How perfect are perfect vortex beams?

How Practice Makes Perfect

Perfect Constraints Are Tractable

By using recent results from graph theory, including the Strong Perfect Graph Theorem, we obtain a unifying framework for a number of tractable classes of constraint problems. These include problems with chordal microstructure; problems with chordal microstructure complement; problems with tree structure; and the “all-different” constraint. In each of these cases we show that the associated mic...

Generation of perfect vortex and vector beams based on Pancharatnam-Berry phase elements

Perfect vortex beams are the orbital angular momentum (OAM)-carrying beams with fixed annular intensities, which provide a better source of OAM than traditional Laguerre-Gaussian beams. However, ordinary schemes to obtain the perfect vortex beams are usually bulky and unstable. We demonstrate here a novel generation scheme by designing planar Pancharatnam-Berry (PB) phase elements to replace al...

Antiwebs are rank-perfect

We discuss a nested collection of three superclasses of perfect graphs: near-perfect, rank-perfect, and weakly rank-perfect graphs. For that we start with the description of the stable set polytope for perfect graphs and allow stepwise more general facets for the stable set polytopes of the graphs in each superclass. Membership in those three classes indicates how far a graph is away from being...

How Good is Almost Perfect?

Heuristic search using algorithms such as A and IDA is the prevalent method for obtaining optimal sequential solutions for classical planning tasks. Theoretical analyses of these classical search algorithms, such as the well-known results of Pohl, Gaschnig and Pearl, suggest that such heuristic search algorithms can obtain better than exponential scaling behaviour, provided that the heuristics ...