External-memory graph algorithms

We present a collection of new techniques for designing and analyzing efficient external-memory algorithms for graph problems and illustrate how these techniques can be applied to a wide variety of specific problems. Our results include: -neighboring. We present a simple for deriving external-memory lower bounds reductions from a problem we call the “proximate neighbors” problem. We use this technique to derive non-trivial lower bounds for such problems as list ranking, expression tree evaluation, and connected components. PRAM simulation. We give methods for efficiently PRAM computations in external memory, even for some cases in which the PRAM algorithm is not work-optimal. We apply this to derive a number of optimal (and simple) external-memory graph algorithms. -forward processing. We present a general for evaluating circuits (or “circuit-like”) in external memory. We also usethis in a deterministic list ranking algorithm. 3-coloring of a cycle. We give optimal methods for 3-coloring a cycle, can be used as a subroutine for finding large sets for list ranking. Our ideas go a straightforward PRAM simulation, and be of independent interest. depth-first search. We discuss a method performing depth first search and solving related efficiently in external memory. Our can be used in conjunction with ideas to Ullman and Yannakakis in order to solve problems involving closed semi-ring computations even when their assumption that vertices fit in main memory does not hold. techniques apply to a number of problems, including list ranking, which we discuss in detail, finding Euler tours, expression-tree evaluation, centroid decomposition of a tree, least-common ancestors, minimum spanning tree verification, connected and biconnected components, minimum spanning forest, ear decomposition, topological sorting, reachability, graph drawing, and visibility representation.