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Given a permutation of n elements, stored as an array, we address the problem of replacing the permutation by its k th power. We aim to perform this operation quickly using o(n) bits of extra storage. To this end, we first present an algorithm for inverting permutations that uses O(lg 2 n) additional bits and runs in O(n lg n) worst case time. This result… (More)

Given a partition of an n element set into equivalence classes, we study the problem of assigning unique labels to these elements in order to support the query that asks whether the elements corresponding to two given labels belong to the same equivalence class. This has various applications including for testing whether two vertices are in the same… (More)

Let S be a set of n points in an [n] d grid, such that each point is assigned a color. Given a query range Q = [a 1 , b 1 ] × [a 2 , b 2 ] ×. .. × [a d , b d ], the geometric range mode query problem asks to report the most frequent color (i.e., a mode) of the multiset of colors corresponding to points in S ∩ Q. When d = 1, Chan et al. (STACS 2012 [2]) gave… (More)

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