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The top-k data structure at each node is constructed based on the values existing in the subtrees of that node and is meant to answer one-sided range top-k queries. Please note that for a one-dimensional array A {\displaystyle A} , a range tree can be constructed by dividing A {\displaystyle A} into two halves and recursing on both halves ...
In 2016, Blelloch et al. formally proposed the join-based algorithms, and formalized the join algorithm for four different balancing schemes: AVL trees, red–black trees, weight-balanced trees and treaps. In the same work they proved that Adams' algorithms on union, intersection and difference are work-optimal on all the four balancing schemes.
Fundamentally based index funds have higher expense ratios than the traditional capitalization weighted index funds. For example, the Powershares fundamentally based ETFs have an expense ratio of 0.6% (the U.S. index ETF has an expense ratio of 0.39%) while the PIMCO Fundamental IndexPLUS TR Fund charges 1.14% in annual expenses. [25]