On the geometric graph isomorphism problem Original Research Article

Given two finite subsets A, B of Rk (of Ck) we test in time (ek4 nl)O(1) whether there exists an isometry f of Rk (resp. of Ck) such that f(A) = B where n is the maximum of the cardinalities of A and B, and I is the maximum size of a vector belonging to A union or logical sum B. In contrast to the trivial (nk l)O(1)-test, our algorithm is polynomial time not only for a fixed k but also for k = O(2√logn).