Solving Connected Subgraph Problems in Wildlife Conservation

Abstract. We investigate mathematical formulations and solution techniques for a variant of the Connected Subgraph Problem. Given a connected graph with costs and profits associated with the nodes, the goal is to find a connected subgraph that contains a subset of distinguished vertices. In this work we focus on the budget-constrained version, where we maximize the total profit of the nodes in the subgraph subject to a budget constraint on the total cost. We propose several mixed-integer formulations for enforcing the subgraph connectivity requirement, which plays a key role in the combinatorial structure of the problem. We show that a new formulation based on subtour elimination constraints is more effective at capturing the combinatorial structure of the problem, providing significant advantages over the previously considered encoding which was based on a single commodity flow. We test our formulations on synthetic instances as well as on real-world instances of an important pr...

• Type: Conference
• Year: 2010
• Where: CPAIOR
• Authors: Bistra N. Dilkina, Carla P. Gomes
• Keywords: Combinatorial Structure, Connected Subgraph, Connected Subgraph Problem, CPAIOR 2010, Operations Research