Matching Nuts and Bolts Faster

The problem of matching nuts and bolts is the following Given a collection of n nuts of distinct sizes and n bolts such that there is a one to one correspondence between the nuts and the bolts nd for each nut its corresponding bolt We can only compare nuts to bolts That is we can neither compare nuts to nuts nor bolts to bolts This humble restriction on the comparisons appears to make this problem very hard to solve In fact the best deterministic solution to date is due to Alon et al and takes n log n time Their solution uses e cient graph expanders In this paper we give a simpler O n log n time algorithm which uses only a simple and not so e cient expander