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We present an on-line strategy that enables a mobile robot with vision to explore an unknown simple polygon. We prove that the resulting tour is less than 26.5 times as long as the shortest watchman tour that could be computed off-line. Our analysis is doubly founded on a novel geometric structure called the angle hull. Let D be a connected region inside a(More)
The detour and spanning ratio of a graph embedded in measure how well approximates Euclidean space and the complete Euclidean graph, respectively. In this paper we describe " ! $ # & % ') (time algorithms for computing the detour and spanning ratio of a planar polygonal path. By generalizing these algorithms, we obtain " ! $ # & % 1 0 2) (time algorithms(More)
Next-generation sequencing technologies can be used to analyse genetically heterogeneous samples at unprecedented detail. The high coverage achievable with these methods enables the detection of many low-frequency variants. However, sequencing errors complicate the analysis of mixed populations and result in inflated estimates of genetic diversity. We(More)
We present a competitive strategy for walking into the kernel of an initially unknown star-shaped polygon. From an arbitrary start point, s, within the polygon, our strategy finds a path to the closest kernel point, k, whose length does not exceed 5.3331. .. times the distance from s to k. This is complemented by a general lower bound of √ 2. Our analysis(More)
Let G be an embedded planar graph whose edges may be curves. For two arbitrary points of G, we can compare the length of the shortest path in G connecting them against their Euclidean distance. The maximum of all these ratios is called the geometric dilation of G. Given a finite point set, we would like to know the smallest possible dilation of any graph(More)