A faster hafnian formula for complex matrices and its benchmarking on a supercomputer

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Abstract

We introduce new and simple algorithms for the calculation of the number of perfect matchings of complex weighted, undirected graphs with and without loops. Our compact formulas for the hafnian and loop hafnian of n × n complex matrices run in O(n32n/2) time, are embarrassingly parallelizable and, to the best of our knowledge, are the fastest exact algorithms to compute these quantities. Despite our highly optimized algorithm, numerical benchmarks on the Titan supercomputer with matrices up to size 56 × 56 indicate that one would require the 288,000 CPUs of this machine for about 6 weeks to compute the hafnian of a 100 × 100 matrix.

Detaljer

Författare
Enheter & grupper
Externa organisationer
  • Xanadu
Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Diskret matematik
  • Signalbehandling
  • Data- och informationsvetenskap

Nyckelord

Originalspråkengelska
Artikelnummer1.11
Antal sidor17
TidskriftACM Journal of Experimental Algorithmics
Volym24
Utgivningsnummer1
StatusPublished - 2019 jun
PublikationskategoriForskning
Peer review utfördJa