This paper is basically a survey to show a number of combinatorial optimization problems arising from VLSI circuit design. Some of them including the existence problem, minimax problem, net representation, bend minimi...This paper is basically a survey to show a number of combinatorial optimization problems arising from VLSI circuit design. Some of them including the existence problem, minimax problem, net representation, bend minimization, area minimization, placement problem, routing problem, etc. are especially discussed with new results and theoretical ideas for treating them. Finally, a number of problems for further research are mentioned.展开更多
In the design of certain kinds of electronic circuits the following question arises:given a non-negative integer k, what graphs admit of a plane embedding such that every edge is a broken lineformed by horizontal and ...In the design of certain kinds of electronic circuits the following question arises:given a non-negative integer k, what graphs admit of a plane embedding such that every edge is a broken lineformed by horizontal and vertical segments and having at mort k bends? Any such graph is said tobe k--rectilinear. No matter what k is, an obvious necessary condition for k-rectilinearity is that thedegree of each vertex does not exceed four.Our main result is that every planar graph H satisfying this condition is 3--rectilinear:in fact,it is 2--rectilinear with the only exception of the octahedron. We also outline a polynomial-timealgorithm which actually constructs a plane embedding of H with at most 2 bends (3 bends if H isthe octahedron) on each edge. The resulting embedding has the property that the total number ofbends does not exceed 2n, where n is the number of vertices of H.展开更多
文摘This paper is basically a survey to show a number of combinatorial optimization problems arising from VLSI circuit design. Some of them including the existence problem, minimax problem, net representation, bend minimization, area minimization, placement problem, routing problem, etc. are especially discussed with new results and theoretical ideas for treating them. Finally, a number of problems for further research are mentioned.
文摘In the design of certain kinds of electronic circuits the following question arises:given a non-negative integer k, what graphs admit of a plane embedding such that every edge is a broken lineformed by horizontal and vertical segments and having at mort k bends? Any such graph is said tobe k--rectilinear. No matter what k is, an obvious necessary condition for k-rectilinearity is that thedegree of each vertex does not exceed four.Our main result is that every planar graph H satisfying this condition is 3--rectilinear:in fact,it is 2--rectilinear with the only exception of the octahedron. We also outline a polynomial-timealgorithm which actually constructs a plane embedding of H with at most 2 bends (3 bends if H isthe octahedron) on each edge. The resulting embedding has the property that the total number ofbends does not exceed 2n, where n is the number of vertices of H.