layers using wires of length O

Abstract The 3-D channel routing is a fundamental problem on the physical design of 3-D integrated circuits. The 3-D channel is a 3-D grid G and the terminals are vertices of G located in the top and bottom layers. A net is a set of terminals to be connected. The object of the 3-D channel routing problem is to connect the terminals in each net with a tree (wire) in G using as few layers as possible and as short wires as possible in such a way that wires for distinct nets are disjoint. This paper shows that any set of n 2-terminal nets can be routed in a 3-D channel with O