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Description

We initiate the study of testing properties of images that correspond to {em sparse/} $0/1$-valued matrices of size $n imes n$. Our study is related to but different from the study initiated by Raskhodnikova ({em Proceedings of RANDOM, 2003/}), where the images correspond to {em dense/} $0/1$-valued matrices. Specifically, while distance between images in the model studied by Raskhodnikova is the fraction of entries on which the images differ taken with respect to all $n^2$ entries, the distance measure in our model is defined by the fraction of such entries taken with respect to the actual number of $1$'s in the matrix. We study several natural properties: connectivity, convexity, monotonicity, and being a line. In all cases we give testing algorithms with sublinear complexity, and in some of the cases we also provide corresponding lower bounds.

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