TY - JOUR

T1 - Computing the Tutte polynomial of lattice path matroids using determinantal circuits

AU - Morton, Jason

AU - Turner, Jacob

N1 - Funding Information:
This work was partially supported by the Air Force Office of Scientific Research under contract FA8650-13-M-1563 . We are grateful to two anonymous reviewers for helpful and detailed comments.

PY - 2015/9/20

Y1 - 2015/9/20

N2 - We give a quantum-inspired O(n4) algorithm computing the Tutte polynomial of a lattice path matroid, where n is the size of the ground set of the matroid. Furthermore, this can be improved to O(n2) arithmetic operations if we evaluate the Tutte polynomial on a given input, fixing the values of the variables. The best existing algorithm, found in 2004, was O(n5), and the problem has only been known to be polynomial time since 2003. Conceptually, our algorithm embeds the computation in a determinant using a recently demonstrated equivalence of categories useful for counting problems such as those that appear in simulating quantum systems.

AB - We give a quantum-inspired O(n4) algorithm computing the Tutte polynomial of a lattice path matroid, where n is the size of the ground set of the matroid. Furthermore, this can be improved to O(n2) arithmetic operations if we evaluate the Tutte polynomial on a given input, fixing the values of the variables. The best existing algorithm, found in 2004, was O(n5), and the problem has only been known to be polynomial time since 2003. Conceptually, our algorithm embeds the computation in a determinant using a recently demonstrated equivalence of categories useful for counting problems such as those that appear in simulating quantum systems.

UR - http://www.scopus.com/inward/record.url?scp=84941600003&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84941600003&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2015.07.042

DO - 10.1016/j.tcs.2015.07.042

M3 - Article

AN - SCOPUS:84941600003

VL - 598

SP - 150

EP - 156

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

M1 - 10391

ER -