Boost C++ Libraries

The Interval Container Library (ICL) provides intervals and two kinds of interval containers: interval_sets and interval_maps.

Two Aspects

Interval_sets and interval_maps expose two different aspects in their interfaces: (1) The functionality of a set or a map, which is the more abstract aspect. And (2) the functionality of a container of intervals which is the more specific and implementation related aspect. In practice both aspects are useful and are therefore supported.

The first aspect, that will be called fundamental aspect, is the more important one. It means that we can use an interval_set or interval_map like a set or map of elements. It exposes the same functions.

interval_set<int> mySet;
mySet.insert(42);
bool has_answer = contains(mySet, 42);

The second aspect, that will be called segmental aspect, allows to exploit the fact, that the elements of interval_sets and interval_maps are clustered in intervals or segments that we can iterate over.

// Switch on my favorite telecasts using an interval_set
interval<seconds>::type news(make_seconds("20:00:00"), make_seconds("20:15:00"));
interval<seconds>::type talk_show(make_seconds("22:45:30"), make_seconds("23:30:50"));
interval_set<seconds> myTvProgram;
myTvProgram.add(news).add(talk_show);

// Iterating over elements (seconds) would be silly ...
for(interval_set<seconds>::iterator telecast = myTvProgram.begin(); 
    telecast != myTvProgram.end(); ++telecast)
    //...so this iterates over intervals
   TV.switch_on(*telecast);

Working with interval_sets and interval_maps can be beneficial whenever the elements of sets appear in contiguous chunks: intervals. This is obviously the case in many problem domains, particularly in fields that deal with computations related to date and time.

Addabitlity and Subtractability

Unlike std::sets and maps, interval_sets and interval_maps implement concept Addable and Subtractable. So interval_sets define an operator += that is naturally implemented as set union and an operator -= that is consequently implemented as set difference. In the Icl interval_maps are addable and subtractable as well. It turned out to be a very fruitful concept to propagate the addition or subtraction to the interval_map's associated values in cases where the insertion of an interval value pair into an interval_map resulted in a collision of the inserted interval value pair with interval value pairs, that are already in the interval_map. This operation propagation is called aggregate on overlap.

Aggregate on Overlap

This is a first motivating example of a very small party, demonstrating the aggregate on overlap principle on interval_maps:

In the example Mary enters the party first. She attends during the time interval [20:00,22:00). Harry enters later. He stays within [21:00,23:00).

typedef std::set<string> guests;
interval_map<time, guests> party; 
party += make_pair(interval<time>::right_open(time("20:00"), time("22:00")), guests("Mary"));
party += make_pair(interval<time>::right_open(time("21:00"), time("23:00")), guests("Harry")); 
// party now contains
[20:00, 21:00)->{"Mary"} 
[21:00, 22:00)->{"Harry","Mary"} //guest sets aggregated on overlap
[22:00, 23:00)->{"Harry"}

On overlap of intervals, the corresponding name sets are accumulated. At the points of overlap the intervals are split. The accumulation of content on overlap of intervals is done via an operator += that has to be implemented for the associated values of the interval_map. In the example the associated values are guest sets. Thus a guest set has to implement operator += as set union.

As can be seen from the example an interval_map has both a decompositional behavior (on the time dimension) as well as an accumulative one (on the associated values).

Addability and aggregate on overlap are useful features on interval_maps implemented via function add and operator +=. But you can also use them with the traditional insert semantics that behaves like std::map::insert generalized for interval insertion.

In addition to interval containers we can work with containers of elements that are behavioral equal to the interval containers: On the fundamental aspect they have exactly the same functionality. An std::set of the STL is such an equivalent set implementation. Due to the aggregation facilities of the icl's interval maps std::map is fundamentally not completely equivalent to an interval_map. Therefore there is an extra icl::map class template for maps of elements in the icl.

The following tables give an overview over the main class templates provided by the icl.

Statically bounded intervals always have the same kind of interval borders, e.g. right open borders[a..b) for right_open_interval. Dynamically bounded intervals can have different borders. Refer to the chapter about intervals for details.

Std::set is placed in paretheses, because it is not a class template of the ICL. It can be used as element container though that is behavioral equal to the ICL's interval sets on their fundamental aspect. Column style refers to the different ways in which interval containers combine added intervals. These combining styles are described in the next section.

When we add intervals or interval value pairs to interval containers, the intervals can be added in different ways: Intervals can be joined or split or kept separate. The different interval combining styles are shown by example in the tables below.

  {[1      3)          }
+       [2      4)
+                 [4 5)
= {[1                5)}

  {[1      3)}         }
+       [2      4)
+                 [4 5)
= {[1           4)[4 5)}

  {[1      3)          }
+       [2      4)
+                 [4 5)
= {[1 2)[2 3)[3 4)[4 5)}

  {[1      3)->1          }
+       [2      4)->1
+                 [4 5)->1
= {[1 2)[2 3)[3      5)   }
  | ->1  ->2     ->1      |

  {[1      3)->1          }
+       [2      4)->1
+                 [4 5)->1
= {[1 2)[2 3)[3 4)[4 5)   }
  | ->1  ->2  ->1  ->1    |

Note that interval_sets A, B and C represent the same set of elements {1,2,3,4} and interval_maps D and E represent the same map of elements {1->1, 2->2, 3->1, 4->1}. See example program Interval container for an additional demo.

Joining interval containers

Interval_set and interval_map are always in a minimal representation. This is useful in many cases, where the points of insertion or intersection of intervals are not relevant. So in most instances interval_set and interval_map will be the first choice for an interval container.

Splitting interval containers

Split_interval_set and split_interval_map on the contrary have an insertion memory. They do accumulate interval borders both from additions and intersections. This is specifically useful, if we want to enrich an interval container with certain time grids, like e.g. months or calendar weeks or both. See example time grids for months and weeks.

Separating interval containers

Separate_interval_set implements the separating style. This style preserves borders, that are never passed by an overlapping interval. So if all intervals that are inserted into a separate_interval_set are generated form a certain grid that never pass say month borders, then these borders are preserved in the separate_interval_set.