We also need the well-known notion of the clique complex or flag complex Cliq(G) of a simple graph G: it is the simplicial complex whose vertices are the vertices of G and whose simplices
are the subsets of vertices that induce a complete subgraph.
Lipschitz bound over simplices
based on the function values at the vertices and the radius of the circumscribed sphere
Let K be the set of small n-dimensional simplices
constructed by partition of an n-dimensional simplex [DELTA].
1] represent the number of vertices, respective simplices
, of the triangulation.
However, Ghrist and Baryshnikov have shown that it's possible to calculate this sum using a variation of the Euler characteristic that counts the points, lines, and other simplices
in the Rips complex not just once each but according to how many boats that each sensor can see.
They are of the same optimal order as a standard finite element method on an auxiliary finer mesh consisting of simplices
A triangulation of a point configuration A is a collection T of simplices
with vertices in A, which we call cells, that cover the convex hull of A and such that any pair of simplices
of T intersects in a common face.
of K as the simplicial complex with vertices the barycenters of the simplices
of K, and whose simplices
are finite non-empty collections of barycentres of simplices
totally ordered by the face relations of K.
In n-dimensions, a triangulation of a set of points V is a set of non-intersecting simplices
T(V), whose vertices form V, and whose union completely fills the convex hull of V.
A polytope P is simplicial if all proper faces of P are simplices
H] be a subdivision of [OMEGA] into simplices
The feasible region should be initially covered by simplices
for simplex-based branch-and-bound.