Illustration of the four categories of hash functions discussed in this survey. For scattering hash functions, there are many collisions in B. For permutations, there are no collisions. For the minimum perfect hash function (MPHF), blue dots represent the subset of the universe provided in advance, with red dots representing the rest. The blue edges should not have any collisions, but the behavior of the red edges is undefined. For the locality-sensitive hash function (LSH) category, the vertical line segment represents the metric space on which the universe elements lie, and elements with a small distance are more likely to have the same hash value. For this category, collisions are desired for elements that are nearby in U.