Approximate K nearest neighbor (AKNN) search is a fundamental and challenging problem. We observe that in high-dimensional space, the time consumption of nearly all AKNN algorithms is dominated by that of the distance comparison operations (DCOs). For each operation, it scans full dimensions of an object and thus, runs in linear time wrt the dimensionality. To speed it up, we propose a randomized algorithm named ADSampling which runs in logarithmic time wrt to the dimensionality for the majority of DCOs and succeeds with high probability. In addition, based on ADSampling we develop one general and two algorithm-specific techniques as plugins to enhance existing AKNN algorithms. Both theoretical and empirical studies confirm that: (1) our techniques introduce nearly no accuracy loss and (2) they consistently improve the efficiency.