Evader Interdiction and Collateral Damage

Abstract

In network interdiction problems, evaders (e.g., hostile agents or data packets) may be moving through a network towards targets and we wish to choose locations for sensors in order to intercept the evaders before they reach their destinations. The evaders might follow deterministic routes or Markov chains, or they may be reactive, i.e., able to change their routes in order to avoid sensors placed to detect them. The challenge in such problems is to choose sensor locations economically, balancing security gains with costs, including the inconvenience sensors inflict upon innocent travelers. We study the objectives of 1) maximizing the number of evaders captured when limited by a budget on sensing cost and 2) capturing all evaders as cheaply as possible. We give optimal sensor placement algorithms for several classes of special graphs and hardness and approximation results for general graphs, including for deterministic or Markov chain-based and reactive or oblivious evaders. In a similar-sounding but fundamentally different problem setting posed by [7] where both evaders and innocent travelers are reactive, we again give optimal algorithms for special cases and hardness and approximation results on general graphs.

Providing homeland security strategies against interdictions in the city transportation network: A case study in Turkey

“…Wood developed a 'min-max' formulation to reformulate the maximum flow NIP and reduced it to a one-level integer programming model (IP) [17]. With the study of Wood, the number of NIP studies has increased and NIP becomes a well-studied research topic from many different scopes, such as minimizing the maximum flow or maximizing the shortest path on a given network, national defense [18,19], humanitarian logistics [20], facility or sensor locations [21,22], nuclear smuggling interdiction [23,24].…”

“…The objective function (20) determines the total distance of the shortest path used by the network user after the interdictions of the attacker. Constraint sets (21)(22)(23)(24) are dual constraints. The constraint set (25) ensures that the total cost of interdictions is smaller or equal to the budge.…”

“…Besides the network 𝐺 (9,20) discussed in Section 3, the performance of I-Model(F) is tested on the networks 𝐺 (21,79), 𝐺 (43,234), 𝐺(86, 476), and 𝐺 (190,1542) in terms of runtime (in seconds). The experimental results are summarized in terms of attained runtimes achieved and objective function values for each level of the interdiction budget and given in Table 4 for all generated instances.…”

“…There is no optimal solution since the objective function value takes an abnormally value. In this analysis, changes in the objective function are observed under varying numbers of source and sink nodes for the network 𝐺 (21,79) given in Figure 8. In this regard, nodes 1, 2, 3, 4, and 5 are selected for the source nodes, while nodes 17, 18, 19, 20, and 21 are selected for the sink nodes on the addressed network.…”

“…13) 0.46 2 (4-25) 0.58 3(10)(11) 0.74 3(15)(16)(17)(18)(19)(20)(21)(22)(23) 0.74 3 (22-23) 0.35 2 (27-34) 0.49 2 (2-15) 0.27 2 (4-29) 0.52 3 (11-12) 0.58 3 (16-17) 0.85 4 (22-25) 0.42 2 (28-31) 00.92 4 (12-16) 0.55 3 (17-30) 0.92 4 (25-28) 0.49 2 (31-32) 0.72 3 (3-25) 0.55 3 (7-8) 0.49 2 (13-16) 0.61 3 (18-19) 0.45 2 (25-29) 0.63 3 (32-33) 0.56 3 (3-26) 0.60 3 (7-12) 0.77 4 (13-19) 0.72 3 (18-24) 0.53 3 (25-31) 0.55 3 (33-34) 0.38 2 A, D, and I.C. represent arcs, distances (km), and interdiction cost (number of required equipments), respectively.…”