Showing papers by "John Iacono published in 2007"
TL;DR: This is the first major progress on Sleator and Tarjan's dynamic optimality conjecture of 1985 that O(1)-competitive binary search trees exist and presents an O(lg lg n)-competitive online binary search tree.
Abstract: We present an $O(\lg \lg n)$-competitive online binary search tree, improving upon the best previous (trivial) competitive ratio of $O(\lg n)$. This is the first major progress on Sleator and Tarjan’s dynamic optimality conjecture of 1985 that $O(1)$-competitive binary search trees exist.
76 citations
TL;DR: A dynamic comparison-based search structure that supports insertions, deletions, and searches within the unified bound that generalizes the working-set and dynamic-finger properties of splay trees.
50 citations
TL;DR: It is proved that, unlike persistence, efficient retroactivity is not always achievable, so it is going on to present several specific retroactive data structures.
Abstract: We introduce a new data structuring paradigm in which operations can be performed on a data structure not only in the present, but also in the past. In this new paradigm, called retroactive data structures, the historical sequence of operations performed on the data structure is not fixed. The data structure allows arbitrary insertion and deletion of operations at arbitrary times, subject only to consistency requirements. We initiate the study of retroactive data structures by formally defining the model and its variants. We prove that, unlike persistence, efficient retroactivity is not always achievable. Thus, we present efficient retroactive data structures for queues, doubly ended queues, priority queues, union-find, and decomposable search structures.
25 citations
TL;DR: An O(n log k)-time algorithm for finding a ham-sandwich geodesic is presented and it is shown that this algorithm is optimal in the algebraic computation tree model when parameterizing the running time with respect to n and k.
Abstract: Let P be a simple polygon with m vertices, k of which are reflex, and which contains r red points and b blue points in its interior. Let n = m + r + b. A ham-sandwich geodesic is a shortest path in P between two points on the boundary of P that simultaneously bisects the red points and the blue points. We present an O(n log k)-time algorithm for finding a ham-sandwich geodesic. We also show that this algorithm is optimal in the algebraic computation tree model when parameterizing the running time with respect to n and k.
16 citations
Proceedings Article•
01 Jan 2007
TL;DR: The smallest square that wraps the unit sphere is characterized, it is shown that a 0.1% smaller equilateral triangle suffices, and a 20% smaller shape is found that still tiles the plane.
Abstract: We study wrappings of the unit sphere by a piece of paper (or, perhaps more accurately, a piece of foil). Such wrappings differ from standard origami because they require infinitely many infinitesimally small “folds” in order to transform the flat sheet into a positive-curvature sphere. Our goal is to find shapes that have small area even when expanded to shapes that tile the plane. We characterize the smallest square that wraps the unit sphere, show that a 0.1% smaller equilateral triangle suffices, and find a 20% smaller shape that still tiles the plane.
1 citations