New algorithm for calculating cycle intersection indices

Abstract

Background. The objects of study are triangulated compact polyhedron P , which are n -dimensional manifolds with boundary. The goal is to create new efficient algorithms for calculating modulo 2 intersection indices. Materials and methods. The construction of a closed n-dimensional path along a given absolute one-dimensional cycle is used. Results. An algorithm has been developed to calculate the intersection index of a given absolute one-dimensional cycle with an arbitrary relative cycle of dimension (n −1) . A rigorous mathematical justification of the algorithm is given. Conclusions. For the problem under consideration, the solution algorithm was developed for the first time. Its computational complexity is O(n2N + m), where n is the dimension of the manifold P , N is the number of its n -dimensional simplices, and m is the number of edges that make up the cycle x .

Keywords

• algorithm
• polyhedron
• cycle
• intersection index