Blocking for external graph searching

In this paper we consider the problem of using disk blocks efficiently in searching graphs that are too large to fit in internal memory. Our model allows a vertex to be represented any number of times on the disk in order to take advantage of redundancy. We give matching upper and lower bounds for completed-ary trees andd-dimensional grid graphs, as well as for classes of general graphs that intuitively speaking have a close to uniform number of neighbors around each vertex. We also show that, for the special case of grid graphs blocked with isothetic hypercubes, there is a provably better speed-up if even a small amount of redundancy is permitted.Support was provided in part by an IBM Graduate Fellowship, by NSF Research Grants CCR-9007851 and IRI-9116451, and by Army Research Office Grant DAAL03-91-G-0035.Support was provided in part by NSF Grants CCR-9003299, CCR-9300079, and IRI-9116843, and by NSF/DARPA Grant CCR-8908092.Support was provided in part by a National Science Foundation Presidential Young Investigator Award CCR-9047466 with matching funds from IBM, by NSF Research Grant CCR-9007851, and by Army Research Office Grant DAAL03-91-G-0035.