Abstract: Data in a database describe an application domain such as a satisfiability problem. The data are represented in a manner that expresses the structure inherent in the data and one such representation uses group theory and represents the data as one or more “augmented clauses,” where each clause has a pair (c,G) including a database element c and a group G of group elements g acting on it. A query is encoded in a group theory representation and is executed on the group theory representation of the data to identify database elements and associated group elements satisfying the query. If desired, the satisfying database elements are converted from the group theory representation to the native representation of the data.

Abstract: Data in a database describe an application domain such as a satisfiability problem. The data are represented in a manner that expresses the structure inherent in the data and one such representation uses group theory and represents the data as one or more “augmented clauses,” where each clause has a pair (c, G) including a database element c and a group G of group elements g acting on it. A query is encoded in a group theory representation and is executed on the group theory representation of the data to identify database elements and associated group elements satisfying the query. If desired, the satisfying database elements are converted from the group theory representation to the native representation of the data.

Abstract: Increased efficiency and lower cost job scheduling is provided by a system and method that optimizes for cost instead of makespan, and minimizes fluctuations in resource utilization. A schedule is constructed using a workflow scheduling system that includes a load leveler, a cost minimizer, and a manpower planner. The load leveler minimizes makespan, subject to resource limits, and then lowers the resource limits, repeating the process in order to create a flatter schedule. The cost minimizer generates an initial solution, and then incrementally improves it, using the manpower planner to evaluate the different possible solutions. The manpower planner calculates, for a given schedule, the optimal hire/fire decisions to minimize total cost.