A Note on Adaptivity in Testing Properties of Bounded Degree Graphs

We show that in the bounded degree model for graph property testing, adaptivity is essential. An algorithm is non-adaptive if it makes all queries to the input before receiving any answers. We call a property non-trivial if it does not depend only on the degree distribution of the nodes. We show that every tester for a non-trivial property that makes o ( n/d) queries to the input graph on n vertices of degree at most d has to be adaptive.

• Type: Journal
• Year: 2006
• Where: ECCC
• Authors: Sofya Raskhodnikova, Adam Smith
• Keywords: Degree Model, ECCC 2006, Graph Property Testing, Non-trivial