A faster parallel connectivity algorithm on cographs

Abstract

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 Δ ( G ) ) time using O ( ( n + m ) log log log Δ ( G ) ) processors on a common CRCW PRAM, or in O ( log Δ ( G ) ) time using O ( ( n + m ) log Δ ( G ) ) processors on an EREW PRAM, where Δ ( 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.