Computing the Tutte polynomial of lattice path matroids using determinantal circuits

Jason Ryder Morton, Jacob Turner

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Article number10391
Pages (from-to)150-156
Number of pages7
JournalTheoretical Computer Science
Volume598
DOIs
StatePublished - Sep 20 2015

Fingerprint

Tutte Polynomial
Lattice Paths
Matroid
Polynomials
Networks (circuits)
Computing
Counting Problems
Quantum Systems
Polynomial time
Determinant
Equivalence
Evaluate

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

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Computing the Tutte polynomial of lattice path matroids using determinantal circuits. / Morton, Jason Ryder; Turner, Jacob.

In: Theoretical Computer Science, Vol. 598, 10391, 20.09.2015, p. 150-156.

Research output: Contribution to journalArticle

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