EFFICIENT EVADER DETECTION IN MOBILE SENSOR NETWORKS

The paper explicitly formulates the discrete-time evasion subproblem (Problem 4.1), defines H_n, and states Lemma 4.2: that iteratively solving Problem 4.1 yields a solution to the continuous decision problem (Problem 3.2) and the discrete analog of the detection-time problem (Problem 3.3). It remarks this follows by a simple inductive argument, without spelling it out. The candidate solution supplies exactly that induction: it proves K_n = H_n by concatenation/restriction of evasion paths and then identifies the largest grid time t_n with H_n ≠ ∅ as the discrete detection time, including the monotonicity argument. This matches the intent and content of Lemma 4.2 and the discrete-time framework in Section 4.1, using the evasion-path definition and detection-time definition from Section 3 (Definition 3.1; Problems 3.2 and 3.3). Hence both are correct, and the model’s proof is a faithful, explicit version of the paper’s stated inductive argument (Problem 4.1 and Lemma 4.2, and their role in the algorithm are described in the text). Citations: Problem 4.1 and Lemma 4.2 are stated in Section 4.1 ; the evasion path and the problems are defined in Section 3 (Definition 3.1, Problem 3.2, and Problem 3.3) . The discretization assumption (Δt sufficiently small) and adaptive substepping are noted in Section 4.1–4.2, but they are not needed for the logical equivalence K_n = H_n itself; they are implementation assumptions for the local step .