Abstract
A theoretical study which allows determination of the minimum number of vias for realizable multilayer channel routing under a topological model is presented. The theory is sufficiently general to solve a variety of problems under different technological constraints, e.g. VLSI multilayer switchbox and channel routing, through-hole printed circuit board (PCB) channels, and single-layer routing. Topological routing is concerned with wire intersection but not area, zero-width wires and zero-area vias being assumed. Unconstrained via minimization (UVM) is not constrained to a prerouted topology. This paper presents restrictive cases of UVM, finding most to be NP-hard, but the case resulting from constraints of traditional switchbox or channel routing to be solvable in O(kn/sup 2/), where k is the maximum number of pins of a net layer and n is the number of pins. The minimum number of vias for various switchbox and channel routing benchmarks are reported.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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