Abstract

With few exceptions, proximity search algorithms in metric spaces based on the use of pivots select them at random among the objects of the metric space. However, it is well known that the way in which the pivots are selected can drastically a#ect the performance of the algorithm. Between two sets of pivots of the same size, better chosen pivots can largely reduce the search time. Alternatively, a better chosen small set of pivots (requiring much less space) can yield the same e#ciency as a larger, randomly chosen, set. We propose an e#ciency measure to compare two pivot sets, combined with an optimization technique that allows us to select good sets of pivots. We obtain abundant empirical evidence showing that our technique is e#ective, and it is the first that we are aware of in producing consistently good results in a wide variety of cases and in being based on a formal theory. We also show that good pivots are outliers, but that selecting outliers does not ensure that good pivots are selected.

Citations