Efficient algorithms for orthogonal polygon approximation

In applications such as VLSI floorplanning, pattern recognition and image processing, an important problem is to compress the data needed to represent certain geometric structures subject to some approximation criteria so that manipulating these structures would not require excessive amount of computing resources. Techniques based on polygonal approximation have been used increasingly in such applications. In this paper, we present two efficient yet very simple algorithms to solve the convex orthogonal polygon approximation problem. One of our algorithms takes O(n³ log k/√(log n)) time and O(n²) space. The other algorithm only takes O(n) space with the time complexity of O(n³k). The previously best known algorithm solves the same problem using O(n⁵) time and O(n ⁴) space. In addition to the improvement in both time and space complexities, our algorithms are also simple to understand and simple to implement. Our techniques and observations are quite general in their own right and may be applicable to other problems