Walk2Privacy: Limiting target link privacy disclosure against the adversarial link prediction

The disclosure of an important yet sensitive link may cause serious privacy crisis between two users of a social graph. Only deleting the sensitive link referred to as a target link which is often the attacked target of adversaries is not enough, because the adversarial link prediction can deeply forecast the existence of the missing target link. Thus, to defend some specific adversarial link prediction, a budget limited number of other non-target links should be optimally removed. We first propose a path-based dissimilarity function as the optimizing objective and prove that the greedy link deletion to preserve target link privacy referred to as the GLD2Privacy which has monotonicity and submodularity properties can achieve a near optimal solution. However, emulating all length limited paths between any pair of nodes for GLD2Privacy mechanism is impossible in large scale social graphs. Secondly, we propose a Walk2Privacy mechanism that uses self-avoiding random walk which can efficiently run in large scale graphs to sample the paths of given lengths between the two ends of any missing target link, and based on the sampled paths we select the alternative non-target links being deleted for privacy purpose. Finally, we compose experiments to demonstrate that the Walk2Privacy algorithm can remarkably reduce the time consumption and achieve a very near solution that is achieved by the GLD2Privacy.