Layer assignment problem for three-layer routing

Constrained via minimization

“…In this column, the times are on a Sun3/110c workstation and the programming language used is C. This column is taken from [CHAN89]. We do not present the corresponding figures for the heuristic of Chang and Du [CHAN88] as Chang, Jyu, and Feng [CHAN89] have established that their heuristic is superior. As can be seen from remaining heuristics in seven of the eight cases.…”

“…While their development is not confined to HVH inputs, their experimentation was limited to HVH CVM instances. The heuristic of Chang and Du [CHAN88] attempts to reduce the number of vias by considering the vias in the initial layout one at a time. When a via is considered, an attempt is made to eliminate it by modifying the layer assignment of some wire segments.…”

“…The three layer CVM problem was first shown to be NP-hard by Chung and Du [CHAN88]. They did this by reducing the planar graph three colorability problem to the 3 layer CVM problem.…”

“…Both Chang and Du [CHAN88] and Chang, Jyu, and Feng [CHAN89] develop heuristics for the 3CVM problem. Experimental studies performed by [CHAN89] indicate that their heuristic is superior to that of [CHAN88]. Heuristics for the gridless 2CVM problem are proposed in [NACL87].…”

Multi-layer constrained via minimization with conjugate conflict continuation graphs

“…A solution to a CVM is more useful than that to a TVM because the solution can be readily accepted as a layout for the final mask production. Most of the previous work focuses on 2-layer CVM [2][3][4][5][6] or 3-layer CVM [7,8] and less on multi-layer CVM [9,10]. Two-layer CVM is first investigated in [2].…”