A faster parallel connectivity algorithm on cographs

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 G can be optimally found in O(log log log (G)) time using O( (n+m) log log log (G) ) processors on a common CRCW PRAM, or in O(log (G)) time using O( (n+m) log (G) ) processors on an EREW PRAM, where (G) is the maximum degree of G, and n and m respectively are the numbers of vertices and edges of G. These are faster than the previously best known result on general graphs. c © 2006 Elsevier Ltd. All rights reserved.