practical algorithm for the beltway problem with a complexity parameter introduction

The beltway problem is a famous computational geometry challenge relevant to fields like bioinformatics and crystallography. not only is the complexity class of the beltway problem not known but there is no practical non-polynomial time algorithm to solve it. this paper models the problem as a constraint satisfactionproblem (csp) and applies a backtracking approach with forward-checking to explore the solution space. moreover, it introduces a multiplicity rate parameter to measure the input’s complexity, observingthat higher multiplicity generally increases run-time. to the best of the author’s knowledge, no deterministic algorithm exists that can solve large instances of the beltway problem.experimental results indicate that the algorithmperforms efficiently for low-multiplicity instances and acceptably under higher multiplicities.