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

TL;DR

This paper introduces a new polynomial-size integer linear programming model for the Steiner tree problem with revenues, budgets, and hop constraints, successfully solving large benchmark instances to optimality for the first time.

Contribution

A novel binary linear program based on partial-ordering that efficiently solves all benchmark instances of the STPRBH problem to optimality.

Findings

Successfully solves all DIMACS benchmark instances up to 500 nodes

First to solve large STPRBH instances optimally

Demonstrates effectiveness of the new ILP model

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.