A new Integer Linear Program for the Steiner Tree Problem with Revenues, Budget and Hop Constraints

Abstract: The Steiner tree problem with revenues, budgets and hop constraints (STPRBH) is a variant of the classical Steiner tree problem. This problem asks for a subtree in a given graph with maximum revenues corresponding to its nodes, where its total edge costs respect the given budget, and the number of edges between each node and its root does not exceed the hop limit. We introduce a new binary linear program with polynomial size based on partial-ordering, which (up to our knowledge) for the first time solves all STPRBH instances from the DIMACS benchmark set to optimality. The set contains graphs with up to 500 nodes and 12500 edges.