Additive Approximation for Layer Minimization of Manhattan Switchbox Routing

Switchbox routing is one of the many problems arising in the field of VLSI routing. It requires interconnecting given sets of terminals that are placed on the boundaries of a rectangular circuit board using a 3-dimensional grid in a vertex-disjoint way. ortant special case is the Manhattan Switchbox Routing problem. Her minimizing the number of layers of a routing (that is, the height of the grid) is known to be NP-hard. In this paper we provide a linear time algorithm that solves any such problem on a number of layers that is greater by at most 5 than the optimum.