We study the static and dynamic planar range skyline reporting problem in the external memory model with block size B, under a linear space budget. The problem asks for an O(n/B) space data structure that stores n points in the plane, and supports reporting the k maximal input points (a.k.a. skyline) among the points that lie within a givenone of its edges is grounded, two variants arise: topopen for β2 = ∞ and left-open for α1 = −∞ (symmetrically bottom-open and right-open) queries.We present optimal static data structures for top-open queries, for the cases where the universe is R 2 , a U × U grid, and rank space [O(n)] 2 . We also show that left-open queries are harder, as they require Ω((n/B) + k/B) I/Os for > 0, when only linear space is allowed. We show that the lower bound is tight, by a structure that supports 4-sided queries in matching complexities. Interestingly, these lower and upper bounds coincide with those of the planar orthogonal range reporting problem, i.e., the skyline requirement does not alter the problem difficulty at all! Finally, we present the first dynamic linear space data structure that supports top-open queries in O(log 2B n + k/B 1− ) and updates in O(log 2B n) worst case I/Os, for ∈ [0, 1]. This also yields a linear space data structure for 4-sided queries with optimal query I/Os and O(log(n/B)) amortized update I/Os. We consider of independent interest the main component of our dynamic structures, a new realtime I/O-efficient and catenable variant of the fundamental structure priority queue with attrition by Sundar. * The full version is found on http://arxiv.org under the same title.

Abstract. In this paper we present an implicit dictionary with the working set property i.e. a dictionary supporting insert(e), delete(x) and predecessor(x) in O(log n) time and search(x) in O(log ) time, where n is the number of elements stored in the dictionary and is the number of distinct elements searched for since the element with key x was last searched for. The dictionary stores the elements in an array of size n using no additional space. In the cache-oblivious model the operations insert(e), delete(x) and predecessor(x) cause O(log B n) cache-misses and search(x) causes O(log B ) cache-misses.

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