An optimal solution to a wire-routing problem (preliminary version)

A wire-routing problem which arises commonly in the layout of circuits for very large scale integration (VLSI) is discussed. Given the coordinates of terminals u<subscrpt>1</subscrpt>, u<subscrpt>2</subscrpt>, ..., u<subscrpt>n</subscrpt> of one component and v<subscrpt>1</subscrpt>, v<subscrpt>2</subscrpt>, ..., v<subscrpt>n</subscrpt> of another, the problem is to lay out n wires so that the i<underline>th</underline> wire connects u<subscrpt>i</subscrpt> to v<subscrpt>i</subscrpt>, and adjacent wires are separated at least by some fixed distance. The solution with minimum wire length is characterized, and an optimal algorithm which constructs it is presented.