Polynomially solvable cases of multifacility distance constraints on cyclic networks

Distance Constraints Problem is to locate one or more new facilities on a network so that the distances between new and existing facilities as well as between pairs of new facilities do not exceed given upper bounds. The problem is AfV-Complete on cyclic networks and polynomially solvable on trees. Although theory for tree networks is well-developed, there is virtually no theory for cyclic networks. In this thesis, we identify a special class of instances for which we develop theory and algorithms that are applicable to any metric space defining the location space. We require that the interaction between new facilities has a tree structure. The method is based on successive applications of EXPANSION and INTERSECTION operations defined on subsets of the location space. Application of this method to general networks yields strongly polynomial algorithms. Finally, we give an algorithm that constructs an e-optimal solution to a related minimax problem.