A new framework for designing parallel algorithms on series parallel graphs

The authors propose a novel framework for designing efficient parallel algorithms on series parallel graphs. Recently, a novel approach for recognizing series parallel graphs was presented by D. Eppstein. Eppstein explored characterizations of the ear decomposition of series parallel graphs, which can be identified efficiently, in parallel. The authors extend Eppstein's results and show in a unified manner how to solve problems on series parallel graphs efficiently, in parallel, by finding a special ear decomposition of the graph. They demonstrate the utility of their novel framework by presenting O(log n) concurrent read exclusive write (CREW) parallel random access machine (PRAM) algorithms for the construction of a depth-first spanning tree, st-numbering, and a breadth-first spanning tree on series parallel graphs.<>