## The Interval Skip List: A Data Structure for Finding All Intervals That Overlap a Point (1992)

Venue: | In Proc. of the 2nd Workshop on Algorithms and Data Structures |

Citations: | 23 - 3 self |

### BibTeX

@INPROCEEDINGS{Hanson92theinterval,

author = {Eric N. Hanson and Theodore Johnson},

title = {The Interval Skip List: A Data Structure for Finding All Intervals That Overlap a Point},

booktitle = {In Proc. of the 2nd Workshop on Algorithms and Data Structures},

year = {1992},

pages = {153--164},

publisher = {Springer}

}

### Years of Citing Articles

### OpenURL

### Abstract

A problem that arises in computational geometry, pattern matching, and other applications is the need to quickly determine which of a collection of intervals overlap a point. Requests of this type are called stabbing queries. A recently discovered randomized data structure called the skip list can maintain ordered sets efficiently, just as balanced binary search trees can, but is much simpler to implement than balanced trees. This paper introduces an extension of the skip list called the interval skip list, or IS-list, to support interval indexing. The IS-list allows stabbing queries and dynamic insertion and deletion of intervals. A stabbing query using an IS-list containing n intervals takes an expected time of O(log n). Inserting or deleting an interval in an IS-list takes an expected time of O(log 2 n) if the interval endpoints are chosen from a continuous distribution. Moreover, the IS-list inherits much of the simplicity of the skip list -- it can be implemented in a relativ...

### Citations

2341 | R-trees: A dynamic index structure for spatial searching
- GUTTMAN
- 1984
(Show Context)
Citation Context ...Ede83a, Ede83b]. Unfortunately, as with the segment tree, all the intervals must be known in advance to construct an interval tree. A data structure that can index intervals dynamically is the R-tree =-=[Gut84]-=-. R-trees are a multidimensional extension of B-trees in which each tree node contains a set of possibly overlapping n-dimensional rectangles. Subtrees of each index node contain only data that lies w... |

1625 |
An Introduction to Probability Theory and its
- Feller
- 1971
(Show Context)
Citation Context ...ed on e w . The endpoints of the interval are uniformly randomly chosen, so that the joint distribution of (a; b) has the distribution of a two element order statistic. The theory of order statistics =-=[Fel70]-=- tells us that the density of the joint distribution g(a; b) is a constant 2 in the region b 2 [0; 1], a 2 [0; b]. Let us define w 1 and w 2 to be the lower and higher endpoints of e w . We can also s... |

1227 |
The Design and Analysis of Spatial Data Structures
- Samet
- 1989
(Show Context)
Citation Context ...ortant problem that arises in a number of computer applications is the need to find all members of a set of intervals that overlap a particular point. Queries of this kind are called stabbing queries =-=[Sam90]-=-. This paper introduces a data structure called the interval skip list (IS-list), which is designed to handle stabbing queries efficiently. The IS-list is an extension of the randomized list structure... |

185 |
An algorithm for the organization of information
- Adelâ€™son-Velâ€™skii, Landis
- 1962
(Show Context)
Citation Context ...the search times is also quite low, making the probability that a search will take significantly longer than log n time vanishingly small. Comparing actual implementations of skip lists and AVL trees =-=[AVL62]-=-, skip lists perform as well as or better than highly-tuned non-recursive implementations of AVL trees, yet programmers tend to agree that skip lists are significantly easier to implement than AVL tre... |

179 |
Priority search trees
- McCreight
- 1985
(Show Context)
Citation Context ...n degenerate rapidly. Another data structure which solves the stabbing query problem efficiently (among others), and does allow dynamic insertion and deletion of intervals is the priority search tree =-=[McC85]-=-. An advantage of the priority search tree is that it requires only O(n) space to index n intervals. However, the priority search tree in its balanced form is very complex to implement [Wir86]. In add... |

87 |
Algorithms + data structures = programs
- Wirth
- 1976
(Show Context)
Citation Context ...ch tree [McC85]. An advantage of the priority search tree is that it requires only O(n) space to index n intervals. However, the priority search tree in its balanced form is very complex to implement =-=[Wir86]-=-. In addition, for a priority search tree to handle a set of intervals with non-unique lower bounds, a special transformation must be used to transform the set of intervals into one where the interval... |

60 |
Lists: A Probabilistic Alternative to Balanced Trees
- Skip
(Show Context)
Citation Context ...interval skip list (IS-list), which is designed to handle stabbing queries efficiently. The IS-list is an extension of the randomized list structure known as the skip list recently discovered by Pugh =-=[Pug90]-=-. In Section 2, other methods for solving stabbing queries are discussed. Section 3 describes the interval skip list data structure and methods for searching and updating it. Section 4 gives an analys... |

54 | A new approach to rectangle intersections - Edelsbrunner - 1983 |

29 | A skip list cookbook - Pugh |

2 |
and Moez Chaabouni. The IBS tree: A data structure for finding all intervals that overlap a point
- Hanson
- 1990
(Show Context)
Citation Context ...e interval binary search tree (IBS-tree) can handle stabbing queries, and can be balanced more easily and is easier to implement than the priority search tree, although it requires O(n log n) storage =-=[HC90]-=-. We conjecture that balanced IBS-trees require O(log n) time for searching and O(log 2 n) average time for insertion and deletion, though a definitive performance analysis has not been done. A data s... |

1 |
Direct dynamic strucutures for some line segment problems
- Gonnet, Munro, et al.
- 1983
(Show Context)
Citation Context ...rmance analysis has not been done. A data structure closely related to the IBS-tree called the stabbing tree has been developed to find the stabbing number for a point given a collection of intervals =-=[GMW83]-=-. The stabbing number is the number of intervals that overlap a point. In contrast, the IBS-tree and the IS-list return a stabbing set containing all the intervals overlapping the query point, not jus... |