CHAPTER 23 - Combinatorial Search Problems

Abstract

This chapter discusses combinatorial search problems. There are many practical problems of this type. Wasserman-type blood test of a large population is such a problem. X is the set of some men. The test can be divided into two parts: (1) a sample of blood is drawn from every man and (2) the blood sample is subjected to a laboratory analysis that reveals the presence or absence of syphilitic antigen. The presence of syphilitic antigen is a good indication of infection; for the second step, instead of carrying out the test individually some samples can be poured together. Diagnosis of a sick TV set is another problem. X is the set of parts of the TV set. First one sees that there is a good picture. The trouble should be in the sound-channel, which is a subset of the set of parts of the TV set. Similarly, by different tests, it can be determined whether certain subsets contain the ill part or not. Chemical analysis is another problem. The third problem explains how to identify an unknown chemical element. X is the set of chemical elements. Pour some chemical to the unknown one; if its color turns red, then it belongs to a subset of the set of chemical elements; in the contrary case, it does not. After carrying out some such tests, the unknown element can be identified.