Fast algorithm for optimal layer assignment

Given the geometry of wires for inteconnections, we want to assign two conducting layers to the segments of these wires so that the number of vias required is minimized. This layer assignment problem, also referred to as the via minimization problem, has been formulated as finding a maximum cut of a planar graph. In this paper, we propose a new algorithm for optimal layer assignment under a general model where the planar graph has real-valued edge weights. The time complexity of the proposed algorithm is , where is the number of wire-segment clusters in a given layout. In contrast, all existing optimal algorithms for layer assignment have the time complexity of O(). None of these existing algorithms can find an optimal layer assignment under such a general model.