Eunjin Oh

A Time-Space Trade-Off for Triangulations of Points in the Plane

In this paper, we consider time-space trade-offs for reporting a triangulation of points in the plane. The goal is to minimize the amount of working space while keeping the total running time small. We present the first multi-pass algorithm on the problem that returns the edges of a triangulation with their adjacency information. This even improves the previously best known random-access algorithm.

Minimum-Width Annulus with Outliers: Circular, Square, and Rectangular Cases

We study the problem of computing a minimum-width annulus with outliers. Specifically, given a set of n points in the plane and a nonnegative integer \(k \le n\), the problem asks to find a minimum-width annulus that contains at least \(n-k\) input points. The k excluded points are considered as outliers of the input points. In this paper, we are interested in particular in annuli of three different shapes: circular, square, and rectangular annuli. For the three cases, we present first and improved algorithms to the problem.

Minimum-Width Square Annulus Intersecting Polygons

For k (possibly overlapping) polygons of total complexity n in the plane, we present an algorithm for computing a minimum-width square annulus that intersects all input polygons in \(O(n^2\alpha (n)\log ^3 n)\) time, where \(\alpha (\cdot )\) is the inverse Ackermann function. When input polygons are pairwise disjoint, the running time becomes \(O(n\log ^3 n)\). We also present an algorithm for computing a minimum-width square annulus for k convex polygons of total complexity n. The running times are \(O(n\log k)\) for possibly overlapping convex polygons and \(O(n+k\log n)\) for pairwise disjoint convex polygons.

On Romeo and Juliet Problems: Minimizing Distance-to-Sight

We introduce a variant of the watchman route problem, which we call the quickest pair-visibility problem. Given two persons standing at points

Polygon Queries for Convex Hulls of Points

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The geodesic 2-center problem in a simple polygon

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Computing the Center Region and Its Variants

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Dynamic Geodesic Convex Hulls in Dynamic Simple Polygons

in a simple polygon

Faster Algorithms for Growing Prioritized Disks and Rectangles

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A Near-Optimal Algorithm for Finding an Optimal Shortcut of a Tree

with no holes, we want to minimize the distance they travel in order to see each other in