Guruswami, Venkatesan ;
Velingker, Ameya ;
Velusamy, Santhoshini
Streaming Complexity of Approximating Max 2CSP and Max Acyclic Subgraph
Abstract
We study the complexity of estimating the optimum value of a Boolean 2CSP (arity two constraint satisfaction problem) in the singlepass streaming setting, where the algorithm is presented the constraints in an arbitrary order. We give a streaming algorithm to estimate the optimum within a factor approaching 2/5 using logarithmic space, with high probability. This beats the trivial factor 1/4 estimate obtained by simply outputting 1/4th of the total number of constraints.
The inspiration for our work is a lower bound of Kapralov, Khanna, and Sudan (SODA'15) who showed that a similar trivial estimate (of factor 1/2) is the best one can do for Max CUT. This lower bound implies that beating a factor 1/2 for Max DICUT (a special case of Max 2CSP), in particular, to distinguish between the case when the optimum is m/2 versus when it is at most (1/4+eps)m, where m is the total number of edges, requires polynomial space. We complement this hardness result by showing that for DICUT, one can distinguish between the case in which the optimum exceeds (1/2+eps)m and the case in which it is close to m/4.
We also prove that estimating the size of the maximum acyclic subgraph of a directed graph, when its edges are presented in a singlepass stream, within a factor better than 7/8 requires polynomial space.
BibTeX  Entry
@InProceedings{guruswami_et_al:LIPIcs:2017:7557,
author = {Venkatesan Guruswami and Ameya Velingker and Santhoshini Velusamy},
title = {{Streaming Complexity of Approximating Max 2CSP and Max Acyclic Subgraph}},
booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
pages = {8:18:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959770446},
ISSN = {18688969},
year = {2017},
volume = {81},
editor = {Klaus Jansen and Jos{\'e} D. P. Rolim and David Williamson and Santosh S. Vempala},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/7557},
URN = {urn:nbn:de:0030drops75570},
doi = {10.4230/LIPIcs.APPROXRANDOM.2017.8},
annote = {Keywords: approximation algorithms, constraint satisfaction problems, optimization, hardness of approximation, maximum acyclic subgraph}
}
11.08.2017
Keywords: 

approximation algorithms, constraint satisfaction problems, optimization, hardness of approximation, maximum acyclic subgraph 
Seminar: 

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)

Issue date: 

2017 
Date of publication: 

11.08.2017 