Fractional cascading simplified

Abstract

We give an alternate implementation of the fractional cascading data-structure of Chazelle and Guibas to do iterative search for a key in multiple ordered lists. The construction of our data-structure uses randomization and simplifies the algorithm of Chazelle and Guibas vastly making it practical to implement. Although our bounds are asymptotically similar to the earlier ones, there are improvements in the constant factors. Our analysis is novel and captures some of the inherent difficulties associated with the fractional casading data structure. In particular, we use tools from branching process theory and derive some useful asymptotic bounds. The probability of deviation from the expected performance bounds decreases rapidly with number of keys.

Part of this research was done when the author was a post-doctoral Member of Technical Staff at AT&T Bell Labs, Murray Hill, NJ during the year 1990–1991