COMPRESSING INCONSISTENT DATA

In a frequent practical situation we possess inconsistent fragmentary data concerning some industrial process or natural phenomenon. It is an interesting and reasonable task to assess what the most concise way to store or transmit them would be. In this paper we consider the zero-error case of the problem, i.e., we would like to save all these data incorporating them into the most concise but necessarily alternative consistent data structures. More precisely, we want to find a set of alternatives which requires the minimum total storage place. From the mathematical viewpoint our model is information-theoretic and gives a common framework to deal with many combinatorial problems in the theory of extremal hypergraphs. From the practical viewpoint the interest of the mathematical theory is to produce new information measures capturing the inconsistency in the data.