On the Complexity of Matroid Isomorphism Problem

We study the complexity of testing if two given matroids are isomorphic. The problem is easily seen to be in Σ p 2. In the case of linear matroids, which are represented over polynomially growing fields, we note that the problem is unlikely to be Σ p 2-complete and is coNP-hard. We show that when the rank of the matroid is bounded by a constant, linear matroid isomorphism, and matroid isomorphism are both polynomial time many-one equivalent to graph isomorphism. We give a polynomial time Turing reduction from graphic matroid isomorphism problem to the graph isomorphism problem. Using this, we are able to show that graphic matroid isomorphism testing for planar graphs can be done in deterministic polynomial time. We then give a polynomial time many-one reduction from bounded rank matroid isomorphism problem to graphic matroid isomorphism, thus showing that all the above problems are polynomial time equivalent. Further, for linear and graphic matroids, we prove that the automorphism ...

• Type: Journal
• Year: 2011
• Where: MST
• Authors: B. V. Raghavendra Rao, Jayalal M. N. Sarma
• Keywords: Graph Isomorphism Problem, Hardware, Isomorphism Problems, MST 2011, Polynomial Time Turing