Information availability vs. solution space size in a knowledge acquisition problem

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Several authors have studied a special form of a combinatorial game called the Matching Identification Problem (MIP). It is also a special case of a knowledge acquisition problem. The problem involves identifying a chosen subset of size K out of N symbols through a series of inquiries and corresponding responses. Previous heuristics and optimal algorithms for minimizing the average inquiries required were proposed for only the unordered MIP, where the order of the K symbols in each subset is irrelevant. In this paper, the ordered MIP is introduced, whose initial solution space is K! times larger, but whose structure allows it to gain more information at each inquiry. Three previously proposed heuristics are extended from the Unordered MIP and applied to the Ordered MIP in a computational study. The purpose is to observe how the availability of extra information can help reduce a solution space more quickly. The results show that in many cases the Ordered MIP can be solved more quickly than the corresponding Unordered MIP. This implies that information can be valuable in reducing a large solution space quickly. Scope and purpose Reducing a large number of possible solutions quickly is a common problem in many areas. Creating knowledge-based expert systems requires acquisition of relevant information from a large set of data. Searching the Internet for a particular company’s home page also requires reducing a large number of possibilities to one. Since there are costs associated with the steps involved in reducing a large number of possibilities, we would like to accomplish this reduction as quickly as possible. The Matching Identification Problem (MIP) is a combinatoric problem that begins with a large number of possible solutions, and through a series of steps, reduces the number of possible solutions to one. In the context of the MIP, this paper proposes that extra information can outweigh an increase in the number of possible solutions. Therefore, information availability can outweigh increased solution space size in the context of the MIP.