# Chapter 56
Interval Skip List

Andreas Fabri

This chapter presents the interval skip list introduced by Hanson [Han91], and derived from the skip list data structure [Pug90].

The data structure stores intervals and allows to perform stabbing queries, that is to test wether a point is covered by any of the intervals. It further allows to find all intervals that contain a point.

The interval skip list is, as far as its functionality is concerned, related to the Segment_tree. Both allow to do stabbing queries and both allow to find all intervals that contain a given point. The implementation of segment trees in CGAL works in higher dimensions, whereas the interval skip list is limited to the 1D case. However, this interval skip list implementation is fully dynamic, whereas the segment tree implementation in CGAL is static, that is all intervals must be known in advance.

This package has one concept, namely for the interval with which the interval skip list class is parameterized.

### Concepts

Interval

### Classes

CGAL::Interval_skip_list<Interval>
CGAL::Interval_skip_list_interval<Value>
CGAL::Level_interval<FaceHandle>

### Alphabetical List of Reference Pages

- Interval_skip_list<Interval>

- Interval

- Interval_skip_list_interval<Value>

- Level_interval<FaceHandle>