In this paper, we give an algorithm for the node-to-set disjoint paths problem in a transposition graph. The algorithm is of polynomial order of n for an n-transposition graph. It is based on recursion and divided into two cases according to the distribution of destination nodes. The maximum length of each path and the time complexity of the algorithm are estimated theoretically to be O(n 7) and 3n − 5, respectively, and the average performance is evaluated based on computer experiments.

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In this paper, we consider the problem of lens distortion adjustment of semiconductor lithography equipment. The objective of adjustment is to minimize the maximum absolute value of distortion. Formerly, an approximate solution method based on the least-squares method has been used. Recently, an approximate solution method based on iterative least-squares method with weight was proposed. However, calculation of that method often takes long time and a better calculation method has been desired. In this paper, we propose an exact solution method based on LP(Linear Programming) to minimize the maximum absolute value of distortion. Now, LP solvers find an optimal solution very fast owing to the progress in linear programming research. Consequently, optimal solutions for 20 instances obtained by our method provided adjustment parameter settings about 29% from 27% better than that by the solution method based on the least-squares method.

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