John Iacono

Bio: John Iacono is an academic researcher from Université libre de Bruxelles. The author has contributed to research in topics: Data structure & Amortized analysis. The author has an hindex of 24, co-authored 170 publications receiving 2130 citations. Previous affiliations of John Iacono include New York University & Aarhus University.

Grid vertex-unfolding orthostacks

Abstract: An algorithm was presented in [BDD+98] for unfolding orthostacks into one piece without overlap by using arbitrary cuts along the surface. It was conjectured that orthostacks could be unfolded using cuts that lie in a plane orthogonal to a coordinate axis and containing a vertex of the orthostack. We prove the existence of a vertex-unfolding using only such cuts.

Data structures for halfplane proximity queries and incremental voronoi diagrams

Abstract: We consider preprocessing a set S of n points in the plane that are in convex position into a data structure supporting queries of the following form: given a point q and a directed line in the plane, report the point of S that is farthest from (or, alternatively, nearest to) the point q subject to being to the left of line . We present two data structures for this problem. The first data structure uses O(n 1+e ) space and preprocessing time, and answers queries in O(2 1/e logn) time. The second data structure uses O(n log 3 n) space and polynomial preprocessing time, and answers queries in O(log n) time. These are the first solutions to the problem with O(logn) query time and o(n 2 ) space. In the process of developing the second data structure, we develop a new representation of nearest-point and farthest-point Voronoi diagrams of points in convex position. This representation supports insertion of new points in counterclockwise order using only O(log n.) amortized pointer changes, subject to supporting O (log n)-time point-location queries, even though every such update may make ⊖(n) combinatorial changes to the Voronoi diagram. This data structure is the first demonstration that deterministically and incrementally constructed Voronoi diagrams can be maintained in o(n) pointer changes per operation while keeping O(log n)-time point-location queries.

On the hierarchy of distribution-sensitive properties for data structures

Abstract: In this paper new dependencies are added to the hierarchy of the distribution-sensitive properties for data structures. Most remarkably, we prove that the working-set property is equivalent to the unified-bound property; a fact that had gone unnoticed since the introduction of such bounds in the Eighties by Sleator and Tarjan.

Subquadratic encodings for point configurations

Abstract: For many algorithms dealing with sets of points in the plane, the only relevant information carried by the input is the combinatorial configuration of the points: the orientation of each triple of points in the set (clockwise, counterclockwise, or collinear). This information is called the order type of the point set. In the dual, realizable order types and abstract order types are combinatorial analogues of line arrangements and pseudoline arrangements. Too often in the literature we analyze algorithms in the real-RAM model for simplicity, putting aside the fact that computers as we know them cannot handle arbitrary real numbers without some sort of encoding. Encoding an order type by the integer coordinates of a realizing point set is known to yield doubly exponential coordinates in some cases. Other known encodings can achieve quadratic space or fast orientation queries, but not both. In this contribution, we give a compact encoding for abstract order types that allows an efficient query of the orientation of any triple: the encoding uses \( O(n^2) \) bits and an orientation query takes \(O(\log n)\) time in the word-RAM model with word size \(w \geq \log n\). This encoding is space-optimal for abstract order types. We show how to shorten the encoding to \(O(n^2 {(\log\log n)}^2 / \log n)\) bits for realizable order types, giving the first subquadratic encoding for those order types with fast orientation queries. We further refine our encoding to attain \(O(\log n/\log\log n)\) query time at the expense of a negligibly larger space requirement. In the realizable case, we show that all those encodings can be computed efficiently. Finally, we generalize our results to the encoding of point configurations in higher dimension.

Triangulating a simple polygon in linear time

Abstract: We give a deterministic algorithm for triangulating a simple polygon in linear time. The basic strategy is to build a coarse approximation of a triangulation in a bottom-up phase and then use the information computed along the way to refine the triangulation in a top-down phase. The main tools used are the polygon-cutting theorem, which provides us with a balancing scheme, and the planar separator theorem, whose role is essential in the discovery of new diagonals. Only elementary data structures are required by the algorithm. In particular, no dynamic search trees, of our algorithm.

Programming curvature using origami tessellations

Abstract: Origami describes rules for creating folded structures from patterns on a flat sheet, but does not prescribe how patterns can be designed to fit target shapes. Here, starting from the simplest periodic origami pattern that yields one-degree-of-freedom collapsible structures-we show that scale-independent elementary geometric constructions and constrained optimization algorithms can be used to determine spatially modulated patterns that yield approximations to given surfaces of constant or varying curvature. Paper models confirm the feasibility of our calculations. We also assess the difficulty of realizing these geometric structures by quantifying the energetic barrier that separates the metastable flat and folded states. Moreover, we characterize the trade-off between the accuracy to which the pattern conforms to the target surface, and the effort associated with creating finer folds. Our approach enables the tailoring of origami patterns to drape complex surfaces independent of absolute scale, as well as the quantification of the energetic and material cost of doing so.