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- Hicham El-Zein, J. Ian Munro, Siwei Yang
- ISAAC
- 2015

- Hicham El-Zein, J. Ian Munro, Venkatesh Raman
- ISAAC
- 2014

- Hicham El-Zein, Moshe Lewenstein, J. Ian Munro, Venkatesh Raman, Timothy M. Chan
- Algorithmica
- 2016

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)

In this thesis, we address the problem of quickly inverting the standard representation of a permutation on n elements in place. First, we present a naive algorithm to do it using O(log n) extra bits in O(n) time in the worst case. We then improve that algorithm, using a small bit vector, to use O( √ n) extra bits in O(n √ n) time. Using a different… (More)

- Hicham El-Zein, J. Ian Munro, Matthew Robertson
- ISAAC
- 2016

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)

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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