TY - GEN

T1 - MULTI-LAYER GRID EMBEDDINGS.

AU - Aggarwal, Alok

AU - Klawe, Maria

AU - Lichtenstein, David

AU - Linial, Nathan

AU - Wigderson, Avi

PY - 1985

Y1 - 1985

N2 - The authors propose two new multilayer grid models for VLSI layout, both of which take into account the number of contact cuts used. For the first model, in which nodes exist on only one layer, a tight tradeoff area multiplied by (number of contact cuts) equals O(n**2) is proved for embedding any degree 4n-node planar graph in two layers. For the second models in which nodes exist simultaneously on all layers, a number of bounds on the area needed to embed graphs using no contact cuts are proved. For example, it is proved that any n-node graph which is the union of two planar subgraphs can be embedded on two layers in O(n**2) area without contact cuts. This bound is tight even if more layers and an unbounded number of contact cuts are allowed. It is also shown that planar graphs of bounded degree can be embedded on two layers in O(n**1**. **6) area without contact cuts.

AB - The authors propose two new multilayer grid models for VLSI layout, both of which take into account the number of contact cuts used. For the first model, in which nodes exist on only one layer, a tight tradeoff area multiplied by (number of contact cuts) equals O(n**2) is proved for embedding any degree 4n-node planar graph in two layers. For the second models in which nodes exist simultaneously on all layers, a number of bounds on the area needed to embed graphs using no contact cuts are proved. For example, it is proved that any n-node graph which is the union of two planar subgraphs can be embedded on two layers in O(n**2) area without contact cuts. This bound is tight even if more layers and an unbounded number of contact cuts are allowed. It is also shown that planar graphs of bounded degree can be embedded on two layers in O(n**1**. **6) area without contact cuts.

UR - http://www.scopus.com/inward/record.url?scp=0022188124&partnerID=8YFLogxK

U2 - 10.1109/sfcs.1985.37

DO - 10.1109/sfcs.1985.37

M3 - Conference contribution

AN - SCOPUS:0022188124

SN - 0818606444

SN - 9780818606441

T3 - Annual Symposium on Foundations of Computer Science (Proceedings)

SP - 186

EP - 196

BT - Annual Symposium on Foundations of Computer Science (Proceedings)

PB - IEEE

ER -