A simple parallel algorithm for the maximal independent set problem
SIAM Journal on Computing
New Connectivity and MSF Algorithms for Shuffle-Exchange Network and PRAM
IEEE Transactions on Computers
A simple randomized parallel algorithm for list-ranking
Information Processing Letters
High probability parallel transitive-closure algorithms
SIAM Journal on Computing
An introduction to parallel algorithms
An introduction to parallel algorithms
Communication complexity
The space complexity of approximating the frequency moments
Journal of Computer and System Sciences
External-memory graph algorithms
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
External memory algorithms
Fast, small-space algorithms for approximate histogram maintenance
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Models and issues in data stream systems
Proceedings of the twenty-first ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Reductions in streaming algorithms, with an application to counting triangles in graphs
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
An Approximate L1-Difference Algorithm for Massive Data Streams
SIAM Journal on Computing
List-ranking on interconnection networks
Information and Computation
Efficient algorithms for new computational models
Efficient algorithms for new computational models
On the Streaming Model Augmented with a Sorting Primitive
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Graph distances in the streaming model: the value of space
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Approximate quantiles and the order of the stream
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Machine models and lower bounds for query processing
Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Tribeca: a system for managing large databases of network traffic
ATEC '98 Proceedings of the annual conference on USENIX Annual Technical Conference
Approximate and exact parallel scheduling with applications to list, tree and graph problems
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Finding Biconnected Componemts And Computing Tree Functions In Logarithmic Parallel Time
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
Trading off space for passes in graph streaming problems
ACM Transactions on Algorithms (TALG)
Hi-index | 5.23 |
In this paper we show how parallel algorithms can be turned into efficient streaming algorithms for several classical combinatorial problems in the W-Stream model. In this model, at each pass one input stream is read, one output stream is written, and data items have to be processed using limited space; streams are pipelined in such a way that the output stream produced at pass i is given as input stream at pass i+1. We first introduce a simulation technique that allows turning efficient PRAM algorithms into optimal W-Stream ones, for many classical combinatorial problems, including list ranking and Euler tour of a tree. For other problems, most notably graph problems, however, this technique leads to suboptimal algorithms. To overcome this difficulty we introduce the RelaxedPRAM (RPRAM) computational model, as an intermediate model between PRAM and W-Stream. RPRAM allows every processor to access a non-constant number of memory cells per parallel round, albeit with some restrictions. The RPRAM model, while being more powerful than the PRAM model, can be simulated in W-Stream within the same asymptotic bounds. The extra power provided by RPRAM allows us in many cases to substantially reduce the number of processors, while maintaining the same number of parallel rounds, leading to more efficient W-Stream simulations of parallel algorithms. Our RPRAM technique gives new insights on developing streaming algorithms and yields efficient algorithms for several classical problems in this model including sorting, connectivity, minimum spanning tree, biconnected components, and maximal independent set. In addition to allowing smooth space-passes tradeoffs, our algorithms are also shown, by proving almost-tight communication complexity-based lower bounds in W-Stream, to be optimal up to polylog factors.