Optimal per-edge processing times in the semi-streaming model

We present semi-streaming algorithms for basic graph problems that have optimal per-edge processing times and therefore surpass all previous semi-streaming algorithms for these tasks. The semi-streaming model, which is appropriate when dealing with massive graphs, forbids random access to the input...

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Bibliographic Details
Published in:Information processing letters Vol. 104; no. 3; pp. 106 - 112
Main Author: Zelke, Mariano
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 31.10.2007
Elsevier Science
Elsevier Sequoia S.A
Subjects:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Combinatorics
Combinatorics. Ordered structures
Computer science; control theory; systems
Exact sciences and technology
Graph algorithms
Graph theory
Graphs
Information processing
Information retrieval. Graph
Mathematical models
Mathematics
Miscellaneous
Per-edge processing time
Random access memory
Sciences and techniques of general use
Streaming algorithms
Studies
Theoretical computing
Streaming algorithms
Graph algorithms
Per-edge processing time
Access time
Vertex
Computer theory
Random access memory
Processing time
Computing
Random graph
Input
Graph connectivity
Information processing
Fast algorithm
Algorithm analysis
Graph algorithm
ISSN:0020-0190, 1872-6119
Online Access:Get full text
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Summary:We present semi-streaming algorithms for basic graph problems that have optimal per-edge processing times and therefore surpass all previous semi-streaming algorithms for these tasks. The semi-streaming model, which is appropriate when dealing with massive graphs, forbids random access to the input and restricts the memory to O ( n ⋅ polylog n ) bits. Particularly, the formerly best per-edge processing times for finding the connected components and a bipartition are O ( α ( n ) ) , for determining k-vertex and k-edge connectivity O ( k 2 n ) and O ( n ⋅ log n ) respectively for any constant k and for computing a minimum spanning forest O ( log n ) . All these time bounds we reduce to O ( 1 ) . Every presented algorithm determines a solution asymptotically as fast as the best corresponding algorithm up to date in the classical RAM model, which therefore cannot convert the advantage of unlimited memory and random access into superior computing times for these problems.
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ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2007.06.004