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.

Proximate point searching

Abstract: In the 2D point searching problem, the goal is to preprocess n points P = {P1,..., pn} in the plane so that, for an online sequence of query points q1, ...,qm, it can quickly be determined which (if any) of the elements of P are equal to each query point qi. This problem can be solved in O(logn) time by mapping the problem to one dimension. We present a data structure that is optimized for answering queries quickly when they are geometrically close to the previous successful query. Specifically, our data structure executes queries in time O(log d(qi-1, qi)), where d is some distance function between two points, and uses O(n logn) space. Our structure works with a variety of distance functions. In contrast, it is proved that, for some of the most intuitive distance functions d, it is impossible to obtain an O (log d(qi-1, qi)) runtime, or any bound that is o(log n).

Subquadratic Algorithms for Algebraic 3SUM

Abstract: The 3SUM problem asks if an input n-set of real numbers contains a triple whose sum is zero. We qualify such a triple of degenerate because the probability of finding one in a random input is zero. We consider the 3POL problem, an algebraic generalization of 3SUM where we replace the sum function by a constant-degree polynomial in three variables. The motivations are threefold. Raz et al. gave an $$O(n^{11/6})$$ upper bound on the number of degenerate triples for the 3POL problem. We give algorithms for the corresponding problem of counting them. Gronlund and Pettie designed subquadratic algorithms for 3SUM. We prove that 3POL admits bounded-degree algebraic decision trees of depth $$O(n^{12/7+\varepsilon })$$ , and we prove that 3POL can be solved in $$O(n^2 {(\log \log n)}^{3/2} / {(\log n)}^{1/2})$$ time in the real-RAM model, generalizing their results. Finally, we shed light on the General Position Testing (GPT) problem: “Given n points in the plane, do three of them lie on a line?”, a key problem in computational geometry: we show how to solve GPT in subquadratic time when the input points lie on a small number of constant-degree polynomial curves. Many other geometric degeneracy testing problems reduce to 3POL.

Proximate planar point location

Abstract: A new data structure is presented for planar point location that executes a point location query quickly if it is spatially near the previous query. Given a triangulation T of size n and a sequence of point location queries A=q1, qm, the structure presented executes qi in time O(log d(qi-1,qi)). The distance function, d, that is used is a two dimensional generalization of rank distance that counts the number of triangles in a region from qi-1 to qi. The data structure uses O(n log log n) space.

Worst-Case Optimal Tree Layout in a Memory Hierarchy

Abstract: Consider laying out a fixed-topology tree of N nodes into external memory with block size B so as to minimize the worst-case number of block memory transfers required to traverse a path from the root to a node of depth D. We prove that the optimal number of memory transfers is

Entropy, triangulation, and point location in planar subdivisions

Abstract: A data structure is presented for point location in connected planar subdivisions when the distribution of queries is known in advance. The data structure has an expected query time that is within a constant factor of optimal. More specifically, an algorithm is presented that preprocesses a connected planar subdivision G of size n and a query distribution D to produce a point location data structure for G. The expected number of point-line comparisons performed by this data structure, when the queries are distributed according to D, is H˜ + O(H˜1/2+1) where H˜=H˜(G,D) is a lower bound on the expected number of point-line comparisons performed by any linear decision tree for point location in G under the query distribution D. The preprocessing algorithm runs in O(n log n) time and produces a data structure of size O(n). These results are obtained by creating a Steiner triangulation of G that has near-minimum entropy.

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.