601 research outputs found
simpcomp -- A GAP toolbox for simplicial complexes
simpcomp is an extension (a so called package) to GAP, the well known system
for computational discrete algebra. The package enables the user to compute
numerous properties of (abstract) simplicial complexes, provides functions to
construct new complexes from existing ones and an extensive library of
triangulations of manifolds.Comment: 4 page
Greedy algorithms and poset matroids
We generalize the matroid-theoretic approach to greedy algorithms to the
setting of poset matroids, in the sense of Barnabei, Nicoletti and Pezzoli
(1998) [BNP]. We illustrate our result by providing a generalization of Kruskal
algorithm (which finds a minimum spanning subtree of a weighted graph) to
abstract simplicial complexes
MV-algebras freely generated by finite Kleene algebras
If V and W are varieties of algebras such that any V-algebra A has a reduct
U(A) in W, there is a forgetful functor U: V->W that acts by A |-> U(A) on
objects, and identically on homomorphisms. This functor U always has a left
adjoint F: W->V by general considerations. One calls F(B) the V-algebra freely
generated by the W-algebra B. Two problems arise naturally in this broad
setting. The description problem is to describe the structure of the V-algebra
F(B) as explicitly as possible in terms of the structure of the W-algebra B.
The recognition problem is to find conditions on the structure of a given
V-algebra A that are necessary and sufficient for the existence of a W-algebra
B such that F(B) is isomorphic to A. Building on and extending previous work on
MV-algebras freely generated by finite distributive lattices, in this paper we
provide solutions to the description and recognition problems in case V is the
variety of MV-algebras, W is the variety of Kleene algebras, and B is finitely
generated--equivalently, finite. The proofs rely heavily on the Davey-Werner
natural duality for Kleene algebras, on the representation of finitely
presented MV-algebras by compact rational polyhedra, and on the theory of bases
of MV-algebras.Comment: 27 pages, 8 figures. Submitted to Algebra Universali
Building Efficient and Compact Data Structures for Simplicial Complexes
The Simplex Tree (ST) is a recently introduced data structure that can
represent abstract simplicial complexes of any dimension and allows efficient
implementation of a large range of basic operations on simplicial complexes. In
this paper, we show how to optimally compress the Simplex Tree while retaining
its functionalities. In addition, we propose two new data structures called the
Maximal Simplex Tree (MxST) and the Simplex Array List (SAL). We analyze the
compressed Simplex Tree, the Maximal Simplex Tree, and the Simplex Array List
under various settings.Comment: An extended abstract appeared in the proceedings of SoCG 201
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