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Fast Zeta Transforms for Lattices with Few Irreducibles
Vise andre og tillknytning
2016 (engelsk)Inngår i: ACM Transactions on Algorithms, ISSN 1549-6325, E-ISSN 1549-6333, Vol. 12, nr 1, artikkel-id 4Artikkel i tidsskrift (Fagfellevurdert) Published
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Abstract [en]

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.

sted, utgiver, år, opplag, sider
Association for Computing Machinery (ACM), 2016. Vol. 12, nr 1, artikkel-id 4
Emneord [en]
Arithmetic circuit, fast multiplication, lattice, zeta transform, Mobius transform, Mobius inversion, semigroup algebra
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Identifikatorer
URN: urn:nbn:se:kth:diva-184971DOI: 10.1145/2629429ISI: 000371364600004Scopus ID: 2-s2.0-84954312180OAI: oai:DiVA.org:kth-184971DiVA, id: diva2:917799
Konferanse
23rd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), JAN 17-19, 2012, Kyoto, JAPAN
Forskningsfinansiär
Science for Life Laboratory - a national resource center for high-throughput molecular bioscience
Merknad

QC 20160407

Tilgjengelig fra: 2016-04-07 Laget: 2016-04-07 Sist oppdatert: 2018-01-10bibliografisk kontrollert

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