Mario Nakamori

Node-Disjoint Paths Algorithm in a Transposition Graph

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(n7) and 3n - 5, respectively, and the average performance is evaluated based on computer experiments.

Container problem in substring reversal graphs

In this paper, we propose an algorithm that solves the container problem in n-substring reversal graphs in polynomial order time of n. Its correctness is proved and estimates of time complexity and sum of path lengths are given. We also report the results of computer experiment conducted to measure the average performance of our algorithm.

Algorithms for the Circle-Packing Problem via Extended Sequence-Pair

The circle-packing problem is a problem of packing circles into a two dimensional area such that none of them overlap with each other. Each of the former methods has its own difficulty; some of them are only applicable to the case that the area the circles are to be packed into has a special shape; some of them require different search technique according as the shape of the area. Also, most of the former methods search in a restricted neighbor. In addition, there exist unsearchable location of circles. These facts mean former methods cannot assure global optimization. Hence, in the present paper, we propose sequence-pair for circle packing (SPC), a method of representing relative location of circle pairs, which is an extended version of sequence-pair for rectangles. We propose also a method of obtaining an approximate solution of the circle-packing problem, where all constraints are replaced by approximate linear inequalities.