Library which contains several time-dependent data and index structures (e.g., IntervalTree, BucketTimeSeries), as well as algorithms.
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Breinify: Leading Temporal AI Engine


Maven Central License Features: IntervalTree, BucketTimeSeries, ContainerBucketTimeSeries

When should I use the Library

This library was mainly developed to make the life of developers easier, when working with temporal data. The library provides index- and data-structures used to handle real-time temporal data (e.g., time-points, time-intervals).

Usage: Maven Central

The library is available on Maven Central. Just download the library or add it as dependency.


Available Index Structures

The current implementation of the library offers the following index structures:

  • com.brein.time.timeintervals.indexes.IntervalTree (since 1.5.0)


The IntervalTree is an often used index-structure to find intervals within a data-set. There are several implementations available, e.g., [1][2], and for other languages [3][4], as well as the relational interval tree, which can be used within relational database management systems. The presented Java implementation is not only well tested, it can also be persisted and can use a database management system to retrieve the different intervals data from an established database system, as well as utilize caching techniques.

Further information regarding the actual implementation can be found here, [5] and [6].

final IntervalTree tree = IntervalTreeBuilder.newBuilder()
                .collectIntervals(interval -> new ListIntervalCollection())
tree.add(new LongInterval(1L, 5L));
tree.add(new LongInterval(2L, 5L));
tree.add(new LongInterval(3L, 5L));

final Collection<IInterval> overlap = tree.overlap(new Interval(2L, 2L));
overlap.forEach(System.out::println); // will print out [1, 5] and [2, 5]

final Collection<IInterval> find = tree.find(new Interval(2L, 5L));
find.forEach(System.out::println);    // will print out only [2, 5]

The IntervalTree implements the Collection interface and therefore can be used as such for Interval-instances. In addition, it provides some functionality only meaningful for intervals. The following table shows the different functionality, the runtime-complexity, and if available the equivalent Collection method.

IntervalTree Collection Complexity
insert add O(log n)
delete remove O(log n)
find contains O(log n)
overlap n/a O(log n)

Furthermore, the provided implementation offers the following features:

  • storing and querying for multiple (equal) intervals (since 1.5.0), e.g.:
    • calling insert(new IntegerInterval(1, 2)) twice will actually insert two intervals, using a ListIntervalCollection
    • calling insert(new IntegerInterval(1, 2)) twice will only be inserted once, using a SetIntervalCollection
    • calling insert(new IdInteval<>("ID1", 1, 2))) and insert(new IdInteval<>("ID2", 1, 2))) will inserted two intervals (independent of the storage)
  • easy extendable IInterval type, so that every type of data associated to intervals can be handled (since 1.5.0)
  • IntervalTree implements Collection interface (since 1.5.0)
  • IntervalTree provides a real Stream for overlap(...) operation, see Streaming (since 1.6.3)
  • Interval (see documentation) implements Allen's Interval Algebra (since 1.5.2)
  • store, cache, and persist, see documentation (since 1.6.0)
    • use IntervalCollectionObserver and ObservableIntervalCollection to keep your database (storage) up-to-date
    • use the (sample) cache-implementation CaffeineIntervalCollectionFactory, utilizing Caffeine
    • persist the in-memory IntervalTree on shut-down and avoid re-building, utilizing the methods IntervalTreeBuilder.saveToFile() and IntervalTreeBuilder.loadFromFile()
  • auto-balancing, disable balancing, and manuel balancing
    • auto-balancing (activated by default): IntervalTree.setAutoBalancing(true) (since 1.5.0)
    • disable balancing: IntervalTree.setAutoBalancing(false) (since 1.5.0)
    • manual balancing: IntervalTree.balance() (since 1.5.0)
  • time optimized (handling temporal intervals) (to be added in 1.8.0)

Further information regarding this implementation of the IntervalTree are documented here.

Available Data Structures

The current implementation of the library offers the following data structures:

  • com.brein.time.timeseries.BucketTimeSeries (since 1.0.0)
  • com.brein.time.timeseries.ContainerBucketTimeSeries (since 1.0.0)


The BucketTimeSeries is used to group time-points into buckets and keep a time-series for these buckets. As all of the time-series of this library, this time-series is also a rolling time-series regarding the now time point, i.e., it contains information about now and n time-buckets into the pass. The following illustration explains the structure:

 The data structure (which is based on an array) can be explained best with
 an illustration (with n == timeSeriesSize):

   [0] [1] [2] [3] [4] [5] [6] ... [n]

 Each array field is a bucket of time-stamps (ordered back from now):

   [1] ==> [1456980000, 1456980300) ← now, 1 == currentNowIdx
   [2] ==> [1456970700, 1456980000)
   [n] ==> ...
   [0] ==> ...

Whenever the now time point "moves" forward using:

public void setNow(final long unixTimeStamp) throws IllegalTimePointMovement

the data structure is updated using:

 Getting the new currentNowIdx is done by calculating the
 difference between the old now and the new now and moving
 the currentNowIdx forward.

  [0] [1] [2] [3] [4] [5] [6]

 Assume we move the now time stamp forward by three buckets:

  [0] [1] [2] [3] [4] [5] [6]

 So the calculation is done in two steps:
 1.) get the bucket of the new now
 2.) determine the difference between the buckets, if it's negative => error,
     if it is zero => done, otherwise => erase the fields in between and reset
     to zero or null


The current implementation of the library offers the following additional utilities:

  • com.brein.time.expressions.Exp4JTemporalExpressionEvaluator (since 1.7.0)

Temporal Expression Evaluator

With version 1.7.0 of the library a new feature was added, which enables developers to evaluate "temporal" expressions. In general, a TemporalExpression can be understood as a formel expression (i.e., a formula), which contains temporal elements, e.g., now() + 4h. The syntax of the expression may depend on the underlying implementation, thus it is recommended to have a closer look at the provided documentation (for the selected implementation).

The following concrete implementations are currently available: