Notes on computing peaks in k-levels and parametric spanning trees
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Detecting cuts in sensor networks
IPSN '05 Proceedings of the 4th international symposium on Information processing in sensor networks
Detecting cuts in sensor networks
ACM Transactions on Sensor Networks (TOSN)
A dynamic data structure for 3-D convex hulls and 2-D nearest neighbor queries
Journal of the ACM (JACM)
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Minimizing the error of linear separators on linearly inseparable data
Discrete Applied Mathematics
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We present a randomized algorithm for computing portions of an arrangement of n arcs in the plane, each pair of which intersect in at most t points. We use this algorithm to perform online walks inside such an arrangement (i.e., compute all the faces that a curve, given in an online manner, crosses) and to compute a level in an arrangement, both in an output-sensitive manner. The expected running time of the algorithm is $O(\lambda_{t+2}(m+n)\log n)$, where m is the number of intersections between the walk and the given arcs. No similarly efficient algorithm is known for the general case of arcs. For the case of lines and for certain restricted cases involving line segments, our algorithm improves the best known algorithm of [M. H. Overmars and J. van Leeuwen, J. Comput. System Sci., 23 (1981), pp. 166--204] by almost a logarithmic factor.