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Assignment of Different-Sized Inputs in MapReduce Shantanu Sharma 2 joint work with Foto N. Afrati 1, Shlomi Dolev 2, Ephraim Korach 2, and Jeffrey D. Ullman 3 1 National Technical University of Athens, Greece 2 Ben-Gurion University of the Negev, Israel 3 Stanford University, USA 28th International Symposium on Distributed Computing (DISC 2014) Austin, Texas, USA (12-15 October 2014)

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Cluster Computing – Terabytes or Petabytes amount of data cannot be processed on a single computer – Cluster of computers – How to mask failures, e.g., hardware failures MapReduce is a programming model used for parallel processing over large-scale data Introduction 2

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3 Worker Master process Worker fork Assign map tasks Assign reduce tasks Read Local write Remote read, sort Output File 0 Output File 1 Write Chunk 0 Chunk 1 Chunk 2 Input Data MapReduce job: Map Phase and Reduce Phase Map Phase: applies a user-defined Map function Reduce Phase: applies a user-defined Reduce function

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Mapper 1 Reducer for I Mapper 2 1 1 I 1 1 like Introduction MapReduce working example – Word Count 2 2 apple Reducer for like Reducer for apple Reducer for is Reducer for banana Reducer for fruit (I, 2) (like, 2) (apple, 2) (is, 1) (fruit, 1) (banana, 1) I like apple. Apple is fruit. I like banana. 1 1 fruit 1 1 is 1 1 I 1 1 like 1 1 banana

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Mapper 1 Reducer for I Mapper 2 1 1 I 1 1 like Introduction Inputs and outputs in our context 2 2 apple Reducer for like Reducer for apple Reducer for is Reducer for banana Reducer for fruit (I, 2) (like, 2) (apple, 2) (is, 1) (fruit, 1) (banana, 1) I like apple. Apple is fruit. I like banana. 1 1 fruit 1 1 is 1 1 I 1 1 like 1 1 banana Inputs Outputs

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Values, provided by each mapper, have some sizes (input size) Reduce capacity: an upper bound on the sum of the sizes of the values that are assigned to the reducer Example: reducer capacity to be the size of the main memory of the processors on which reducers run We consider two special matching problems Reducer Capacity 6

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State-of-the-Art F. Afrati, A.D. Sarma, S. Salihoglu, and J.D. Ullman, “Upper and Lower Bounds on the Cost of a Map- Reduce Computation,” PVLDB, 2013. Unit input size Reducer Size – Maximum number of inputs that a given reducer can have. 7

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Problem Statement Communication cost between the map and the reduce phases is a significant factor How we can reduce the communication cost? – A lesser number of reducers, and hence, a smaller communication cost – How to minimize the total number of reducers while respecting their limited capacity? Not an easy task – All-to-All mapping schema problem – X-to-Y mapping schema problem 8 Mapper for 1 st input Reducer for k 1 ( 1, 2 ) Reducer for k 2 ( 1, 3 ) Reducer for k 3 ( 2, 3 ) Mapper for 2 nd input Mapper for 3 rd input input 1 k1k1 k2k2 input 2 k1k1 k3k3 input 3 k2k2 k3k3 Mapper for 1 st input Reducer for k 1 ( 1, 2, 3 ) Mapper for 2 nd input Mapper for 3 rd input input 1 k1k1 input 2 k1k1 input 3 k1k1 input 1 input 2 input 3 input 1 input 2 input 3 Notation k i : key

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A set of inputs is given Each pair of inputs corresponds to one output Example – Computing common friends Lists of friends of m persons are given Find common friends of the given m persons Every two friend lists must be assigned to a single common reducer A2A Mapping Schema Problem 9

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Mapper for 1 st friend fl 2 fl 3 fl 1 Reducer for k 1 (1, 2, 3) fl 4 Reducer for k 2 (1, 2, 4) Reducer for k 3 (3, 4) Mapper for 2 nd friend Mapper for 3 rd friend Mapper for 4 th friend fl 1 k1k1 k2k2 fl 2 k1k1 k2k2 fl 3 k1k1 k3k3 fl 4 k2k2 k3k3 Reducer capacity is enough to hold some of the friend lists together 10 Notations k i : key fl i : i th friend list 1, 21, 32, 32, 41, 43, 4 A2A Mapping Schema Problem

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Mapper for 1 st friend fl 2 fl 3 fl 1 Reducer for k 1 (1, 2, 3, 4) fl 4 Mapper for 2 nd friend Mapper for 3 rd friend Mapper for 4 th friend fl 1 k1k1 fl 2 k1k1 fl 3 k1k1 fl 4 k1k1 Reducer capacity is enough to hold all the friend lists together 11 Notations k i : key fl i : i th friend list 1, 2 1, 3 1, 4 2, 3 2, 4 3, 4 A2A Mapping Schema Problem

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What to do? – Assigns the given m inputs to the given number of reducers, without exceeding q, in a manner that every given input is coupled with every other given input in at least one reducer in common Polynomial time solution for one and two reducers NP-hard for z > 2 reducers 12 A2A Mapping Schema Problem

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Heuristics for A2A Mapping Schema Problem Based on – First-Fit Decreasing (FFD) or Best-Fit Decreasing (BFD) bin-packing algorithm – Pseudo-polynomial bin-packing algorithm * – 2-step Algorithms – The selection of a prime number p A fixed reducer capacity is given 13 * D. R. Karger and J. Scott. Efficient algorithms for fixed-precision instances of bin packing and euclidean tsp. In APPROX-RANDOM, pages 104–117, 2008.

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Two disjoint sets X and Y are given Each pairs of element x i, y j (where x i X, y j Y, i, j) of the sets X and Y corresponds to one output Example – Skew Join Two relations X(A, B) and Y(B, C) are given where lots of tuple have a common “b” value Every tuple with an identical “b” value is required to assign to at least one reducer X2Y Mapping Schema Problem 14

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X2Y Mapping Schema Problem What to do? – Assigns each input of the set X with each input of the set Y to at least one reducer in common, without exceeding q Polynomial for one reducer – Can we assign all the inputs of the sets X and Y to a single reducer NP-hard for z > 1 reducers 15

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Heuristics for X2Y Mapping Schema Problem Based on – First-Fit Decreasing (FFD) or Best-Fit Decreasing (BFD) bin-packing algorithm A fixed reducer capacity is given 16

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Conclusion Reducer capacity – An important parameter to be considered in all MapReduce algorithms – The capacity is in terms of, not necessarily identical, memory auxiliary size, augmented and added to the index of the data item(s) Two assignment schemas of MapReduce are given – All-to-All (A2A) mapping schema problem – X-to-Y (X2Y) mapping schema problem Several heuristics for A2A and X2Y mapping schema problems are provided 17

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Foto Afrati 1, Shlomi Dolev 2, Ephraim Korach 3, Shantanu Sharma 2, and Jeffrey D. Ullman 4 1 School of Electrical and Computing Engineering, National Technical University of Athens, Greece afrati@softlab.ece.ntua.gr 2 Department of Computer Science, Ben-Gurion University of the Negev, Israel {dolev,sharmas}@cs.bgu.ac.il 3 Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Israel korach@bgu.ac.il 4 Department of Computer Science, Stanford University, USA ullman@cs.stanford.edu Presentation is available at http://www.cs.bgu.ac.il/~sharmas/publication.html

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Foto Afrati — National Technical University of Athens Anish Das Sarma — Google Research Semih Salihoglu — Stanford University Jeff Ullman — Stanford University.

Foto Afrati — National Technical University of Athens Anish Das Sarma — Google Research Semih Salihoglu — Stanford University Jeff Ullman — Stanford University.

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