Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1145/2629429 | ACM Trans. Algorithms |
Field | DocType | Volume |
Discrete mathematics,Combinatorics,Congruence lattice problem,Lattice (order),Map of lattices,Orthogonal basis,Lattice problem,Lattice (group),Integer lattice,Mathematics,Reciprocal lattice | Journal | 12 |
Issue | Citations | PageRank |
1 | 0 | 0.34 |
References | Authors | |
10 | 6 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Andreas Björklund | 1 | 219 | 16.65 |
| Thore Husfeldt | 2 | 733 | 40.87 |
| Petteri Kaski | 3 | 912 | 66.03 |
| Mikko Koivisto | 4 | 803 | 55.81 |
| Jesper Nederlof | 5 | 294 | 24.22 |
| Pekka Parviainen | 6 | 79 | 8.95 |