Decomposing manifolds into Cartesian products

Cartesian Products of Contractible Open Manifolds

Composing Navigation Functions on Cartesian Products of Manifolds with Boundary

Given two compact, simply connected manifolds with boundary, and a navigation function (NF) on each manifold, this paper presents a simple composition law that yields a new NF on the cross product space. The method provides tunable “hooks” for shaping the new potential function while still guaranteeing obstacle avoidance and essentially global convergence. The composition law is associative, an...

Embedding Cartesian Products of Graphs into De Bruijn Graphs Embedding Cartesian Products of Graphs into De Bruijn Graphs

(m 2) of nontrivial connected graphs G i and the n-dimensional base B de Bruijn graph D = D B (n), we investigate whether or not there exists a spanning subgraph of D which is isomorphic to G. We show that G is never a spanning subgraph of D when n is greater than three or when n equals three and m is greater than two. For n = 3 and m = 2, we can show for wide classes of graphs that G cannot be...

Decomposing Cavities in Digital Volumes into Products of Cycles

The homology of binary 3–dimensional digital images (digital volumes) provides concise algebraic description of their topology in terms of connected components, tunnels and cavities. Homology generators corresponding to these features are represented by nontrivial 0– cycles, 1–cycles and 2–cycles, respectively. In the framework of cubical representation of digital volumes with the topology that...

Embedding Cartesian Products of Graphs into de Bruijn Graphs

Integration of concepts for the parallelization of image processing algorithms into parallel compiler technology. Abstract Given a Cartesian product G = G 1 : : : G m (m 2) of nontrivial connected graphs G i and the n{dimensional base B de Bruijn graph D = D B (n), it is investigated whether or not G is a spanning subgraph of D. Special attention is given to graphs G 1 : : : G m which are relev...