OPTIMAL ROUTING ON NARROW CHANNELS

Abstract

Channel routing is one of the basic problems in VLSI routing. While the minimum width can be found in linear time in the single row routing problem, the complexity of the channel routing problem is not fully understood yet. A solution can be found, even in linear time, in the unconstrained model, but the complexity of determining the minimum width is not known. The present article concentrates on the Manhattan model where horizontal and vertical wire segments are positioned on different sides of the board. In this case, the routing problem is known to be NP-complete. Hence there is no hope to find an algorithm whose running time is polynomial both in the length and the width of the channel. The width of the channel is usually much smaller than the length, thus, an algorithm, whose running time is exponential in the width and polynomial' in the length can be efficient in the case of a narrow channel. We show that the channel routing problem in the Manhattan model is solvable in linear time if the length of the input is proportional to the length of the channel, and the width does not belong to the input.