The Lee Path Connection Algorithm

Abstract

The Lee path connection algorithm is probably the most widely used method for finding wire paths on printed circuit boards. It is shown that the original claim of generality for the path cost function is incorrect, and a restriction, called the pathconsistency property, is introduced. The Lee algorithm holds for those path cost functions having this property. Codings for the cells of the grid are proposed which will allow the correct operation of the algorithm under the most general path cost function, using the minimum number of states possible, six states per cell. Then methods for reducing the number of calculations by increasing the number of states are presented.Storing computed cell masses is introduced as a method for reducing the amount of calculation for each iteration of the algorithm. Adding the distance from the goal to the path cost function, and expanding the most recently encountered cell, are shown to substantially reduce the number of iterations needed. Index Terms-Cell coding, heuristic search, Lee algorithm, path cost function, printed circuit board, rectangular grids, shortest path problem, wire routing.

Automatic layout optimization of an EMC filter

“…The chosen algorithm relies on the same bases than the existing ones [7][8][9]. The path between two points is defined by a weight, either governed by the geometry, either by another parameter.…”

“…The component models using PEEC representation will be detailed in section III and validated in section IV. The algorithm for the automatic layout generation, based on a variation of Lee & Dijkstra algorithms [7][8][9], will be used in section V.…”

Combinatorial Problems in Chip Design

“…• A well-known idea for speeding up Dijkstra's algorithm in practice is to replace the cost of an edge (v, w), originally c({v, w}), by c (v, w) := c({v, w}) − π(v) + π(w), where π : V (G) → R satisfies π(t) = 0 for t ∈ T and π(v) ≤ c({v, w}) + π(w) for {v, w} ∈ E(G) (and hence π(v) is a lower bound on the length of a path from v to T ) (Pohl [1971], Rubin [1974]). The better this lower bound is, the shorter is the distance from S to T with respect to c , and the fewer vertices are labelled by Dijkstra's algorithm.…”

Unsupervised connectivity-based thresholding segmentation of midsagittal brain MR images

“…One of the most widely used path connection algorithms is the Lee path algorithm [21] which always ®nds a path if any exists. There are also many variants of this algorithm to speed up the search procedure [22]. We propose to use this search technique to adaptively select a proper threshold that separates two objects.…”