In this paper, we study sensor enabled landmine networks by formulating a minimum-cost mine selection problem. The problem arises in a target defence scenario, where the objective is to destroy the intruding targets using the minimum-cost pre-deployed mines. Due to the problem complexity, we first transform it using a novel bucket-tub model, and then propose several approximation algorithms. Among them, it is shown that the layering algorithm can achieve an approximation ratio of α · f, where α ≥ 1 is the tunable relaxation factor and f is the maximum number of mines that a target is associated with, and that the greedy algorithm has an approximation ratio of Σ j Rj, where R j is the coefficient in the related integer program. We also present a localized greedy algorithm which is shown to produce the same solution set as the global greedy algorithm. Theoretical analysis and extensive simulations demonstrate the effectiveness of the proposed algorithms.