Matching Nuts and Bolts Extended Abstract

We describe a procedure which may be helpful to any disorganized carpenter who has a mixed pile of bolts and nuts and wants to nd the corresponding pairs of bolts and nuts. The procedure uses our (and the carpenter's) ability to construct e ciently highly expanding graphs. The problem considered is given a collection of n bolts of distinct widths and n nuts such that there is a 1-1 correspondence between the nuts and bolts. The goal is to nd for each bolt its corresponding nut by comparing nuts to bolts but not nuts to nuts or bolts to bolts. Our objective is to minimize the number of operations of this kind (as well as the total running time). To appear in Fifth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 94) January 23-25, 1994, Arlington,