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We show that finding the optimistic shortest path on an uncertain terrain is NP-hard using a reduction similar to Canny and Reif's reduction of 3SAT to 3D Euclidean shortest path. Shortest path problems are a well-studied class of problems in theoretical computer science. One particularly applicable type of shortest path problem is to find the geodesic… (More)

We present new results for three problems dealing with a set <i>P</i> of <i>n</i> convex constant-complexity fat polyhedra in 3-space. (i) We describe a data structure for vertical ray shooting in <i>P</i> that has <i>O</i>(log<sup>2</sup> <i>n</i>) query time and uses <i>O</i>(<i>n</i> log<sup>2</sup> <i>n</i>) storage. (ii) We give an algorithm to compute… (More)

In this paper we consider imprecise terrains, that is, triangulated terrains with a vertical error interval in the vertices. In particular, we study the problem of removing as many local extrema (minima and maxima) as possible from the terrain. We show that removing only minima or only maxima can be done optimally in O(n log n) time, for a terrain with n… (More)

- Jane Bierstedt, Aaron Gooze, Chris Gray, Josh Peterman, Leon Raykin, Jerry Walters
- 2014

We present a data structure for ray-shooting queries in a set of convex fat polyhedra of total complexity <i>n</i> in <i>R</i><sup>3</sup>. The data structure uses <i>O(n</i><sup>2+ε</sup>) storage and preprocessing time, and queries can be answered in <i>O</i>(log<sup>2</sup> <i>n</i>) time. A trade-off between storage and query time is also possible:… (More)

We study optimization problems in an imprecision model for polyhedral terrains. An imprecise terrain is given by a triangulated point set where the height component of the vertices is specified by an interval of possible values. We restrict ourselves to 1.5-dimensional terrains: an imprecise terrain is given by an x-monotone polyline, and the y-coordinate… (More)

We investigate the problem of creating fast evacuation plans for buildings that are modeled as grid polygons, possibly containing exponentially many cells. We study this problem in two contexts: the " confluent " context in which the routes to exits remain fixed over time, and the " non-confluent " context in which routes may change. Confluent evacuation… (More)

- Los Angeles, Christopher Cunningham Frost, Todd D Millstein, Lixia Zhang, Edmund B Nightingale, Edward W Kohler +320 others
- 2010

his entropy and sense of style, showing me the importance of making software simple and writing concrete, always asking about the why behind the what and how, and his support and inspiration. Two years and some change ago I received an email that lead to what became BPFS. Thank you, Ed Nightingale and Jeremy Condit, for reaching out, for convincing me it… (More)

- G Aloupis, P Bose, V Dujmovic, C Gray, S Langerman, B Speckmann
- 2007

In this paper we study three related problems: (i) Given a fat polygon P , we show how to find a set G of points in P such that every point on the boundary of P sees at least one point of G. The set G is said to guard the boundary of P and its cardinality depends on the shape parameters of P. Fat polygons are often used to model more realistic inputs. (ii)… (More)