Traversing the Machining Graph

Zigzag pocket machining (or 2D-milling) plays an important role in the manufacturing industry. The objective is to minimize the number of tool retractions in the zigzag machining path for a given pocket (i.e., a planar domain). We give an optimal linear time dynamic programming algorithm for simply connected pockets, and a linear plus O(1) time optimal algorithm for pockets with h holes. If the dual graph of the zigzag line segment partition of the given pocket is a partial k-tree of bounded degree or a k-outerplanar graph, for a fixed k, we solve the problem optimally in time O(n log n). Finally, we propose a polynomial time algorithm for finding a machining path for a general pocket with h holes using at most OPT + h retractions, where OPT is the smallest possible number of retractions and > 0 is any constant.