A Moment of Perfect Clarity I: The Parallel Census Technique

We discuss the history and uses of the parallel census technique---an elegant tool in the study of certain computational objects having polynomially bounded census functions. A sequel will discuss advances (including Cai, Naik, and Sivakumar [CNS95] and Glasser [Gla00]), some related to the parallel census technique and some due to other approaches, in the complexity-class collapses that follow if NP has sparse hard sets under reductions weaker than (full) truth-table reductions.