Assignment Problems of Different-Sized Inputs in MapReduce

Author:

Afrati Foto1,Dolev Shlomi2,Korach Ephraim2,Sharma Shantanu2,Ullman Jeffrey D.3

Affiliation:

1. National Technical University of Athens, Zografou, Greece

2. Ben-Gurion University, Beer-Sheva, Israel

3. Stanford University, Stanford, CA, USA

Abstract

A MapReduce algorithm can be described by a mapping schema , which assigns inputs to a set of reducers, such that for each required output there exists a reducer that receives all the inputs participating in the computation of this output. Reducers have a capacity that limits the sets of inputs they can be assigned. However, individual inputs may vary in terms of size. We consider, for the first time, mapping schemas where input sizes are part of the considerations and restrictions. One of the significant parameters to optimize in any MapReduce job is communication cost between the map and reduce phases. The communication cost can be optimized by minimizing the number of copies of inputs sent to the reducers. The communication cost is closely related to the number of reducers of constrained capacity that are used to accommodate appropriately the inputs, so that the requirement of how the inputs must meet in a reducer is satisfied. In this work, we consider a family of problems where it is required that each input meets with each other input in at least one reducer. We also consider a slightly different family of problems in which each input of a list, X , is required to meet each input of another list, Y , in at least one reducer. We prove that finding an optimal mapping schema for these families of problems is NP-hard, and present a bin-packing-based approximation algorithm for finding a near optimal mapping schema.

Funder

project Handling Uncertainty in Data Intensive Applications

Operational Program “Education and Lifelong Learning,” under the program THALES

European Union (European Social Fund) and Greek national funds

Rita Altura Trust Chair in Computer Sciences

Infrastructure Research in the Field of Advanced Computing and Cyber Security

Israel Science Foundation

Lynne and William Frankel Center for Computer Sciences

Cabarnit Cyber Security MAGNET Consortium

Ministry of Science and Technolog

Publisher

Association for Computing Machinery (ACM)

Subject

General Computer Science

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4. E. G. Coffman Jr. M. R. Garey and D. S. Johnson. 1997. Approximation algorithms for bin packing: a survey. In Approximation Algorithms for NP-Hard Problems. PWS Publishing Co. 46--93. E. G. Coffman Jr. M. R. Garey and D. S. Johnson. 1997. Approximation algorithms for bin packing: a survey. In Approximation Algorithms for NP-Hard Problems. PWS Publishing Co. 46--93.

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