Paper Info
Title
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 single-pass 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 1/4-th of the total number of constraints.The inspiration for our work is a lower bound of Kapralov, Khanna, and Sudan (SODAu002715) 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 single-pass stream, within a factor better than 7/8 requires polynomial space.
Year
Venue
Field
2017
APPROX-RANDOM
Discrete mathematics,Combinatorics,Arity,Streaming algorithm,Upper and lower bounds,Directed graph,Constraint satisfaction problem,PSPACE,Mathematics,Maximum cut,Special case
DocType
Citations 
PageRank 
Conference
0
0.34
References 
Authors
0
3
Name
Order
Citations
PageRank
V. Guruswami13205247.96
Ameya Velingker2354.95
Santhoshini Velusamy312.05