Suppose one has a line segment arrangement consisting entirely of vertical and horizontal segments, and one wants to find the shortest path from one point to another along these segments. Using known algorithms one can solve this in O(n2) time and in O(n2) space. We show that it is possible to find a shortest path in time O(n2 log n) and space O(n1.5). Furthermore, if only one path endpoint is known in advance, it is possible to preprocess the arrangement in the same time and space and then find shortest paths for query points in time O(log n).
CITATION STYLE
Eppstein, D., & Hart, D. W. (1997). An efficient algorithm for shortest paths in vertical and horizontal segments. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1272, pp. 234–247). Springer Verlag. https://doi.org/10.1007/3-540-63307-3_63
Mendeley helps you to discover research relevant for your work.