Fast Zeta Transforms for Lattices with Few Irreducibles

Tutkimustuotos: Lehtiartikkelivertaisarvioitu

Tutkijat

Organisaatiot

  • Lund University
  • University of Helsinki
  • Utrecht University
  • KTH Royal Institute of Technology

Kuvaus

We investigate fast algorithms for changing between the standard basis and an orthogonal basis of idempotents for Mobius algebras of finite lattices. We show that every lattice with v elements, n of which are nonzero and join-irreducible (or, by a dual result, nonzero and meet-irreducible), has arithmetic circuits of size O(vn) for computing the zeta transform and its inverse, thus enabling fast multiplication in the Mobius algebra. Furthermore, the circuit construction in fact gives optimal (up to constants) monotone circuits for several lattices of combinatorial and algebraic relevance, such as the lattice of subsets of a finite set, the lattice of set partitions of a finite set, the lattice of vector subspaces of a finite vector space, and the lattice of positive divisors of a positive integer.

Yksityiskohdat

AlkuperäiskieliEnglanti
Artikkeli4
Sivumäärä19
JulkaisuACM Transactions on Algorithms
Vuosikerta12
Numero1
TilaJulkaistu - helmikuuta 2016
OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu
TapahtumaACM-SIAM Symposium on Discrete Algorithms - Kyoto, Japani
Kesto: 17 tammikuuta 201219 tammikuuta 2012
Konferenssinumero: 23

ID: 2007032