Study of Graphs and Algorithms for Design of Nano-Circuits

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We proposed the orthogonal ray graph which is an intersection graph of a set of horizontal and vertical rays (half-lines), and showed some characterizations of orthogonal ray graphs. Based on the theory of orthogonal ray graphs, we showed that the subgraph isomorphism problem is NP-hard and thus intractable for orthogonal ray graphs, while the balanced complete bipartite subgraph problem can be solved in polynomial time and thus tractable for orthogonal ray graphs. The problems play important role in the defect- tolerant design of nano-circuits.