On the curve equipartition problem: a brief exposition of basic issues

We describe briefly the problem of partitioning a con-tinuous curve into N parts with equal chords. (The length of a chord may be defined by any smooth dis-tance metric applied on its endpoints-the Euclidean metric being one of them.) A have proved that a deci-sion variation of this problem is NP-complete, yet for any continuous curve and any N there always exists at least one equipartition. In this work, we propose an approximate algorithm and also a steepest descent method that converges to an exact solution.