Fast zeta transforms for lattices with few irreducibles

Andreas Björklund, Thore Husfeldt, Petteri Kaski, Mikko Koivisto, Jesper Nederlof, Pekka Parviainen

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

15 Citaten (Scopus)

Samenvatting

We investigate fast algorithms for changing between the standard basis and an orthogonal basis of idempotents for Möbius 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 Möbius 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.

Originele taal-2Engels
Artikelnummer4
Aantal pagina's19
TijdschriftACM Transactions on Algorithms
Volume12
Nummer van het tijdschrift1
DOI's
StatusGepubliceerd - 1 dec. 2015

Vingerafdruk

Duik in de onderzoeksthema's van 'Fast zeta transforms for lattices with few irreducibles'. Samen vormen ze een unieke vingerafdruk.

Citeer dit