Abstract: Based on events corresponding to operations performed with respect to a data store, a measure is computed that represents an instantaneous consistency level, at a point in time, of data that is subject to the operations.

Abstract: A method for determining priority of recovery for a RAID implementation includes detecting a first failure of the RAID implementation; detecting a second failure of the RAID implementation; assigning a first priority to the first failure and a second priority to the second failure; and setting the priority of the recovery based on the first priority and the second priority.

Abstract: Based on events corresponding to operations performed with respect to a data store, a measure is computed that represents an instantaneous consistency level, at a point in time, of data that is subject to the operations.

Abstract: A multi-geography cloud storage system includes a first data center, with a first key-lookup server to access a first lookup table; and a first fragment server to store data or meta data associated with keys; and a second data center, with a second key-lookup server to access a second lookup table; and a second fragment server to store data associated with the keys; and a storage device to store a redundancy specification.

Abstract: A method for determining priority of recovery for a RAID implementation includes detecting a first failure of the RAID implementation; detecting a second failure of the RAID implementation; assigning a first priority to the first failure and a second priority to the second failure; and setting the priority of the recovery based on the first priority and the second priority.

Abstract: Erasure-encoded data is stored across a plurality of storage devices in a data storage system. The erasure-encoded data includes k data elements to store on k data storage devices and m parity elements to store on m parity storage devices, wherein for a given minimum Hamming distance d of the data storage system and m?(d?1), data elements are assigned only to corresponding unique combinations of parity elements of size (d?1).

Abstract: A method for measuring consistability of a distributed storage system is disclosed. The method includes determining at least one consistency level that the distributed storage system can provide. A plurality of failure classes can be determined for the distributed storage system. A probability of the distributed storage system to be in each of the plurality of failure classes can be measured. Each failure class can be mapped to the at least one consistency level. The probability of each failure class for each consistency level can be summed to determine an expected portion of time that the distributed storage system provides each consistency level.

Abstract: A technique is provided for determining an allocation of the symbols of an erasure code across a plurality of devices. A list of erasure patterns is provided for the erasure code and, based on the list, minimal erasures of minimal weight are identified for the code's symbols. Precedences of the symbols are determined based on the size of the corresponding MEMW. An allocation of the symbols across a plurality of devices is determined based on the precedences.

Abstract: A technique for selecting an erasure code from a plurality of erasure codes for use in a fault tolerant system comprises generating a preferred set of erasure codes based on characteristics of the codes' corresponding Tanner graphs. The fault tolerances of the preferred codes are compared based at least on the Tanner graphs. A more fault tolerant code is selected based on the comparison.

Abstract: A data storage system including a storage device. The storage device may include a plurality of data storage drives that may be logically divided into a plurality of groups and arranged in a plurality of rows and a plurality of columns such that each column contains only data storage drives from distinct groups. Furthermore, the storage device may include a plurality of parity storage drives that correspond to the rows and columns of data storage drives.

Abstract: A method for determining a fault tolerance of an erasure code includes deriving base erasure patterns from a generator matrix of an erasure code, determining which of the base erasure patterns are adjacent to one another and XORing the adjacent base erasure patterns with one another to produce child erasure patterns of the erasure code. The method further includes combining the base erasure patterns and the child erasure patterns to form a minimal erasures list (MEL) for the erasure code, whereby the MEL corresponds to the fault tolerance of the erasure code. Also provided are methods for communicating and storing data by using the fault tolerance of erasure codes.

Abstract: Erasure-encoded data is stored across a plurality of storage devices in a data storage system. The erasure-encoded data includes k data elements to store on k data storage devices and m parity elements to store on m parity storage devices, wherein for a given minimum Hamming distance d of the data storage system and m?(d?1), data elements are assigned only to corresponding unique combinations of parity elements of size (d?1).

Abstract: A fault tolerant system is simulated to determine the occurrence of data loss in the fault tolerant system. A list of erasure patterns corresponding to an erasure code implemented across the devices in the system is provided and a device event is simulated. The list of erasure patterns is updated based on the device event, and the occurrence of data loss is determined based on the updated list.

Abstract: A method for measuring consistability of a distributed storage system is disclosed. The method includes determining at least one consistency level that the distributed storage system can provide. A plurality of failure classes can be determined for the distributed storage system. A probability of the distributed storage system to be in each of the plurality of failure classes can be measured. Each failure class can be mapped to the at least one consistency level. The probability of each failure class for each consistency level can be summed to determine an expected portion of time that the distributed storage system provides each consistency level.

Abstract: A fault tolerant system is simulated to determine the occurrence of data loss in the fault tolerant system. A list of erasure patterns corresponding to an erasure code implemented across the devices in the system is provided and a device event is simulated. The list of erasure patterns is updated based on the device event, and the occurrence of data loss is determined based on the updated list.

Abstract: A technique for selecting an erasure code from a plurality of erasure codes for use in a fault tolerant system comprises generating a preferred set of erasure codes based on characteristics of the codes' corresponding Tanner graphs. The fault tolerances of the preferred codes are compared based at least on the Tanner graphs. A more fault tolerant code is selected based on the comparison.

Abstract: A technique is provided for determining an allocation of the symbols of an erasure code across a plurality of devices. A list of erasure patterns is provided for the erasure code and, based on the list, minimal erasures of minimal weight are identified for the code's symbols. Precedences of the symbols are determined based on the size of the corresponding MEMW. An allocation of the symbols across a plurality of devices is determined based on the precedences.

Abstract: A method for determining a fault tolerance of an erasure code comprises deriving base erasure patterns from a generator matrix of an erasure code, determining which of the base erasure patterns are adjacent to one another and XORing the adjacent base erasure patterns with one another to produce child erasure patterns of the erasure code. The method further comprises combining the base erasure patterns and the child erasure patterns to form a minimal erasures list (MEL) for the erasure code, whereby the MEL corresponds to the fault tolerance of the erasure code. Also provided are methods for communicating and storing data by using the fault tolerance of erasure codes.