Abstract: Methods, computer systems, and computer program products for calculating a remainder by division of a sequence of bytes interpreted as a first number by a second number are provided. A first remainder by division associated with a first subset of the sequence of bytes is calculated with a first processor. A second remainder by division associated with a second subset of the sequence of bytes is calculated with a second processor. The calculating of the second remainder by division may occur at least partially during the calculating of the first remainder by division. A third remainder by division is calculated based on the calculating of the first remainder by division and the calculating of the second remainder by division.

Abstract: Methods, computer systems, and computer program products for calculating a remainder by division of a sequence of bytes interpreted as a first number by a second number is provided. A pseudo-remainder by division associated with a first subsequence of the sequence of bytes is calculated. A property of this pseudo-remainder is that the first subsequence of the sequence of bytes, interpreted as a third number, and the pseudo-remainder by division have the same remainder by division when divided by the second number. A second subsequence of the sequence of bytes interpreted as the first number is appended to the pseudo-remainder, interpreted as a sequence of bytes, so as to create a sequence of bytes interpreted as a fourth number. The first number and the fourth number have the same remainder by division when divided by the second number.

Abstract: Systems and methods enabling search of a repository for the location of data that is similar to input data, using a defined measure of similarity, in a time that is independent of the size of the repository and linear in a size of the input data, and a space that is proportional to a small fraction of the size of the repository. The similar data segments thus located are further analyzed to determine their common (identical) data sections, regardless of the order and position of the common data sections in the repository and input, and in a time that is linear in the segment size and in constant space.

Abstract: Systems and methods enabling search of a repository for the location of data that is similar to input data, using a defined measure of similarity, in a time that is independent of the size of the repository and linear in a size of the input data, and a space that is proportional to a small fraction of the size of the repository. The similar data segments thus located are further analyzed to determine their common (identical) data sections, regardless of the order and position of the common data sections in the repository and input, and in a time that is linear in the segment size and in constant space.

Abstract: Systems and methods enabling search of a repository for the location of data that is similar to input data, using a defined measure of similarity, in a time that is independent of the size of the repository and linear in a size of the input data, and a space that is proportional to a small fraction of the size of the repository. The similar data segments thus located are further analyzed to determine their common (identical) data sections, regardless of the order and position of the common data sections in the repository and input, and in a time that is linear in the segment size and in constant space.

Abstract: Systems and methods enabling search of a repository for the location of data that is similar to input data, using a defined measure of similarity, in a time that is independent of the size of the repository and linear in a size of the input data, and a space that is proportional to a small fraction of the size of the repository. The similar data segments thus located are further analyzed to determine their common (identical) data sections, regardless of the order and position of the common data sections in the repository and input, and in a time that is linear in the segment size and in constant space.

Abstract: Systems and methods enabling search of a repository for the location of data that is similar to input data, using a defined measure of similarity, in a time that is independent of the size of the repository and linear in a size of the input data, and a space that is proportional to a small fraction of the size of the repository. The similar data segments thus located are further analyzed to determine their common (identical) data sections, regardless of the order and position of the common data sections in the repository and input, and in a time that is linear in the segment size and in constant space.

Abstract: Systems and methods enabling search of a repository for the location of data that is similar to input data, using a defined measure of similarity, in a time that is independent of the size of the repository and linear in a size of the input data, and a space that is proportional to a small fraction of the size of the repository. The similar data segments thus located are further analyzed to determine their common (identical) data sections, regardless of the order and position of the common data sections in the repository and input, and in a time that is linear in the segment size and in constant space.

Abstract: Systems and methods enabling search of a repository for the location of data that is similar to input data, using a defined measure of similarity, in a time that is independent of the size of the repository and linear in a size of the input data, and a space that is proportional to a small fraction of the size of the repository. The similar data segments thus located are further analyzed to determine their common (identical) data sections, regardless of the order and position of the common data sections in the repository and input, and in a time that is linear in the segment size and in constant space.

Abstract: Systems and methods enabling search of a repository for the location of data that is similar to input data, using a defined measure of similarity, in a time that is independent of the size of the repository and linear in a size of the input data, and a space that is proportional to a small fraction of the size of the repository. The similar data segments thus located are further analyzed to determine their common (identical) data sections, regardless of the order and position of the common data sections in the repository and input, and in a time that is linear in the segment size and in constant space.

Abstract: A method for convening an input data character stream into an encoded data stream in a dictionary-based data compression system, which includes determining possible parsing options of the input data character stream; defining a directed labelled graph having vertices and edges, the graph being related to the possible parsing options; finding the elements of an optimal parsing by determining the shortest path between two given vertices of the graph, the finding of the elements of the optimal parsing including eliminating from the graph edges and vertices which cannot form a part of the shortest path; and encoding the elements of the optimal parsing.