A simple linear-time algorithm for generating auxiliary 3-edge-connected subgraphs

A linear-time algorithm for generating auxiliary subgraphs for the 3-edge-connected components of a connected multigraph is presented. The algorithm uses an innovative graph contraction operation and makes only one pass over the graph. By contrast, the previously best-known algorithms make multiple passes over the graph to decompose it into its 2-edge-connected components or 2-vertex-connected components, then its 3-edge-connected components or 3-vertex-connected components, and then construct a cactus representation for the 2-cuts to generate the auxiliary subgraphs for the 3-edge-connected components.Comment: 21 pages, 1 figur

Guardians, Start of a Light Novel Series

The fictional story of Edward Alfred and his friends, a group of teens known simply as the Guardians. They safeguard the planet in secrecy to protect humanity until it is ready to exit childhood and enter the greater interstellar community

Crescent Waves in Optical Cavities

We theoretically and experimentally generate stationary crescent surface solitons pinged to the boundary of a micro-structured vertical cavity surface emission laser by using the intrinsic cavity mode as a background potential. Instead of a direct transition from linear to nonlinear cavity modes, we demonstrate the existence of a symmetry-breaking crescent waves without any analogs in the linear limit. Our results provide an alternative and general method to control lasing characteristics as well as to study optical surface waves.Comment: 3 figure