Optimal interdiction of unreactive Markovian evaders
- Los Alamos National Laboratory
The network interdiction problem arises in a wide variety of areas including military logistics, infectious disease control and counter-terrorism. In the classical formulation one is given a weighted network G(N, E) and the task is to find b nodes (or edges) whose removal would maximally increase the least-cost path from a source node s to a target node r. In practical applications. G represenLs a transportation or activity network; node/edge removal is done by an agent, the 'interdictor' against another agent the 'evader' who wants to traverse G from s to t along the least-cost route. Our work is motivated by cases in which both agents have bounded rationality: e.g. when the authorities set up road blocks to catch bank robbers, neither party can plot its actions with full information about the other. We introduce a novel model of network interdiction in which the motion of (possibly) several evaders i. described by a Markov pr cess on G.We further suppose that the evaden; do not respond to interdiction decisions because of time, knowledge or computational constraint . We prove that this interdiction problem is NP-hard, like the classical formulation, but unlike the classical problem the objective function is submodular. This implies that the solution could be approximated within 1-lie using a greedy algorithm. Exploiting submodularity again. we demonstrate that a 'priority' (or 'lazy') evaluation algorithm can improve performance by orders of magnitude. Taken together, the results bring closer realistic solutions to the interdiction problem on global-scale networks.
- Research Organization:
- Los Alamos National Laboratory (LANL)
- Sponsoring Organization:
- DOE
- DOE Contract Number:
- AC52-06NA25396
- OSTI ID:
- 957745
- Report Number(s):
- LA-UR-08-04427; LA-UR-08-4427
- Country of Publication:
- United States
- Language:
- English
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