Appendix: ALowerBoundofHashCodes ' Performance

Asthefigureshows,any true positives or false positives are assigned with ranksi. From the above demonstration, if any swap happens in a rank list between true and false positives,the mis-rank ofthat true positiveisdefinitely changed and will only result inincrease or decreaseofmandiby1. To determine whether the lower bound is tight is a little bit difficult. We firstly introduce some concepts and assumptions to make it easier. Let us start at the example placed in beginning of AppendixA.