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Using the notions of Q-heaps and fusion trees developed by Fredman and Willard, we develop general transformation techniques to reduce a number of computational geometry problems to their special versions in partially ranked spaces. In particular, we develop a fast fractional cascading technique, which uses linear space and enables sublogarithmic iterative search on catalog trees in the case when the degree of each node is bounded by O(log n), for some constant > 0, where n is the total size ofdoi:10.1137/s0097539703435728 fatcat:zqtvdtkxajcwpgqqrocstd3n5y