Abstract: Methods and systems provide for a notebook interactive programming environment, having out-of-order code-cell execution, which communicates potential cell execution outcomes. If an event handler receives an event (e.g., open notebook, code change, code execution, etc.) for a cell, without a request for a specific type of analysis (e.g., data-leakage, stale-state), intra-cell analysis is executed based-on the cell's abstract semantics, and an abstract state and pre-summaries are output that indicate the cell's propagation dependency (unbounded variables). If an analysis is associated with the event, starting with the stored abstract state, inter-cell analysis is recursively executed on successor cells having propagation dependencies, until a terminating criteria is reached. Outcomes (e.g., affected cell, line number, bug type, metrics, etc.) are sent via the notebook user-interface to warn users, ahead of concrete code execution, of hypothetical unsafe or safe actions in executing the notebook's code cells.

Abstract: A method may use a minimal set of indices for an input query including identifying the input query including primitive searches that are accelerated using indices, and computing a minimal set of indices for the input query using a polynomial-time algorithm by constructing a bi-partite graph comprising a first and a second vertex set. The first and the second vertex set may be a set of searches in both partitions of the bi-partite graph. Each edge of the edge set may connect a vertex in the first vertex set and a vertex in the second vertex set. The method may further include identifying an edge set as a strict subset relation between at least two searches of the set of searches showing up in the first and second vertex set of the bi-partite graph, and performing relational data analysis using the minimal set of indices for input queries.

Abstract: A method may use a minimal set of indices for an input query including identifying the input query including primitive searches that are accelerated using indices, and computing a minimal set of indices for the input query using a polynomial-time algorithm by constructing a bi-partite graph comprising a first and a second vertex set. The first and the second vertex set may be a set of searches in both partitions of the bi-partite graph. Each edge of the edge set may connect a vertex in the first vertex set and a vertex in the second vertex set. The method may further include identifying an edge set as a strict subset relation between at least two searches of the set of searches showing up in the first and second vertex set of the bi-partite graph, and performing relational data analysis using the minimal set of indices for input queries.

Abstract: A method for performing analysis may use a minimal set of indices for an input query including identifying the input query including primitive searches that are accelerated using indices, computing a minimal set of indices for the input query using an optimal, polynomial-time algorithm, and performing relational data analysis using the minimal set of indices for input queries.

Abstract: A method for performing analysis may use a minimal set of indices for an input query including identifying the input query including primitive searches that are accelerated using indices, computing a minimal set of indices for the input query using an optimal, polynomial-time algorithm, and performing relational data analysis using the minimal set of indices for input queries.