This paper presents sparse and large-scale data structure for mathematical information systems. A lot of　studies previously researched are discussed　from the various points of view，which mean information systems，software engineering，artificial intelligence and knowledge information systems. This paper proposes three kinds of sparse data structures，that is，a matrix with rows and columns，the spread sheets and search trees. The first structure is used for the constrained load (power) flow of practical electric power systems. This is an optimization problem which obtains a feasible solution with considering priority orders. The problem becomes large-scale in applying to real cases. The second exploits display expression of too large-scale spread sheet with sparse data structure which is impossible to show the whole sheet on one screen. The display expression of a computer only shows cells with data after automatically dropping other cells of no data. The third is for desirable constraint satisfaction in the field of artificial intelligence. The constraint satisfaction means large-scale assignment problems with priority orders. The solution technique is to search state space by using several search trees. All of the three data structures treat sparse and large-scale in searching and

or its data stored.