Abstract: A method for determining size information related one or more snapshots related to file systems stored in a storage system, the method may include (a) sampling one or more combinations of points in time and logical spaces, the logical spaces are associated with the one or more file systems to provide sampled combinations of sampled portions of file system entities (FSEs) and sampled points in time; (b) searching for relevant snapshots that are relevant to the sampled combinations to provide relevant snapshots at the sampled points in time; and (c) determining physical sizes of the relevant snapshots at the sampled point in time; wherein a number of samples per sampled FSE is indicative of a size of the sampled FSEs.

Abstract: A method for determining size information related one or more file systems stored in a storage system, the method may include (i) sampling one or more logical spaces that are associated with the one or more file systems to provide sampled file system entities (FSEs); wherein a number of samples per sampled FSE is indicative of a size of the sampled FSEs; and (ii) determining logical sizes and physical sizes of different levels of the one or more file systems based on the sampled file system entities.

Abstract: A method for determining size information related one or more snapshots related to file systems stored in a storage system, the method may include (a) sampling one or more combinations of points in time and logical spaces, the logical spaces are associated with the one or more file systems to provide sampled combinations of sampled portions of file system entities (FSEs) and sampled points in time; (b) searching for relevant snapshots that are relevant to the sampled combinations to provide relevant snapshots at the sampled points in time; and (c) determining physical sizes of the relevant snapshots at the sampled point in time; wherein a number of samples per sampled FSE is indicative of a size of the sampled FSEs

Abstract: A method for determining a progress of an execution of a task, the method may include accessing only a portion of a shared task status data structure that (a) is associated with the task, wherein the task is executed by a first plurality of compute elements, and (b) comprises multiple hierarchical levels; wherein an entry of a certain hierarchical level represents an aggregate progress associated with multiple entries of the another hierarchical level; the certain hierarchical level is higher than the other hierarchical level; and determining the progress of the execution of the task based on a content of the portion.

Abstract: A method for adaptively allocating resources to a plurality of jobs. The method comprises selecting a first policy from a plurality of policies for a first job in the plurality of jobs by using a policy selection mechanism, allocating at least one resource to the first job in accordance with the first policy, and in response to completion of the first job, updating the policy selection mechanism to obtain an updated policy selection mechanism by using at least one processor. Updating the policy selection mechanism comprises evaluating the performance of the first policy with respect to the first job by calculating a value of a metric of utility for the first policy based on conditions associated with execution of the first job and updating the policy selection mechanism based on the calculated value and a delay of execution of the first job.

Abstract: A method, system, and computer-readable storage medium for computing a representation of similarity among items in a set of items. Computing a representation of similarity items may comprise generating a first similarity model that represents characteristics of the set of items, the characteristics being indicative of similarity among the items in the set of items. Additionally, computing the representation of similarity may comprise adaptively selecting a subset of the set of items for similarity evaluation based on the first similarity model, receiving a similarity evaluation for the adaptively-selected subset of items, and generating a second similarity model based on the first to similarity model and the received similarity evaluation.

Abstract: A method for adaptively allocating resources to a plurality of jobs. The method comprises selecting a first policy from a plurality of policies for a first job in the plurality of jobs by using a policy selection mechanism, allocating at least one resource to the first job in accordance with the first policy, and in response to completion of the first job, updating the policy selection mechanism to obtain an updated policy selection mechanism by using at least one processor. Updating the policy selection mechanism comprises evaluating the performance of the first policy with respect to the first job by calculating a value of a metric of utility for the first policy based on conditions associated with execution of the first job and updating the policy selection mechanism based on the calculated value and a delay of execution of the first job.

Abstract: A method, system, and computer-readable storage medium for computing a representation of similarity among items in a set of items. Computing a representation of similarity items may comprise generating a first similarity model that represents characteristics of the set of items, the characteristics being indicative of similarity among the items in the set of items. Additionally, computing the representation of similarity may comprise adaptively selecting a subset of the set of items for similarity evaluation based on the first similarity model, receiving a similarity evaluation for the adaptively-selected subset of items, and generating a second similarity model based on the first to similarity model and the received similarity evaluation.

Abstract: A method, system, and computer-readable medium for searching for items in a set of items using a similarity model. These search techniques may be used in an online purchasing system. Receiving orders for items may comprise receiving input from a user indicating a request for a first item in the set of items, picking a first plurality of items from the set of items based on the first item and a similarity model, presenting the first plurality of items to the user, and receiving a request from the user for a second item in the first plurality of items. The similarity model may represent similarity between items in the set of items and may be used to select a subset of items to quickly to lead to identification of an item of interest.