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Moreover, this paper shows that binary trees exhibiting a certain property can be used to represent block placement configurations with symmetry constraints, which is very useful when dealing with device-level placement problems for analog layout. As the number of these trees is proven to be smaller than the number of symmetric-feasible sequence-pairs, using binary trees is better than using either sequence-pairs or O-trees when solving analog placement problems...
        
        
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As the number of these trees is proven to be smaller than the number of symmetric-feasible sequence-pairs, using binary trees is better than using either sequence-pairs or O-trees when solving analog placement problems. A comparative evaluation, substantiating these theoretical results, has been carried out by providing alternative optimization engines to a placement tool operating in an industrial environment...
        
        
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