Optimal algorithms for weighted 1-center problem in deterministic and stochastic tree networks

Abstract

This paper deals with two single facility location problems. The first problem is about the deterministic weighted (DW) 1-center of a deterministic tree network (DTN). The optimality criterion for the DW 1-center is minimizing the weighted distance to the furthest node from the facility. This problem has many applications in the emergency field since it gives satisfactory results for the customers sited at the furthest node of the DTN. The second problem is about the stochastic weighted (SW) 1-center of the stochastic tree network (STN). The criterion for optimality used in the SW 1-center is maximizing the minimum weighted reliability from the nodes of the STN to the facility. The applications of the SW 1-center problem appear in computer and communication fields. Two linear-time algorithms are presented for both problems.