Big Graph Processing: Some Background

Transcription

1 Big Graph Processing: Some Background Bo Wu Colorado School of Mines Part of slides from: Paul Burkhardt (National Security Agency) and Carlos Guestrin (Washington University) Mines CSCI-580, Bo Wu

2 Graphs are everywhere! o A graph is a collection of binary relationships, i.e. networks of pairwise interactions including social networks, digital networks part of Internet Mines CSCI-580, Bo Wu brain network 2

3 Scale of the first graph o Nearly 300 years ago the first graph problem consisted of 4 vertices and 7 edges Seven Bridges of Konigsberg problem Is it possible to cross each of the seven bridges exactly once? Not too hard to fit in memory Mines CSCI-580, Bo Wu 3

4 Scale of real-world graphs o Graph scale in current CS literature on order of billions of edges, tens of gigabytes Mines CSCI-580, Bo Wu 4

5 Big Data begets Big Graphs o Increasing volume,velocity,variety of Big Data are significant challenges to scalable algorithms o How will graph applications adapt to Big Data at petabyte scale? o Ability to store and process Big Graphs impacts typical data structures Mines CSCI-580, Bo Wu 5

6 Social Scale o 1 billion vertices, 100 billion edges 111 PB adjacency matrix 2.92 TB adjacency list 2.92 TB edge list Mines CSCI-580, Bo Wu 6

7 Web scale o 50 billion vertices, 1 trillion edges 271 EB adjacency matrix 29.5 TB adjacency list 29.1 TB edge list Mines CSCI-580, Bo Wu 7

8 Brain scale o 100 billion vertices, 100 trillion edge 2.84 PB adjacency list 2.84 PB edge list Mines CSCI-580, Bo Wu 8

9 Benchmarking scalability on Big Graphs o Big Graph challenge our conventional thinking on both algorithms and computer architecture! o New Graph500.org benchmark provides a foundation for conducting experiments on graph datasets Mines CSCI-580, Bo Wu 9

10 Graph algorithms are challenging o Difficult to parallelize irregular data accesses increase latency skewed data distribution creates bottlenecks Celebrity nodes in social networks o Increased size imposes greater storage overhead IO burden! Mines CSCI-580, Bo Wu 10

11 Problem: How do we store and process Big Graphs? o Conventional approach is to store and compute inmemory o Shared memory Parallel Random Access Machine (PRAM) data in globally-shared memory implicit communication by updating memory fast-random access o Distributed memory Bulk Synchronous Parallel (BSP) data distributed to local, private memory explicit communication by sending messages easier to scale by adding more machines Mines CSCI-580, Bo Wu 11

12 Memory is fast but o Algorithms must exploit computer memory hierarchy designed for spatial and temporal locality registers, L1,L2,L3 cache, TLB, pages, disk... great for unit-stride access common in many scientific codes, e.g. linear algebra o But common graph algorithm implementations have... lots of random access to memory causing... many cache and TLB misses Mines CSCI-580, Bo Wu 12

13 Poor locality increases latency o Question: What is the memory throughput if 90% TLB hit and 0.01% page fault on miss? Mines CSCI-580, Bo Wu 13

14 If it fits o Graph problems that fit in memory can leverage excellent advances in architecture and libraries... Cray XMT2 designed for latency-hiding SGI UV2 designed for large, cache-coherent shared-memory body of literature and libraries Parallel Boost Graph Library (PBGL) Indiana University Multithreaded Graph Library (MTGL) Sandia National Labs GraphCT/STINGER Georgia Tech GraphLab Carnegie Mellon University Giraph Apache Software Foundation Mines CSCI-580, Bo Wu 14

15 We can add more memory, but o Memory capacity is limited by... number of CPU pins, memory controller channels, DIMMs per channel memory bus width o Globally-shared memory limited by... CPU address space cache-coherence Mines CSCI-580, Bo Wu 15

16 Larger systems, greater latency o Increasing memory can increase latency traverse more memory addresses larger system with greater physical distance between machines Fundamental limitation: speed of light o Latency causes significant inefficiency in new CPU architectures Mines CSCI-580, Bo Wu 16

17 Easier to increase capacity using disks o Current Intel Xeon E5 architectures: 384 GB max. per CPU (4 channels x 3 DIMMS x 32 GB) 64 TB max. globally-shared memory (46-bit address space) 3881 dual Xeon E5 motherboards to store Brain Graph 98 racks o Disk capacity not unlimited but higher than memory Larget disk on market: 8TB needs 364 to store Brain Graph which can fit in 5 racks o Disk is not enough applications will still require memory for processing Mines CSCI-580, Bo Wu 17

18 Big Graph Processing Frameworks

19 Why not just map reduce? o Developed by Google o Excellent for embarrassingly massively parallel computations No communication needed Many machine learning algorithms fall into this category o Not efficient for iterative algorithms that have dependences Unnecessary IO traffic 19

20 What s the natural way to program graph computation? 20

21 Most famous parallel graph processing framework 21

22 GAS 22

23 We still need parallelism 23

24 Graph partition: not easy at all at scale 24

25 Power-law distribution count More$than$10 8 $ver+ces$$ have$one$neighbor.$ Top$1%$of$ver+ces$are$ High%Degree)) adjacent$to$ Ver+ces) 50%$of$the$edges!$ degree 25

26 Power-law degree distribution 26

27 Random graph partitioning o Graph parallel abstractions rely on partitioning: Minimize communication Balance computation and storage 10 Machines à 90% of edges cut 100 Machines à 99% of edges cut! Machine 1 Machine 2 27

28 Challenges of high-degree vertices Y Data transmitted across network O(# cut edges) Machine 1 Machine 2 28

29 Idea of vertex cut 29

30 GAS decomposition 30

31 Random Edge- Placement Randomly assign edges to machines Machine 1 Machine 2 Machine 3 Balanced Vertex- Cut Y Spans 3 Machines Z Spans 2 Machines Not cut! YY Y Z 31

32 Greedy Vertex- Cuts Place edges on machines which already have the vertices in that edge. A B B C Machine1 Machine 2 AB DE 32

33 Example What s the popularity of this user? Popular?) 33

34 PargeRank Algorithm R[i] = Rank%of% user%i" X j2nbrs(i) w ji R[j] Weighted%sum%of% neighbors %ranks" o Update ranks in parallel o Iterate until convergence 34

35 PageRank in Graphlab GraphLab_PageRank(i) // Compute sum over neighbors total = 0 foreach( j in in_neighbors(i)): total = total + R[j] * w ji! // Update the PageRank R[i] = total! // Trigger neighbors to run again if R[i] not converged then foreach( j in out_neighbors(i)) signal vertex- program on j Gather Information About Neighborhood Update Vertex Signal Neighbors & Modify Edge Data 35

36 Triangle counting on Twitter 36

37 What if I don t have a cluster? 37

38 GraphChi disk-based GraphLab o Challenge Random disk accesses! o Naive solutions Graph clustering Prefetching! o Solution Novel graph representation in disk Parallel sliding window Minimizes random accesses 38

39 Parallel sliding window layout A shard is easy to fit in memory 39

40 Parallel sliding window execution O(P^2) random accesses per pass on entire graph 40

41 Triangle counting on Twitter graph 41