Answer to: Recommended data structures/algorithms for checking peoples' availability schedules

A sparse matrix can model this kind of data, but it is usually not practical in a database environment and not ideal when the number of users or events is dynamic. Sparse matrices work best when: the dimensions (rows/columns) are fixed the matrix is mostly empty you control the in-memory representation In your case: The number of users is not fixed, so the matrix dimensions change constantly. Your data lives in a database, where you cannot easily implement the linked-node structure that sparse matrices depend on. Most relational and NoSQL databases already store sparse data efficiently using indexes, join tables, or adjacency lists, so you gain very little by trying to emulate a sparse matrix manually. Why a sparse matrix isn’t ideal here Sparse matrices let you quickly traverse neighbors in each dimension (next user, next time slot, next event). But your domain has additional constraints: A user can attend only one event per time slot An event typically spans multiple adjacent time slots This collapses “event × time” into a single interval, which removes the benefit of a true multidimensional sparse structure. What works better In a database setting, the normal and efficient design is: users events event_time_slots user_event_participation (user_id, event_id, timeslot_id) With proper indexes on (user_id, timeslot_id) and (event_id, user_id), you can efficiently query: Which users attend an event What times a user is busy Which event occupies a time slot Conflict detection across users/events/time Databases are already optimized for exactly these operations, so a sparse matrix brings no practical advantage. Conclusion A sparse matrix is conceptually interesting but not a good fit: Dimensions change dynamically Data is managed by a database Database indexes and join tables already give you the performance benefits you would expect from a sparse matrix Stick with relational modeling + proper indexing — it will be simpler, scalable, and much easier to maintain.