Graph algorithms: parallelization and scalability

For computations on large-scale graphs, one often resorts to parallel algorithms. However, parallel algorithms are difficult to write, debug and analyze. Worse still, it is difficult to make algorithms parallelly scalable, such that the more machines are used, the faster the algorithms run. Indeed, it is not yet known whether any PTIME computational problems admit parallelly scalable algorithms on shared-nothing systems. Is it possible to parallelize sequential graph algorithms and guarantee convergence at the correct results as long as the sequential algorithms are correct? Moreover, does a PTIME parallelly scalable problem exist on shared-nothing systems? This position paper answers both questions in the affirmative.