On the geometric graph isomorphism problem

Abstract

Given two finite subsets A, B of R k (of C k ) we test in time ( e k 4 nl) O(1) whether there exists an isometry f of R k (resp. of C k ) 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 ∪ B. In contrast to the trivial ( n k l) O(1) -test, our algorithm is polynomial time not only for a fixed k but also for k = O( 2√logn) .