Abstract: The algorithm indicated in the title builds on Luks's classical framework and introduces new group theoretic and combinatorial tools. We outline the algorithm, with a focus on the core group theoretic routine ("Local Certificates"). Elements of undergraduate-level group theory such as facility with the concepts involved in the Jordan--Holder theorem will be assumed. An in-depth discussion of the technical details will follow at a subsequent Harvard/MIT/MSR Theory Reading Group at Harvard (Pierce 301) on Wednesday, February 3, 2016, 5:00 - 8:00pm.
Helpful reading: Eugene M. Luks: Isomorphism of graphs of bounded valence can be tested in polynomial time. JCSS 25(1) (1982) 42--65.