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.

Necklaces, Convolutions, and X + Y

Abstract: We give subquadratic algorithms that, given two necklaces each with n beads at arbitrary positions, compute the optimal rotation of the necklaces to best align the beads. Here alignment is measured according to the l p norm of the vector of distances between pairs of beads from opposite necklaces in the best perfect matching. We show surprisingly different results for p=1, p even, and p=∞. For p even, we reduce the problem to standard convolution, while for p=∞ and p=1, we reduce the problem to (min,+) convolution and $(\operatorname {median},+)$ convolution. Then we solve the latter two convolution problems in subquadratic time, which are interesting results in their own right. These results shed some light on the classic sorting X+Y problem, because the convolutions can be viewed as computing order statistics on the antidiagonals of the X+Y matrix. All of our algorithms run in o(n 2) time, whereas the obvious algorithms for these problems run in Θ(n 2) time.

Geodesic ham-sandwich cuts

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 any 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 thealgebraic computation tree model when parameterizing the running time with respect to n and k.

Encoding 2d range maximum queries

Abstract: We consider the two-dimensional range maximum query (2D-RMQ) problem: given an array A of ordered values, to pre-process it so that we can find the position of the largest element in a (user-specified) range of rows and range of columns. We focus on determining the effective entropy of 2D-RMQ, i.e., how many bits are needed to encode A so that 2D-RMQ queries can be answered without access to A. We give tight upper and lower bounds on the expected effective entropy for the case when A contains independent identically-distributed random values, and new upper and lower bounds for arbitrary A, for the case when A contains few rows. The latter results improve upon upper and lower bounds by Brodal et al. (ESA 2010). We also give some efficient data structures for 2D-RMQ whose space usage is close to the effective entropy.

Separating point sets in polygonal environments

Abstract: We consider the separability of two point sets inside a polygon by means of chords or geodesic lines. Specifically, given a set of red points and a set of blue points in the interior of a polygon, we provide necessary and sufficient conditions for the existence of a chord and for the existence of a geodesic path that separate the two sets; when they exist we also derive efficient algorithms for their obtention. We also study the separation of the two sets using the minimum number of pairwise non-crossing chords.

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.

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.