Efficient parallel solution of linear systems
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Matching is as easy as matrix inversion
Combinatorica
Techniques for parallel manipulation of sparse matrices
Theoretical Computer Science - Special issue on high performance computer systems
A bridging model for parallel computation
Communications of the ACM
An introduction to parallel algorithms
An introduction to parallel algorithms
Sparse matrix computations on the hypercube and related networks
Journal of Parallel and Distributed Computing
Communication-Efficient Parallel Sorting
SIAM Journal on Computing
Two Fast Algorithms for Sparse Matrices: Multiplication and Permuted Transposition
ACM Transactions on Mathematical Software (TOMS)
Counting Distinct Elements in a Data Stream
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
I/O complexity: The red-blue pebble game
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
The effect of algebraic structure on the computational complexity of matrix multiplication
The effect of algebraic structure on the computational complexity of matrix multiplication
Detecting short directed cycles using rectangular matrix multiplication and dynamic programming
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Communication lower bounds for distributed-memory matrix multiplication
Journal of Parallel and Distributed Computing
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Fast sparse matrix multiplication
ACM Transactions on Algorithms (TALG)
Efficient transitive closure of sparse matrices over closed semirings
Theoretical Computer Science - Algebraic methods in language processing
MapReduce: simplified data processing on large clusters
Communications of the ACM - 50th anniversary issue: 1958 - 2008
A Unified Framework for Numerical and Combinatorial Computing
Computing in Science and Engineering
Challenges and Advances in Parallel Sparse Matrix-Matrix Multiplication
ICPP '08 Proceedings of the 2008 37th International Conference on Parallel Processing
DOULION: counting triangles in massive graphs with a coin
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
Proceedings of the 19th international conference on World wide web
On distributing symmetric streaming computations
ACM Transactions on Algorithms (TALG)
Data-Intensive Text Processing with MapReduce
Data-Intensive Text Processing with MapReduce
A model of computation for MapReduce
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Better size estimation for sparse matrix products
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Filtering: a method for solving graph problems in MapReduce
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
The i/o complexity of sparse matrix dense matrix multiplication
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Sorting, searching, and simulation in the mapreduce framework
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
PARMA: a parallel randomized algorithm for approximate association rules mining in MapReduce
Proceedings of the 21st ACM international conference on Information and knowledge management
Communication optimal parallel multiplication of sparse random matrices
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
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This work explores fundamental modeling and algorithmic issues arising in the well-established MapReduce framework. First, we formally specify a computational model for MapReduce which captures the functional flavor of the paradigm by allowing for a flexible use of parallelism. Indeed, the model diverges from a traditional processor-centric view by featuring parameters which embody only global and local memory constraints, thus favoring a more data-centric view. Second, we apply the model to the fundamental computation task of matrix multiplication presenting upper and lower bounds for both dense and sparse matrix multiplication, which highlight interesting tradeoffs between space and round complexity. Finally, building on the matrix multiplication results, we derive further space-round tradeoffs on matrix inversion and matching.