Abstract
We present an improved deterministic algorithm for Maximum Cardinality Matching on general graphs in the SemiStreaming Model. In the SemiStreaming Model, a graph is presented as a sequence of edges, and an algorithm must access the edges in the given sequence. It can only use O(n polylog n) space to perform computations, where n is the number of vertices of the graph. If the algorithm goes over the stream k times, it is called a kpass algorithm. In this model, McGregor [McGregor, 2005] gave the currently best known randomized (1+epsilon)approximation algorithm for maximum cardinality matching on general graphs, that uses (1/epsilon)^{O(1/epsilon)} passes. Ahn and Guha [Ahn and Guha, 2013] later gave the currently best known deterministic (1+epsilon)approximation algorithms for maximum cardinality matching: one on bipartite graphs that uses O(log log(1/epsilon)/epsilon^2) passes, and the other on general graphs that uses O(log n *poly(1/epsilon)) passes (note that, for general graphs, the number of passes is dependent on the size of the input). We present the first deterministic algorithm that achieves a (1+epsilon)approximation on general graphs in only a constant number ((1/epsilon)^{O(1/epsilon)}) of passes.
BibTeX  Entry
@InProceedings{tirodkar:LIPIcs:2018:9938,
author = {Sumedh Tirodkar},
title = {{Deterministic Algorithms for Maximum Matching on General Graphs in the SemiStreaming Model}},
booktitle = {38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)},
pages = {39:139:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959770934},
ISSN = {18688969},
year = {2018},
volume = {122},
editor = {Sumit Ganguly and Paritosh Pandya},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/9938},
URN = {urn:nbn:de:0030drops99383},
doi = {10.4230/LIPIcs.FSTTCS.2018.39},
annote = {Keywords: Semi Streaming, Maximum Matching}
}
Keywords: 

Semi Streaming, Maximum Matching 
Seminar: 

38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018) 
Issue Date: 

2018 
Date of publication: 

23.11.2018 