  This paper investigated the problem of embedding a simple Hamiltonian Cycle
with n vertices on n points inside a simple polygon. This problem seeks to
embed a straight-line cycle (without bends), which does not intersect either
itself or the sides of the polygon, i.e., it is planar. This problem is a
special case of an open problem to find a simple Hamiltonian (s, X, t)-path (a
simple path that starts at s and ends at t, where s, t, and all other vertices
within the path are a member of set X) inside a simple polygon, which does not
intersect itself or the sides of the polygon. The complexity of the problem in
this paper is not verified yet, and it is an open problem. However, similar
problems are resolved that are NP-Complete. A heuristic algorithm with time
complexity of O(r(n2m + n3)) and space complexity of O(n2 + m) is proposed to
solve the problem.
