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We consider the following motion-planning problem: we are given \mbim unit discs in a simple polygon with \mbin vertices, each at their own start position, and we want to move the discs to a given set of \mbim target positions. Contrary to the standard (labeled) version of the problem, each disc is allowed to be moved to any target position, as long as in(More)
Metrology, the theoretical and practical study of measurement, has applications in automated manufacturing, inspection, robotics, surveying, and healthcare. An important problem within metrology is how to interactively use a measuring device, or probe, to determine some geometric property of an unknown object; this problem is known as geometric probing. In(More)
Clickomania is a classic computer puzzle game (also known as SameGame, Chain-Shot!, and Swell-Foop, among other names). Originally developed by Kuniaki " Morisuke " Moribe under the name Chain-Shot! for the Fujitsu FM-8, and announced in the November 1985 issue of ASCII Monthly magazine, it has since been made available for a variety of digital platforms(More)
In many contexts, it is very useful to have an estimate of the final orientation, or pose, of an object which is dropped onto a flat surface. In this paper, we consider the final orientation of an object which starts with a random orientation, and show how the shape of the object relates to the distribution of its final orientation. We define a notion of(More)
In the classic Traveling Salesman Problem (TSP), the objective is to find the shortest path that visits a set of target locations. This problem is embedded and essential in many planning problems that arise in robotics, particularly in the domains of exploration, monitoring, surveillance, and reconnaissance. In this paper we consider the Stochastic TSP for(More)
Metrology, the theoretical and practical study of measurement, has applications in automated manufacturing, inspection, robotics, surveying, and healthcare. The geometric probing problem considers how to optimally use a probe to measure geometric properties. In this paper, we consider a proximity probe which, given a point, returns the distance to the(More)
The Jordan curve theorem and Brouwer's fixed-point theorem are fundamental problems in topo-logy. We study their computational relationship, showing that a stylized computational version of Jordan's theorem is PPAD-complete, and therefore in a sense computationally equivalent to Brouwer's theorem. As a corollary, our computational result implies that these(More)
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