Testing Forest-Isomorphism in the Adjacency List Model

Mitsuru Kusumoto, Yuichi Yoshida

Abstract: We consider the problem of testing if two input forests are isomorphic or are far from being so. An algorithm is called an ε-tester for forest-isomorphism if given an oracle access to two forests G and H in the adjacency list model, with high probability, accepts if G and H are isomorphic and rejects if we must modify at least εn edges to make G isomorphic to H. We show an ε-tester for forest-isomorphism with a query complexity polylog(n) and a lower bound of \(\Omega(\sqrt{\log{n}})\). Further, with the aid of the tester, we show that every graph property is testable in the adjacency list model with polylog(n) queries if the input graph is a forest.