix-vector multiplication using compressed matrices • All synchronous approaches above could suffer from costly performance penalties • Because, the runtime of each step is determined by the slowest machine in the cluster cause h/w variability, n/w imbalance • Distributed asynchronous approaches • GraphLab is also based on vertex-centric programing model • Vertex kernel is executed in asynchronous parallel on each vertex • However, some algorithms based on asynchronous computation require serializability for correctness

8. Related Work • Distributed asynchronous approaches • PowerGraph • Basically similar to GraphLab • It partitions and store graph by exploiting the properties of real-world graphs of highly skewed power-law degree distribution • However, efficient graph partitioning in the distributed environment for all types of graph operation is inherently hard problem • Single-machine approaches • GraphChi • Disk-based single machine system following the asynchronous vetex-centric programing model • Use PSW • GraphChi is very efficient, and thus able to problems while using only a single machine, there are still four serious

9. Efficient Graph Storage • Disk-based Graph Representation • For the vertices ~ 5 their adjacency list are stored as smallrecords in pages p0~p2 while the adjacency list of 6 is stored as a large record which spans the two pages p3, p4 • Since the size of this RID table is very small, we can safely make it resident in memory The slotted page is known to be very good for supporting efficient updates A record means an adjacency list Buffer pool offset Start LRPL offset # of LA PAGES LRPL offset

10. Efficient Graph Storage(2 core functions) • In-memory Data Structures and Core Operations • Invoke PINPAGE : if the page exists in the buffer?(pinCount++) • Otherwise, it obtains an empty frame by the LRU replacement and loads the page from disk to the frame • Return the memory address of the frame where the page was loaded • UNPINPAGE : (pinCount--) • PINCOMPUTEUNPIN(PageIDpid, list<RID> RIDList, User Object u0) • Provide s asynchronous I/Os to the FlashSSD User defined function for RID processing P0 V1 U0 • Buffer pool Be resident in Memory P0 Callback thread U0 Compute(v1,Iterator (v1, adj)) 1. Execution thread (PinComputeUnpin) FlashSSD Buffer pool : an array of frames

11. Disk-Based Parallel Graph Computation • G = (V,E) • Adjacency Matrix M(G), where vi = i-th vertex in G • Let M(G)i the i-th column vector of M(G) • When we have a column vector X(|X| = |V|), we can define the matrix-vector multiplication • between M(G) and X(Y = M(G) X ) As Y = Xiin the column view Vi

12. Disk-Based Parallel Graph Computation • X : input bit vector • Y : output bit vector • We use bit vectors for the graph • U0 : User object • User-define Compute as one of its methods • Execution thread • (parallel async I/O) • PinComputeUnpin • Callback thread • (concurrently process the vertex) • U0.Compute(v1,Iterator)

13. Disk-Based Parallel Graph Computation • If the page is fully loaded? • Pinned of the fully loaded page • If partially loaded? Using Knapsack 0-1 • PinComputeUnpin • Ordered from the large adjacency list and small adjacency • Using parallel processing, and Compute • To thread safe, we use latch free approach 1 1 2 2 3 3 4 4 5 5

14. Th2 Disk-Based Parallel Graph Computation • Thread safelatch free approach • 5.1 latch free approach? 5 5.1 Th1

15. Disk-Based Parallel Graph Computation • Handling General Vectors • Example 1. We explain our pin-and-slide model handling general vectors by using a PageRank query • Step1 • After first reading pages from disk into the buffer {p0, p1, p2}, We read the first chunk of each attribute vector into memory • Then we join between block1 and chunk1 • Step2 • We read chunk2 of each attribute vector into memory join between block1 and chunk2 and updates of chunk1 of the output vector • Step3 • Since we complete the processing for block1, we read new pages from disk {p3,p4}, then we join block2 and chunk1 and write the results to chunk2 of the output vector • Step4 • We do the final join and update chunk2 of the output vector

16. Disk-Based Parallel Graph Computation chunk2 chunk1 V0V1V2 V3 V4 V5 V6 outDegree v4 prevPR v2 0.143 0.143 0.143 0.143 0.143 v6 1 v0 0.143 output JOIN v3 0.143 0.143 chunk1 V0 V1 V2 V3 V4 V5 V6 v5 0.143 v1 buffer pool p0 p1 p2 p3, p4 block1 • Example of V0 have V1 and V6 # of edges Total of vertex { 0.85 ( 0.143 / 2 ) + (0 / 2) } + (0.15 / 7 ) = 0.082 chunk2 1

17. Disk-Based Parallel Graph Computation chunk2 chunk1 V0V1V2 V3 V4 V5 V6 outDegree v4 prevPR v2 0.143 0.143 0.143 0.143 0.143 v6 v0 2 0.143 output v3 JOIN 0.143 0.143 chunk1 V0 V1 V2 V3 V4 V5 V6 v5 0.143 v1 buffer pool p0 p1 p2 p3, p4 block1 • Example of V0 have V1and V6 # of edges Total of vertex 0.85 { ( 0.143 / 2 ) + (0.143 / 7) } + (0.15 / 7 ) = 0.099 chunk2 2

18. Disk-Based Parallel Graph Computation chunk2 chunk1 V0V1V2 V3 V4 V5 V6 outDegree v4 prevPR v2 0.143 0.143 0.143 0.143 0.143 v6 3 v0 0.143 output JOIN v3 0.143 0.143 chunk1 V0 V1 V2 V3 V4 V5 V6 v5 0.143 v1 buffer pool SLIDE p0 p1 p2 p3, p4 block1 block2 • Example of V6 have recursive V6 # of edges Total of vertex 0.85 { ( 0.143 / 2 ) + ( 0.143 / 2 ) + … ( 0.143 / 2 ) + ( 0.143 / 0 ) } + 0.15/7 = 0.386 chunk2 3

19. Disk-Based Parallel Graph Computation chunk2 chunk1 V0V1V2 V3 V4 V5 V6 outDegree v4 prevPR v2 0.143 0.143 0.143 0.143 0.143 v6 v0 4 0.143 output v3 JOIN 0.143 0.143 chunk1 V0 V1 V2 V3 V4 V5 V6 v5 0.143 v1 buffer pool p0 p1 p2 p3, p4 block1 block2 • Example of V6 have recursive V6 # of edges Total of vertex 0.85 { ( 0.143 / 2 ) + ( 0.143 / 2 ) + … ( 0.143 / 2 ) + ( 0.143 / 7 ) } + 0.15/7 = 0.403 chunk2 4

20. Processing Graph Queries • Targeted Queries( BFSf(Vq) ) • BFS operators • 1-step(out-)neighbors • K-step neighbors • Induced subgraph • l-step egonet • K-step egonet • K-core, Cross-Edges • Global Queries • We have already explained briefly how our model processes the PageRank query in Example 1

21. Experiments • We use three real datasets for the experiments LiveJournal, Twitter, and YahooWeb • The Twitter dataset contains 42M vertices and 1.5B edges • The YahooWeb dataset contains a web graph from Yahoo! With 1.4B vertices and 6.6Edges • Experimentation environment • Intel i7 6-core 3.2GHz CPU and 12 Gbytes DRAM • Two 512GB SSDs of Samsung 840 Series • TurboGraph can be complied in Windows, but GraphChi can be compiled in Linux • Considering that disk I/O performance in Ubuntu is better than that in Windows7

22. Experiments • Breadth-First Search • We additionally perform experiments with a state-of-the-art in-memory graph BFS engine Green-Marl • Varying the buffer Size • Varying the Number of Execution Threads • Green-Mari failed due to lack of memory • GraphChi is very hard to pre-load the graph • GraphChi processes all edges serially

23. Experiments • Targeted Queries • Global Queries

24. Conclusion • In this paper, we presented a fast, parallel graph engine called TurboGraph for efficiently processing billion-scale graphs on a single PC • We proposed a notion of the pin-and-slide model which implements the column view of the matrix-vector multiplication • It utilizes two types of thread, execution threads and callback thread, along with a buffer manager • We show that TurboGraph outperforms the state-of-the-art algorithms by up to four orders of magnitude

25. Discussion • 관련연구 GraphChi의 PSW의 단점들을 제안하는 기법 [e.g)pin-and-slide ]을 이용해서 해결하였고, 그에 따른 성능이 기존 연구보다 우수함을 보임 • 강점 • Flash-SSD 의 비동기I/O를 execution thread를 사용하고, compute를 하기 위해 callback thread를 사용하기 때문에 FULL CPU/ IO processing을 하기 때문에, 기존 연구보다 빠르게 처리 가능 • 최신 기법인 pin-and-silde제안 • 단점 • 그래프 기반의 데이터구조에 쓰일 수 있음 • 쓰레드라는O/S 자원이 필요 • Thank you for listening my presentation : )

26. It is important contents to understand contents • Note that, PPT is summary of my thinking