Abstract
In this paper we present new approximation algorithms for two NP-hard geometric optimization problems: (1) decomposing a triangulation into minimum number of triangle strips (tristrips); (2) covering an n ×n binary neuron image with minimum number of disjoint h ×h boxes such that the total number of connected components within individual boxes is minimized. Both problems share the pattern that overlap is either disallowed or to be minimized. For the problem of decomposing a triangulation into minimum number of tristrips, we obtain a simple approximation with a factor of \(O(\sqrt{nlogn})\); no approximation with o(n) factor is previously known for this problem [6]. For the problem of tiling a binary neuron image with boxes, we present a bi-criteria factor-(2,4h-4) approximation that uses at most twice the optimal number of tiles and results in at most 4h-4 times the optimal number of connected components. We also prove that it is NP-complete to approximate the general problem within some fixed constant.
This research is partially supported by NSF CARGO grant DMS-0138065.
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Jiang, M., Mumey, B., Qin, Z., Tomascak, A., Zhu, B. (2004). Approximations for Two Decomposition-Based Geometric Optimization Problems. In: Laganá, A., Gavrilova, M.L., Kumar, V., Mun, Y., Tan, C.J.K., Gervasi, O. (eds) Computational Science and Its Applications – ICCSA 2004. ICCSA 2004. Lecture Notes in Computer Science, vol 3045. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24767-8_10
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DOI: https://doi.org/10.1007/978-3-540-24767-8_10
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