A new algorithm is presented for constructing auxiliary digital search trees to aid in exact-match substring searching. This algorithm has the same asymptotic running time bound as previously published algorithms, but is more economical in space. Some implementation considerations are discussed, and new work on the modification of these search trees in response to incremental changes in the strings they index (the update problem) is presented.

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Let D be a dynamic set of ordered pairs [x, y] over the set 0, l, , k-of integers. Consider the following operations applied to D:(1) Insert (delete) a pair [x, y] into (from) D.(2) Given test integers x0, xl, and yl, among all pairs Ix, y] in D such that xO<-x<-xl and y<-yl, find a pair whose x is minimal (or maximal).(3) Given test integers x0 and xl, among all pairs Ix, y] in D such that xO<-x<-xl, find a pair whose y is minimal.(4) Given test integers x0, x 1, and y l, enumerate those pairs Ix, y] in D such that x0 <_x _

Organization and maintenance of an index for a dynamic random access file is considered. It is assumed that the index must be kept on some pseudo r .2J-1om access backup store like a disc or a drum. The index organi>,ation described allows retrieval, insertion, and deletion of keys in time proportional to 1½gkI where I is the size of the index and k is a device dependent natural number such that the performance of the scheme becomes near optimal. Storage utilization is at least 50% but generally much higher. The pages of the index are organized in a special data-structure, so-called B-trees. The scheme is analyzed, p,arformance bounds are obtained, and a near optimal k is computed.

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