@article{4099, abstract = {Let S denote a set of n points in the Euclidean plane. A halfplanar range query specifies a halfplane h and requires the determination of the number of points in S which are contained in h. A new data structure is described which stores S in O(n) space and allows us to answer a halfplanar range query in O(nlog2(1+√5)−1) time in the worst case, thus improving the best result known before. The structure can be built in O(n log n) time.}, author = {Herbert Edelsbrunner and Welzl, Emo}, journal = {Information Processing Letters}, number = {5}, pages = {289 -- 293}, publisher = {Elsevier}, title = {{Halfplanar range search in linear space and O(n0.695) query time}}, doi = {10.1016/0020-0190(86)90088-8}, volume = {23}, year = {1986}, }