t2set

t2set, short for time-to-set, is a data representation used to store, for each timestamp, the finite set of elements observed or active at that moment. It is used in time-series and event-processing contexts to capture the evolving membership of items across time. A t2set can be viewed as a mapping from time points to sets, optionally with a specified granularity and ordering to support efficient queries.

Common implementations represent t2sets as an ordered map from timestamps to sets, with support for incremental updates and versioning. Core operations include adding or removing an element at a given time, querying the elements present at a specific time, and performing time-window or time-range queries that return the union or intersection of sets over a span of time. Variants may store deltas between consecutive times to reduce memory use, or use compact encodings for small alphabets. Concurrency considerations and time synchronization semantics are important in distributed environments.

Serialization and interoperability are typical design considerations. t2sets are commonly serialized to JSON, MessagePack, Parquet, or custom binary formats to integrate with data pipelines, databases, and analytics engines. They are used with streaming systems and batch processing to enable temporal feature extraction, event co-occurrence analysis, and set-based pattern mining.

Applications span telemetry and monitoring, user-session modeling, sensor networks, and knowledge-graph construction from time-stamped observations. Design choices—such as time representation, set encoding, and update semantics—affect performance, memory usage, and query latency.