Metric spaces, which generalise the properties of commonly-encountered physical and abstract spaces into a mathematical framework, frequently occur in computer science applications. Three major kinds of questions about metric spaces are considered here: the intrinsic dimensionality of a distribution, the maximum number of distance permutations, and the difficulty of reverse similarity search. Intrinsic dimensionality measures the tendency for points to be equidistant, which is diagnostic of high-dimensional spaces. Distance permutations describe the order in which a set of fixed sites appears while moving away from a chosen point; the number of distinct permutations determines the amount of storage space required by some kinds of indexing data structure. Reverse similarity search problems are constraint satisfaction problems derived from distance-based index structures. Their difficulty reveals details of the structure of the space. Theoretical and experimental results are given for these three questions in a wide range of metric spaces, with commentary on the consequences for computer science applications and additional related results where appropriate.

Metric spaces, which generalise the properties of commonly-encountered physical and abstract spaces into a mathematical framework, frequently occur in computer science applications. Three major kinds of questions about metric spaces are considered here: the intrinsic dimensionality of a distribution, the maximum number of distance permutations, and the difficulty of reverse similarity search. Intrinsic dimensionality measures the tendency for points to be equidistant, which is diagnostic of high-dimensional spaces. Distance permutations describe the order in which a set of fixed sites appears while moving away from a chosen point; the number of distinct permutations determines the amount of storage space required by some kinds of indexing data structure. Reverse similarity search problems are constraint satisfaction problems derived from distance-based index structures. Their difficulty reveals details of the structure of the space. Theoretical and experimental results are given for these three questions in a wide range of metric spaces, with commentary on the consequences for computer science applications and additional related results where appropriate.

With the intensively increasing of digital media new challenges has been created for authentication and protection of digital intellectual property. A hash function extracts certain features of a multimedia object e.g. an image and maps it to a fixed string of bits. A perceptual hash function unlike normal cryptographic hash is change tolerant for image processing techniques. Perceptual hash function also referred to as robust hash, like any other algorithm is prone to errors. These errors are false negative and false positive, of which false positive error is neglected compared to false negative errors. False positive occurs when an unknown object is identified as known. In this work a new method for raising false alarms in robust hash function is devised for evaluation purposes i.e. this algorithm modifies hash key of a target image to resemble a different image’s hash key without any significant loss of quality to the modified image. This algorithm is implemented in MATLAB using block mean value based hash function and successfully reduces hamming distance between target image and modified image with a good result and without significant loss to attacked imaged quality.