Property testing and its connection to learning and approximation

The authors study the question of determining whether an unknown function has a particular property or is /spl epsiv/-far from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the function on instances of its choice. First, they establish some connections between property testing and problems in learning theory. Next, they focus on testing graph properties, and devise algorithms to test whether a graph has properties such as being k-colorable or having a /spl rho/-clique (clique of density /spl rho/ w.r.t. the vertex set). The graph property testing algorithms are probabilistic and make assertions which are correct with high probability utilizing only poly(1//spl epsiv/) edge-queries into the graph, where /spl epsiv/ is the distance parameter. Moreover, the property testing algorithms can be used to efficiently (i.e., in time linear in the number of vertices) construct partitions of the graph which correspond to the property being tested, if it holds for the input graph.