COMPASS: Cardinal Orientation Manipulation and Pattern-Aware Spatial Search

The Spatial Pattern Matching paradigm offers a promising direction for searching with incomplete or imperfect information, but it is badly constrained by dependence on graph-based representations and computationally intensive search algorithms like subgraph matching and constraint satisfaction. To address these limitations, we present COMPASS, a suite of data structures and algorithms that enable pattern-based search by encoding the directional relationships between objects in abstracted matrix representations rather than graph structures. We provide a series of recursive search algorithms that leverage our matrix representations to enable spatial search queries with directional constraints, which are typically too dense for previous graph-based approaches. Our search methods find matches even when the query pattern is not aligned to the global coordinate system, resulting in perfect recall in our evaluation. Computationally, our search methods scale with the number of query objects times the number of database objects squared in the worst case, which is significantly better than previous methods. Our empirical measurements show that the performance is typically even better, approaching logarithmic in the number of query terms.