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Graph theoretical problems in next generation chip design
, 2003
"... A major component of computer chip design is creating an optimal physical layout of a netlist, i.e., determining where to place the functional elements and how to route the wires connecting them when manufacturing a chip. Because of its basic structure, the overall problem of netlist layout contains ..."
Abstract

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A major component of computer chip design is creating an optimal physical layout of a netlist, i.e., determining where to place the functional elements and how to route the wires connecting them when manufacturing a chip. Because of its basic structure, the overall problem of netlist layout contains many questions that lend themselves to graph theoretical modeling and analysis. We will describe the basic principles of netlist layout and present several graph theoretical questions inherent in the problem. Possible approaches to these questions include concepts from hypergraphs, graph partitioning, graph drawing, graph and geometric thickness, tree width, grid graphs, planar embeddings, and geometric graph theory.
Abstract Layout of an Arbitrary Permutation in a Minimal Right Triangle Area
"... In VLSI layout of interconnection networks, routing twopoint nets in some restricted area is one of the central operations. It aims usually to minimize the layout area, while reducing the number of wire bends is also very desirable. Here, we consider connecting sets of N inputs on a line and N outp ..."
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In VLSI layout of interconnection networks, routing twopoint nets in some restricted area is one of the central operations. It aims usually to minimize the layout area, while reducing the number of wire bends is also very desirable. Here, we consider connecting sets of N inputs on a line and N outputs on a perpendicular line, inside a right triangle, where the output order is a given permutation of the order of corresponding inputs. Such triangles were used, for example, by Dinitz, Even and ArtishchevZapolotsky for an optimal layout of the Butterfly network. However, that was some particular permutation, while here we solve an arbitrary permutation case. We show two layouts in the optimal area of 1 2N2 + o(N2), with O(N) bends each. The first one yields the minimal irreducible number of bends, while containing knockknees. The second eliminates knockknees, still keeping a constant number of bends per connection.
Nearly Optimal Three Dimensional Layout of Hypercube Networks ⋆
"... Abstract. In this paper we consider the threedimensional layout of hypercube networks. Namely, we study the problem of laying hypercube networks out on the threedimensional grid with the properties that all nodes are represented as rectangular slices and lie on two opposite sides of the bounding b ..."
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Abstract. In this paper we consider the threedimensional layout of hypercube networks. Namely, we study the problem of laying hypercube networks out on the threedimensional grid with the properties that all nodes are represented as rectangular slices and lie on two opposite sides of the bounding box of the layout volume. We present both a lower bound and a layout method providing an upper bound on the layout volume and the maximum wirelength of the hypercube network.