7 papers
Subquadratic Approximation Algorithms for Separating Two Points with Objects in the Plane
Jayson Lynch, Jack Spalding-Jamieson
The (unweighted) point-separation problem asks, given a pair of points and in the plane, and a set of candidate geometric objects, for the minimum-size subset of objects wh…
The Presort Hierarchy for Geometric Problems
Ivor van der Hoog, Eva Rotenberg, Jack Spalding-Jamieson +1
Many fundamental problems in computational geometry admit no algorithm running in time for planar input points, via classical reductions from sorting. Prominent e…
Reweighted Spectral Partitioning Works: A Simple Algorithm for Vertex Separators in Special Graph Classes
Jack Spalding-Jamieson
We establish that a simple polynomial-time algorithm that we call reweighted spectral partitioning obtains small 2/3-balanced vertex-separators for a number of graph classes, inclu…
Separating Two Points with Obstacles in the Plane: Improved Upper and Lower Bounds
Jack Spalding-Jamieson, Anurag Murty Naredla
Given two points in the plane, and a set of "obstacles" given as curves through the plane with assigned weights, we consider the point-separation problem, which asks for the minimu…
The Analytic Arc Cover Problem and its Applications to Contiguous Art Gallery, Polygon Separation, and Shape Carving
Eliot W. Robson, Jack Spalding-Jamieson, Da Wei Zheng
We show the following problems are in : 1. The contiguous art gallery problem -- a variation of the art gallery problem where each guard can protect a contiguous interv…
Slant/Gokigen Naname is NP-complete, and Some Variations are in P
Jayson Lynch, Jack Spalding-Jamieson
In this paper we show that a generalized version of the Nikoli puzzle Slant is NP-complete. We also give polynomial time algorithms for versions of the puzzle where some constraint…