Optimal Surface Flattening

Authors:
Danny Z. Chen;Ewa Misiołek
Affiliations:
Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, USA IN 46556;Mathematics Department, Saint Mary's College, Notre Dame, USA IN 46556
Venue:
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
Year:
2008

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Abstract

The problem of optimal surface flattening in 3-D finds many applications in engineering and manufacturing. However, previous algorithms for this problem are all heuristics without any quality guarantee and the computational complexity of the problem was not well understood. In this paper, we prove that the optimal surface flattening problem is NP-hard. Further, we show that the problem admits a PTAS and can be solved by a (1 + 驴)-approximation algorithm in O(nlogn) time for any constant 驴 0, where nis the input size of the problem.