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Evasion attack on discrete data is a challenging, while practically interesting research topic. It is intrinsically an NP-hard combinatorial optimization problem. Characterizing the conditions guaranteeing the solvability of an evasion attack task thus becomes the key to understand the adversarial threat. Our study is inspired by the weak submodularity theory. We characterize the attackability of a targeted classifier on discrete data in evasion attack by bridging the attackability measurement and the regularity of the targeted classifier. Based on our attackability analysis, we propose a computationally efficient orthogonal matching pursuit-guided attack method for evasion attack on discrete data. It provides provably computational efficiency and attack performances. Substantial experimental results on real-world datasets validate the proposed attackability conditions and the effectiveness of the proposed attack method.