Contemplations on testing graph properties

Abstract

This article documents two programmatic comments regarding testing graph properties, which I made during the Dagstuhl workshop on Sublinear-Time Algorithms (July 2005). The first comment advocates paying more attention to the dependence of the tester's complexity on the proximity parameter. The second comment advocates paying more attention to the question of testing general graphs (rather than dense or bounded-degree ones). In addition, this article includes a suggestion to view and discuss property testing within the framework of promise problems. © 2011 Springer-Verlag Berlin Heidelberg.