## Papers

- Afrati, Foto N. and Sarma, Anish Das and Menestrina, David and Parameswaran, Aditya and Ullman, Jeffrey D., Fuzzy Joins Using MapReduce, ICDE, 2012.
Fuzzy/similarity joins have been widely studied in the research community and extensively used in real-world applications. This paper proposes and evaluates several algorithms for ﬁnding all pairs of elements from an input set that meet a similarity threshold. The computation model is a single MapReduce job. Because we allow only one MapReduce round, the Reduce function must be designed so a given output pair is produced by only one task; for many algorithms, satisfying this condition is one of the biggest challenges. We break the cost of an algorithm into three components: the execution cost of the mappers, the execution cost of the reducers, and the communication cost from the mappers to reducers. The algorithms are presented ﬁrst in terms of Hamming distance, but extensions to edit distance and Jaccard distance are shown as well. We ﬁnd that there are many different approaches to the similarity-join problem using MapReduce, and none dominates the others when both communication and reducer costs are considered. Our cost analyses enable applications to pick the optimal algorithm based on their communication, memory, and cluster requirements. more

- Foto N. Afrati, Anish Das Sarma, Semih Salihoglu and Jeffrey D. Ullman, Upper and Lower Bounds on the Cost of a Map-Reduce Computation, Proceedings of the VLDB Endowment, Volume 6 Issue 4, February 2013
In this paper we study the tradeo between parallelism and communication cost in a map-reduce computation. For any problem that is not embarrassingly parallel," the ner we partition the work of the reducers so that more parallelism can be extracted, the greater will be the total communication between mappers and reducers. We introduce a model of problems that can be solved in a single round of mapreduce computation. This model enables a generic recipe for discovering lower bounds on communication cost as a function of the maximum number of inputs that can be assigned to one reducer. We use the model to analyze the tradeo for three problems: nding pairs of strings at Hamming distance d, nding triangles and other patterns in a larger graph, and matrix multiplication. For nding strings of Hamming distance 1, we have upper and lower bounds that match exactly. For triangles and many other graphs, we have upper and lower bounds that are the same to within a constant factor. For the problem of matrix multiplication, we have matching upper and lower bounds for one-round map-reduce algorithms. We are also able to explore tworound map-reduce algorithms for matrix multiplication and show that these never have more communication, for a given reducer size, than the best one-round algorithm, and often have signicantly less. more