Flattening topologically spherical surface

Authors:
Danny Z. Chen;Ewa Misiołek
Affiliations:
Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, USA 46556;Mathematics Department, Saint Mary's College, Notre Dame, USA 46556
Venue:
Journal of Combinatorial Optimization
Year:
2012

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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 of flattening a topologically spherical surface admits a PTAS and can be solved by a (1+驴)-approximation algorithm in O(nlog驴n) time for any constant 驴0, where n is the input size of the problem.