1. Introduction. In an earlier paper(2) by one of us, referred to hereafter as A.P.T., arc-preserving transformations were defined and studied in connection with an irreducibility condition on the transformation. It was shown, for example, that if A and B are compact locally connected metric continua which are cyclic (that is, without cut points) any single valued continuous arc-preserving and ...

Order preserving data compression can improve sorting and searching performance, and hence the performance of database systems. We describe a new parsing (tokenization) technique that can be effectively applied to "keys", producing substantial compression. It can be applied to both the uncompressed and compressed strings, permiting a more flexible choice of variable length dictionary entries an...

We initiate the cryptographic study of order-preserving symmetric encryption (OPE), a primitive suggested in the database community by Agrawal et al. (SIGMOD ’04) for allowing efficient range queries on encrypted data. Interestingly, we first show that a straightforward relaxation of standard security notions for encryption such as indistinguishability against chosen-plaintext attack (IND-CPA) ...

We introduce a new string matching problem called order-preserving matching on numeric strings where a pattern matches a text if the text contains a substring whose relative orders coincide with those of the pattern. Order-preserving matching is applicable to many scenarios such as stock price analysis and musical melody matching in which the order relations should be matched instead of the str...

Order preserving encryption (OPE) is a kind of encryption designed to support searches on ciphertexts. OPE encrypts plaintexts to ciphertexts with the same order, making it possible to efficiently compare ciphertexts without decryption. Because of its efficiency, OPE has been used in systems aimed at practical use. However, even though many OPE schemes have been proposed, all suffer from securi...

converge almost everywhere to a finite limit f*(x). It then follows that the limit function/* is integrable and that/*(7x) =/*(x) almost everywhere. This result can be applied to certain cases in which the given measure m is not preserved by the transformation T. In order to discuss this application, we recall some terminology for measures and transformations. If (X, S) is a measurable space, a...

Let H be a separable complex Hilbert space. Denote by G∞(H) the Grassmannian consisting of closed linear subspaces with infinite dimension and codimension. This Grassmannian is partially ordered by the inclusion relation. We show that every continuous order preserving bijective transformation of G∞(H) is induced by an invertible bounded semi-linear operator.