Raising Permutations to Powers in Place

Given a permutation of n elements, stored as an array, we address the problem of replacing the permutation by its kth 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 is then generalized to the situation in which the permutation is to be replaced by its kth power. An algorithm whose worst case running time is O(n lg n) and uses O(lg^2 n + min{k lg n, n^{3/4 + epsilon}}) additional bits is presented

Space Efficient Data Structures and Algorithms in the Word-RAM Model

In modern computation the volume of data-sets has increased dramatically. Since the majority of these data-sets are stored in internal memory, reducing their storage requirement is an important research topic. One way of reducing storage is using succinct and compact data structures which maintain the data in compressed form with extra data structures over it in a way that allows efficient access and query of the data. In this thesis we study space-efficient data structures for various combinatorial objects. We focus on succinct and compact data structures. Succinct data structures are data structures whose size is within the information theoretic lower bound plus a lower order term, whereas compact data structures are data structures whose size is a constant factor from the information theoretic lower bound