Approximate Euclidean shortest paths amid convex obstacles

Authors:
Pankaj K. Agarwal;R. Sharathkumar;Hai Yu
Affiliations:
Duke University;Duke University;Duke University
Venue:
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Year:
2009

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Abstract

We develop algorithms and data structures for the approximate Euclidean shortest path problem amid a set P of K convex obstacles in R2 and R3, with a total of n faces. The running time of our algorithms is linear in n, and the size and query time of our data structure are independent of n. We follow a "core-set" based approach, i.e., we quickly compute a small sketch Q of P whose size is independent of n and then compute approximate shortest paths with respect to Q.