Efficient viewpoint assignment for urban texture documentation
Proceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Approximation algorithms for stochastic orienteering
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Improved algorithms for orienteering and related problems
ACM Transactions on Algorithms (TALG)
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We consider the rooted orienteering problem: Given a set $P$ of $n$ points in the plane, a starting point $r \in P$, and a length constraint $B$, one needs to find a path starting from $r$ that visits as many points of $P$ as possible and of length not exceeding $B$. We present a $(1-\varepsilon)$-approximation algorithm for this problem that runs in $n^{O(1/\varepsilon)}$ time; the computed path visits at least $ (1-\varepsilon)k_{\mathrm{opt}}$ points of $P$, where $k_{\mathrm{opt}}$ is the number of points visited by an optimal solution. This is the first polynomial time approximation scheme for this problem. The algorithm also works in higher dimensions.