In computer science, an interval tree is a tree data structure to hold intervals. Specifically, it allows one to efficiently find all intervals that overlap with any given interval or point. It is often used for windowing queries,[1] for instance, to find all roads on a computerized map inside a rectangular viewport, or to find all visible elements inside a three-dimensional scene. A similar data structure is the segment tree.
The trivial solution is to visit each interval and test whether it intersects the given point or interval, which requires time, where is the number of intervals in the collection. Since a query may return all intervals, for example if the query is a large interval intersecting all intervals in the collection, this is asymptotically optimal; however, we can do better by considering output-sensitive algorithms, where the runtime is expressed in terms of , the number of intervals produced by the query. Interval trees have a query time of and an initial creation time of , while limiting memory consumption to . After creation, interval trees may be dynamic, allowing efficient insertion and deletion of an interval in time. If the endpoints of intervals are within a small integer range (e.g., in the range ), faster and in fact optimal data structures exist[2][3] with preprocessing time and query time for reporting intervals containing a given query point (see[2] for a very simple one).
computer science, an intervaltree is a tree data structure to hold intervals. Specifically, it allows one to efficiently find all intervals that overlap with...
structure is the intervaltree. A segment tree for a set I of n intervals uses O(n log n) storage and can be built in O(n log n) time. Segment trees support searching...
with dynamic number of processes. In 2008, Almeida et al. introduced IntervalTree Clocks. This mechanism generalizes Vector Clocks and allows operation...
the lcp-interval associated with the corresponding node of suffix tree of S can be defined as: Interval [i,..j], 0 ≤ i ≤ j ≤ n is an lcp-interval of lcp-value...
scalability problems in some settings, but can be replaced by IntervalTree Clocks. IntervalTree Clocks generalize version vectors and vector clocks and allows...
In computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search algorithm that finds the position...
range query on a range tree reports the set of points that lie inside a given interval. To report the points that lie in the interval [x1, x2], we start by...
nested set collections (also known as trees or hierarchies) in relational databases. It is based on Nested Intervals, that "are immune to hierarchy reorganization...
generalization of the interval graphs. The connected triangle-free interval graphs are exactly the caterpillar trees. Proper interval graphs are interval graphs that...
"The Sound of Trees" "Assertive" 1916 in poetry Robert Frost Frost, Robert. Mountain Interval (1916), Henry Holt And Company Mountain Interval public domain...
Interval recognition, the ability to name and reproduce musical intervals, is an important part of ear training, music transcription, musical intonation...
search tree can be efficiently queried for a key in a closed interval and for a maximum priority value. That is, one can specify an interval [min_key...
bounding interval hierarchy (BIH) is a partitioning data structure similar to that of bounding volume hierarchies or kd-trees. Bounding interval hierarchies...
consecutive ones property, recognizing interval graphs, and determining whether a graph is planar. If all the leaves of a PQ tree are connected directly to a root...
edges of the tree can be decomposed into. They are the connected graphs of pathwidth one. They are the connected triangle-free interval graphs. They are...
The Spanning Tree Protocol (STP) is a network protocol that builds a loop-free logical topology for Ethernet networks. The basic function of STP is to...
(data structure) diet (see discrete interval encoding tree below) difference (set theory) digital search tree digital tree digraph Dijkstra's algorithm diminishing...
{R} } -tree obtained in the following way is nonsimplicial. Start with the interval [0, 2] and glue, for each positive integer n, an interval of length...
were pruned at intervals of two to six years so their leafy material would be most abundant. Wood pollards were pruned at longer intervals of eight to fifteen...
(counted as the maximal number of levels) of an AVL tree with n {\displaystyle n} nodes lies in the interval:: 460 log 2 ( n + 1 ) ≤ h < log φ ( n + 2...
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