Abstract: A system for information item categorization in which each non-leaf node in a hierarchical organization of nodes represents a category, and each leaf node represents an information item. A number P is associated with each node. For non-leaf nodes, the associated number P is selected from a subset of relatively prime elements chosen from an appropriate Unique Factorization Domain (UFD), such as a set of relatively prime numbers which are a subset of the familiar set of integers. For leaf nodes, P is set to 1. A number M is also associated with each node. For each root node, M is set to the value of P for that node. For each non-root node, M is set to the product of the M's of all parent nodes of the node and the P of that node.

Abstract: A system for information item categorization in which each non-leaf node in a hierarchical organization of nodes represents a category, and each leaf node represents an information item. A number P is associated with each node. For non-leaf nodes, the associated number P is selected from a subset of relatively prime elements chosen from an appropriate Unique Factorization Domain (UFD), such as a set of relatively prime numbers which are a subset of the familiar set of integers. For leaf nodes, P is set to 1. A number M is also associated with each node. For each root node, M is set to the value of P for that node. For each non-root node, M is set to the product of the M's of all parent nodes of the node and the P of that node.

Abstract: A system for information item categorization in which each non-leaf node in a hierarchical organization of nodes represents a category, and each leaf node represents an information item. A number P is associated with each node. For non-leaf nodes, the associated number P is selected from a subset of relatively prime elements chosen from an appropriate Unique Factorization Domain (UFD), such as a set of relatively prime numbers which are a subset of the familiar set of integers. For leaf nodes, P is set to 1. A number M is also associated with each node. For each root node, M is set to the value of P for that node. For each non-root node, M is set to the product of the M's of all parent nodes of the node and the P of that node.

Abstract: A system for information item categorization in which each non-leaf node in a hierarchical organization of nodes represents a category, and each leaf node represents an information item. A number P is associated with each node. For non-leaf nodes, the associated number P is selected from a subset of relatively prime elements chosen from an appropriate Unique Factorization Domain (UFD), such as a set of relatively prime numbers which are a subset of the familiar set of integers. For leaf nodes, P is set to 1. A number M is also associated with each node. For each root node, M is set to the value of P for that node. For each non-root node, M is set to the product of the M's of all parent nodes of the node and the P of that node.

Abstract: A method for information item categorization in which each non-leaf node in a hierarchical organization of nodes represents a category, and each leaf node represents an information item. A number P is associated with each node. For non-leaf nodes, the associated number P is selected from a subset of relatively prime elements chosen from an appropriate Unique Factorization Domain (UFD), such as a set of relatively prime numbers which are a subset of the familiar set of integers. For leaf nodes, P is set to 1. A number M is also associated with each node. For each root node, M is set to the value of P for that node. For each non-root node, M is set to the product of the M's of all parent nodes of the node and the P of that node.

Abstract: A method and system for retrieving records from a database are described. The method and system retrieve a first set of records from the database, determine a number of relevant records in the first set of records, compare the target number of relevant records to the number of relevant records, and retrieve a second set of records from the database when the number of relevant records in the first set of records is less than the target number of relevant records. The second set of records includes the first set of records and at least one additional record. Optionally, the number of records in the second set of records is determined by a second function of an ordered list of functions that are each dependant on at least one of a target value and an access attempt value.

Abstract: A system for information item categorization in which each non-leaf node in a hierarchical organization of nodes represents a category, and each leaf node represents an information item. A number P is associated with each node. For non-leaf nodes, the associated number P is selected from a subset of relatively prime elements chosen from an appropriate Unique Factorization Domain (UFD), such as a set of relatively prime numbers which are a subset of the familiar set of integers. For leaf nodes, P is set to 1. A number M is also associated with each node. For each root node, M is set to the value of P for that node. For each non-root node, M is set to the product of the C's of all parent nodes of the node and the P of that node. As a result, the value of M for any node contains as factors the Ps of all its ancestor nodes in the tree or acyclic graph making up the node hierarchy.

Abstract: A method and system for retrieving records from a database are described. The method and system retrieve a first set of records from the database, determine a number of relevant records in the first set of records, compare the target number of relevant records to the number of relevant records, and retrieve a second set of records from the database when the number of relevant records in the first set of records is less than the target number of relevant records. The second set of records includes the first set of records and at least one additional record. Optionally, the number of records in the second set of records is determined by a second function of an ordered list of functions that are each dependant on at least one of a target value and an access attempt value.