Are Pointer-Based Parallel Algorithms Realistic?

Abstract

Most if not all the recent theoretical work in parallel algorithm design has focus on what I shall refer to as pointer-based algorithm design. By this, I mean those algorithms that spend most of their time chasing pointers. Included in pointer-based sequential problems/algorithms are most graph algorithms such as depth-first search, breadth-first search, and maximum flow. These problems are know to be parallelizable. However, the algorithms do not use pointers, but rather rely on dense matrix operations and thus use an unrealistic number of processors. The theory community realizes that these algorithms at the present time are not efficient. On the other hand, many graph problems can be performed in parallel with only a modest increase in total work done, ie, (time) X (number of processors). These problems graph connectivity, finding maximal independent sets in a graph, and list ranking. Algorithms for these problem are often referred to as processor efficient algorithms, modestly known as “optimal” algorithms. There is a substantial effort underway in the theory community to find additional optimal algorithms. All the algorithms found so far use pointerchasing to decrease the number of processors used.