Systems and methods for operating a database using distributed memory and set operations, and for evaluating graphs stored in the database. Any system may be represented as a graph structure having nodes and edges. The graph structure is stored in a distributed memory system using a key/value schema wherein each node is stored as a key and a set of neighbor nodes is stored as the corresponding value. A short path from one node to another may be determined by traversing the graph in stages, moving outward from each node in stages until common midpoint nodes are found indicating connections between the nodes. When the midpoint nodes are found, the paths connecting the nodes may be reconstructed