MapReduce¶
Dean, J., & Ghemawat, S. (2004). MapReduce: Simplified Data Processing on Large Clusters. 6th USENIX Symposium on Operating Systems Design and Implementation (OSDI '04), 137-150.
Cited by¶
2 citations across 2 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Commutativity
- commutative algebra (the algebraic theory of commutative rings, the foundation of classical algebraic geometry); representation theory (decomposition of group actions often differs between commutative and non-commutative groups); commutative diagrams in category theory. Computer science: Parallel computation (commutative reduce operations enable arbitrary-order parallelization — MapReduce's reduce step typically requires commutativity and associativity, a class of order-independent algorithms catalogued in Knuth (1973) The Art of Computer Programming)
This sourceStates that when the Reduce operator is commutative and associative a Combiner optimization applies, so partial reductions can be applied in any order — directly supports the claim that MapReduce's reduce step typically requires commutativity and associativity. (Re-sourced from Knuth 1973, which does not catalog a class of commutativity-exploiting order-independent algorithms.)
- commutative algebra (the algebraic theory of commutative rings, the foundation of classical algebraic geometry); representation theory (decomposition of group actions often differs between commutative and non-commutative groups); commutative diagrams in category theory. Computer science: Parallel computation (commutative reduce operations enable arbitrary-order parallelization — MapReduce's reduce step typically requires commutativity and associativity, a class of order-independent algorithms catalogued in Knuth (1973) The Art of Computer Programming)
- Search and Retrieval
Verification¶
This reference passed the adversarial substantiation pipeline: it was checked to exist and to support the claim it is attached to. See how references were verified.
Registry ID ref:85d92bb6bb54 · see in the full table