Decision makers of companies often face the dilemma of whether to  release data for 
knowledge discovery, vis a vis the risk of disclosing proprietary or sensitive 
information. Among the various methods employed for ``sanitizing'' the data prior 
to disclosure, we focus in this paper on anonymization, given its widespread use in 
practice. We do due diligence to the question ``just how safe is the anonymized 
data''. We consider both the scenarios when the hacker has no information, and more 
realistically, when the hacker may have partial information about items in the 
domain. We conduct our analyses in the context of frequent set mining and address 
the safety question at two different levels: (i) how likely are the identities of 
individual items cracked (i.e. re-identified by the hacker), and (ii) how likely 
are sets of items cracked.  For capturing the prior knowledge of the hacker, we 
propose a belief function, which amounts to an educated guess of the frequency of 
each item. For various classes of belief functions, which correspond to different 
degrees of prior knowledge, we derive formulas for computing the expected number of 
cracks of single items and for itemsets, the probability of cracking the itemsets. 
While obtaining the exact values for the more general situations is computationally 
hard, we propose a series of heuristics called the O-estimates. They are easy to 
compute, and are shown to be fairly accurate, justified by empirical results on 
real benchmark datasets. Based on the O-estimates, we propose a recipe for the 
decision makers to resolve their dilemma. Our recipe operates at two different 
levels, depending on whether the data owner wants to reason in terms of single 
items or sets of items (or both). Finally, we present techniques using which a 
hacker's knowledge of correlation in terms of co-occurrence of items can be 
incorporated into our framework of disclosure risk analysis and present 
experimental results demonstrating how this knowledge affects the heuristic 
estimates we have developed.