We identify proximity breach as a privacy threat specific to numerical sensitive attributes in anonymized data publication. Such breach occurs when an adversary concludes with high confidence that the sensitive value of a victim individual must fall in a short interval -- even though the adversary may have low confidence about the victim's actual value. None of the existing anonymization principles (e.g., kanonymity, l-diversity, etc.) can effectively prevent proximity breach. We remedy the problem by introducing a novel principle called (, m)-anonymity. Intuitively, the principle demands that, given a QI-group G, for every sensitive value x in G, at most 1/m of the tuples in G can have sensitive values "similar" to x, where the similarity is controlled by . We provide a careful analytical study of the theoretical characteristics of (, m)-anonymity, and the corresponding generalization algorithm. Our findings are verified by experiments with real data. ACM Categories an...