1. Load Balancing for Partition-based Similarity Search Xun Tang, Maha Alabduljalil, Xin Jin, Tao Yang Department of Computer Science University of California at Santa Barbara SIGIR’14

2. Definition: Finding pairs of objects whose similarity is above a certain threshold Application examples:  Document clustering –Near duplicates –Spam detection  Query suggestions  Advertisement fraud detection  Collaborative filtering & recommendation All Pairs Similarity Search (APSS) ≥ τ Sim (d i,d j ) = cos(d i,d j ) didi djdj

3. Big Data Challenges for Similarity Search 20M tweets fit in memory, but take days to process Approximated processing  Df-limit [Lin SIGIR’09]: remove features with their vector frequency exceeding an upper limit Sequential time (hour) Values marked * are estimated by sampling

4. Parallel Solutions for Exact APSS Parallel score accumulation [Lin SIGIR’09; Baraglia et al. ICDM’10  25x faster or more Partition-based Similarity Search (PSS) [Alabduljalil et al. WSDM’13]

5. Focus of This Paper Improves PSS by additional 41%  By improving computation load balancing Key techniques Two-stage load assignment algorithm  First stage constructs a preliminary load assignment  Second stage refines the assignment  Analytical results on competitiveness to support design Improved dissimilarity detection with hierarchical data partitioning

6. Previous Work Filtering  Dynamic computation filtering. [Bayardo et al. WWW’07]  Prefix, positional, and suffice filtering. [Xiao et al. WWW’08] Similarity-based grouping  Inverted indexing. [Arasu et al. VLDB’06]  Parallelization with MapReduce. [Lin SIGIR’09]  Feature-sharing groups. [Vernica et al. SIGMOD’10]  Locality-sensitive hashing. [Gionis et al. VLDB’99; Ture et al. SIGIR’11]  Partition-based similarity comparison. [Alabduljalil et al. WSDM’13] Load balancing and scheduling  Index serving in search systems. [Kayaaslan et al. TWEB’13]  Division scheme with MapReduce. [Wang et al. KDD’13]  Greedy scheduling policy. [Garey and Grahams. SIAM’75]  Delay scheduling with Hadoop. [Zaharia et al. EuroSys’10]

7. Problem of Load Balance in APSS Partition-level comparison is symmetric Choice of comparison direction affects load balance Example: Should P i compare with P j or P j compare with P i ?  Impact communication/load of corresponding tasks PiPi PjPj PjPj Pi

8. Similarity GraphComparison Graph  Load assignment process: Transition from similarity graph to comparison graph

9. Load Balance Measurement & Examples Load balance metric: Graph cost = Max (task cost) Task cost is the sum of  Self comparison, including computation and I/O cost  Comparison to partitions point to itself

10. Challenges of Optimal Load Balance Skewed distribution of node connectivity & partition sizes Empirical data

11. Two-Stage Load Balance Key Idea: tasks with small partitions or low connectivity should absorb more comparisons Stage 1: Initial assignment of edge directions Challenge: How to optimize a sequence of “absorption” steps?

12. Introduce “Potential Weight” of a Task How to find the potentially lightest task?  Define potential weight (PW) as –Self comparison time + Comparison cost to ALL neighboring partitions Each step picks the node with lowest PW and updates the sub-graph  Lightest partitions absorb as much workload as possible

13. A Sequence of Absorption Steps: Example Initial stateStep 1

14. Step 2Step 1

15. Stage 2: Assignment refinement Key Idea: gradually shift load of heavy tasks to their lightest neighbors Only reverse an edge direction if beneficial

16. Gradual Mitigation of Load Imbalance Load imbalance indicators  Maximum / Average  Std. Dev / Average

17. Competitive to Optimal Task Load Balancing Is this two-stage algorithm competitive the optimum?  Optimum = minimum (maximum task weight) Result: Two-stage solution ≤ (2 + δ) Optimum δ is the ratio of I/O and communication cost over task computation cost In our tested cases, δ ≈ 10%

18. Competitive to Optimum Runtime Scheduler Can the solution of task assignment algorithm be competitive to the one produced by the optimum runtime scheduling?  PT opt = Minimum (parallel time on q cores) A greedy scheduler executes tasks produced by two- stage algorithm  E.g. Hadoop MapReduce  Yielded schedule length is PT q Result:

19. Competitive to the Optimum for a Fully Connected Similarity Graph with Equal Sizes For example, a 5-node graph Results for a n-node fully connected graph with equal sizes

20. Evaluations Implementation: Hadoop MapReduce  Parallelized pre-processing and static partitioning  Comparison graph stored in a distributed cache  Hadoop scheduler execute queued tasks on available cores  Exact similarity comparison without approximated preprocessing Datasets  Twitter, ClueWeb, Yahoo! Music Clusters  Intel X5650 2.66GHz  AMD Opteron 2218 2.6GHz

21. Scalability: Parallel Time and Speedup Efficiency decline caused by the increase of I/O overhead among machines in larger clusters YMusic dataset is not large enough to use more cores for amortizing overhead

22. Time Cost Distribution Static partitioning is parallelized and cost is insignificant Computation cost in APSS is dominating and I/O overhead is relatively low, δ ≈ 10% Competitive to optimum rumtime

23. Effectiveness of Two-Stage Load Balance Comparison with Circular Load Assignment [Alabduljalil et al. WSDM’13] Parallel time reduction  Stage 1 up to 39%  Stage 2 up to 11%

24. Conclusions Two-stage load assignment algorithm for APSS  Convert undirected to directed similarity comparison graph  Improvement: up to 41% for the tested cases  Analysis on competitiveness to the optimum  Scalable for large datasets. Improved dissimilarity detection and partitioning  More dissimilarity detected  Hierarchical static data partitioning method for more even sizes  Contributes up to 18% end-performance gain

25. Q & A Thank you! Presenter: Xun Tang xtang@cs.ucsb.edu Look for challenging opportunities.

26. Backup Slides

27. A Naïve Approach: Circular Load Balance Compares a partition with half of other partitions, if they are potentially similar

28. Function of each PSS task Read assigned partition P k and build inverted index. Repeat  Read vectors from a potentially similar partition.  Compare P k with these vectors.  Write similar vector pairs. Until all potentially similar vectors are compared. Compare Coarse-grain task parallelism PkPk

29. Static Partitioning with Dissimilarity Detection Place dissimilar vectors into different partitions. Low-cost partitioning: near linear complexity in identifying pair- wise dissimilarity with no false positive. Dataset Partitions Dissimilarity edges

30. Why do we follow PSS? Normalized Pair-wise comparison time PSS  1.24 ns for Twitter; 0.74 ns for ClueWeb using 300 AMD cores given similarity threshold=0.8 Parallel score accumulation  19.7x to 25x slower than PSS Alternate MapReduce solution: PQ [Lin SIGIR’09]  130.1 ns with approximated processing

31. Improved Data Partitioning: r-norm

32. How Well Does It Work? How does the comparison graph generated by two-stage algorithm compare to the smallest cost possible graph? is defined as the smallest cost of a comparison graph derived from a similarity graph G. Overhead ratio of I/O and communication over computation

33. How Well Does It Work? How is our job completion time compare to the optimal solution? Not knowing the allocated computing resources. is the job completion time of the two-stage load assignment with a greedy scheduler on q cores; is that of an optimal solution.

34. Improved Data Partitioning: Layer Size Uniform: evenly-size partitions Non-uniform: size of partition L k proportional to index k

35. Effect of Recursive Hierarchical Partition Recursively divide a large sublayer by detecting dissimilar vectors inside the sublayer Each partition inherits the dissimilar relationship from its original sublayer The new partitions together with the undivided sublayers form the undirected similarity graph