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Covering a set of points with a minimum number of turns

Collins, Michael J.

Given a finite set of points in Euclidean space, we can ask what is the minimum number of times a piecewise-linear path must change direction in order to pass through all of them. We prove some new upper and lower bounds for a restricted version of this problem in which all motion is orthogonal to the coordinate axes. © Springer-Verlag Berlin Heidelberg 2003.