A faster parallel connectivity algorithm on cographs Original Research Article

Cographs are a well-known class of graphs arising in a wide spectrum of practical applications. In this note, we show that the connected components of a cograph GG can be optimally found in View the MathML sourceO(logloglogΔ(G)) time using View the MathML sourceO((n+m)logloglogΔ(G)) processors on a common CRCW PRAM, or in View the MathML sourceO(logΔ(G)) time using View the MathML sourceO((n+m)logΔ(G)) processors on an EREW PRAM, where View the MathML sourceΔ(G) is the maximum degree of GG, and nn and mm respectively are the numbers of vertices and edges of GG. These are faster than the previously best known result on general graphs.