A Model Classifying Algorithms as Inherently Sequential with Applications to Graph Searching

A model is proposed that can be used to classify algorithms as inherently sequential. The model captures the internal computations of algorithms. Previous work in complexity theory has focused on the solutions algorithms compute. Direct comparison of algorithms within the framework of the model is possible. The model is useful for identifying hard to parallelize constructs that should be avoided by parallel programmers. The model's utility is demonstrated via applications to graph searching. A stack breadthrst search (BFS) algorithm is analyzed and proved inherently sequential. The proof technique used in the reduction is a new one. The result for stack BFS sharply contrasts a result showing that a queue based BFS algorithm is in NC. An NC algorithm to compute greedy depthrst search numbers in a dag is presented, and a result proving that a combination search strategy called breadth-depth search is inherently sequential is also given. 3 List of Symbols I use fractions, superscripts, overlines, boldface, underlines, subcripts, and other combinations of the following symbols. abcdefghijklmnopqrstuvwxyz ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz ABCDEFGHIJKLMNOPQRSTUVWXYZ 1234567890 : \, ; ? " . < > ( ) ( ) [ ] / ' + k1 k2 2 S 0 NC : : : ; + | 1 = jxj log n j 6 = f g ( ) () * e d h i 4