Node-to-Set Disjoint Paths Problem in Bi-rotator Graphs

An algorithm is described for solving the node-to-set disjoint paths problem in bi-rotator graphs, which are obtained by making each edge of a rotator graph bi-directional. The algorithm is of polynomial order of n for an n-bi-rotator graph. It is based on recursion and divided into three cases according to the distribution of destination nodes in the classes into which the nodes in a bi-rotator graph are categorized. We estimated that it obtains 2n − 3 disjoint paths with a time complexity of O(n5), that the sum of the path lengths is O(n3), and that the length of the maximum path is O(n2). Computer experiment showed that the average execution time was O(n3.9) and, the average sum of the path lengths was O(n3.0). key words: node-to-set disjoint paths problem, bi-rotator graphs, fault tolerance, parallel computation, routing algorithm