Computing shortest paths with comparisons and additions
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Approximate distance oracles for geometric graphs
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Approximate Distance Oracles Revisited
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Approximate distance oracles for graphs with dense clusters
Computational Geometry: Theory and Applications
Approximate distance oracles for geometric spanners
ACM Transactions on Algorithms (TALG)
Algorithms and theory of computation handbook
A nearly optimal algorithm for finding L1shortest paths among polygonal obstacles in the plane
ESA'11 Proceedings of the 19th European conference on Algorithms
Computing a maxian point of a simple rectilinear polygon
Operations Research Letters
Computational Geometry: Theory and Applications
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We study the problems of processing single-source and two-point shortest path queries among weighted polygonal obstacles in the rectilinear plane. For the single-source case, we construct a data structure in O(nlog3/2n) time and O(nlog n) space, where n is the number of obstacle vertices; this data structure enables us to report the length of a shortest path between the source and any query point in O(log n) time, and an actual shortest path in O(log n+ k) time, where k is the number of edges on the output path. For the two-point case, we construct a data structure in O(n2 log2n) time and space; this data structure enables us to report the length of a shortest path between two arbitrary query points in O(log2 n) time, and an actual shortest path in O(log2 n + k) time. Our work improves and generalizes the previously best-known results on computing rectilinear shortest paths among weighted polygonal obstacles. We also apply our techniques to processing two-point L1 shortest obstacle-avoiding path queries among arbitrary (i.e., not necessarily rectilinear) polygonal obstacles in the plane. No algorithm for processing two-point shortest path queries among weighted obstacles was previously known.