Adaptive Data Structures for Permutations and Binary Relations

We present new data structures for representing binary relations in an adaptive way, that is, for certain classes of inputs we achieve space below the general information theoretic lower bound, while achieving reasonable space complexities in the worst case. Our approach is derived from a geometric data structure [Arroyuelo et al., TCS 2011]. When used for representing permutations, it converges to a previously known adaptive representation [Barbay and Navarro, STACS 2009]. However, this new way of approaching the problem shows that we can support range searching in the adaptive representation. We extend this approach to representing binary relations, where no other adaptive representations using this chain decomposition have been proposed.

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