Algorithms for the Well-Drilling Layout Problem

Abstract

Given some discrete points in a plane, ones move a grid to maximize the number of the points that can be used. This is the well-drilling layout problem. If only consider the translation motion, we present an algorithm with time complexity of O(n ² r) to compute the translation location instead of the previous algorithms with time complexity of O(n ² r ²), where n is the number of the discrete points and r is the radius of error-round. In consideration of the rotation and translation motion, we present an algorithm with time complexity of O(n ³ d) to compute the rotation angle and the translation location instead of the previous algorithms with time complexity of O(n ³ r ² d), where d is the maximum distance between any two discrete points.

Supported by the Science and Technology Development Foundation from Shandong University at Weihai; the National Natural Science Foundation of China under Grant No.60573024; the National Grand Fundamental Research 973 Program of China under Grant No.2005CCA04500.