Topic
Cartesian tree
About: Cartesian tree is a research topic. Over the lifetime, 185 publications have been published within this topic receiving 9226 citations. The topic is also known as: RBST & randomized binary search tree.
Papers published on a yearly basis
Papers
TL;DR: The multidimensional binary search tree (or k-d tree) as a data structure for storage of information to be retrieved by associative searches is developed and it is shown to be quite efficient in its storage requirements.
Abstract: This paper develops the multidimensional binary search tree (or k-d tree, where k is the dimensionality of the search space) as a data structure for storage of information to be retrieved by associative searches. The k-d tree is defined and examples are given. It is shown to be quite efficient in its storage requirements. A significant advantage of this structure is that a single data structure can handle many types of queries very efficiently. Various utility algorithms are developed; their proven average running times in an n record file are: insertion, O(log n); deletion of the root, O(n(k-1)/k); deletion of a random node, O(log n); and optimization (guarantees logarithmic performance of searches), O(n log n). Search algorithms are given for partial match queries with t keys specified [proven maximum running time of O(n(k-t)/k)] and for nearest neighbor queries [empirically observed average running time of O(log n).] These performances far surpass the best currently known algorithms for these tasks. An algorithm is presented to handle any general intersection query. The main focus of this paper is theoretical. It is felt, however, that k-d trees could be quite useful in many applications, and examples of potential uses are given.
8,209 citations
1 Dec 1984
TL;DR: Three techniques in computational geometry are explored: scaling solves a problem by viewing it at increasing levels of numerical precision; activation is a restricted type of update operation, useful in sweep algorithms; the Cartesian tree is a data structure for problems involving maximums and minimums.
Abstract: Three techniques in computational geometry are explored: Scaling solves a problem by viewing it at increasing levels of numerical precision; activation is a restricted type of update operation, useful in sweep algorithms; the Cartesian tree is a data structure for problems involving maximums and minimums. These techniques solve the minimum spanning tree problem in Rk1 and Rk
609 citations
6 Feb 2014
TL;DR: A new lock-free algorithm for concurrent manipulation of a binary search tree in an asynchronous shared memory system that supports search, insert and delete operations and significantly outperforms all other algorithms for a concurrent binarysearch tree in many cases.
Abstract: We present a new lock-free algorithm for concurrent manipulation of a binary search tree in an asynchronous shared memory system that supports search, insert and delete operations. In addition to read and write instructions, our algorithm uses (single-word) compare-and-swap (CAS) and bit-test-and-set (SETB) atomic instructions, both of which are commonly supported by many modern processors including Intel~64 and AMD64.In contrast to existing lock-free algorithms for a binary search tree, our algorithm is based on marking edges rather than nodes. As a result, when compared to other lock-free algorithms, modify (insert and delete) operations in our algorithm work on a smaller portion of the tree, thereby reducing conflicts, and execute fewer atomic instructions (one for insert and three for delete). Our experiments indicate that our lock-free algorithm significantly outperforms all other algorithms for a concurrent binary search tree in many cases, especially when contention is high, by as much as 100%.
227 citations
TL;DR: The necessary and sufficient conditions for a sequence to represent a binary tree are given, and an algorithm for generating all the feasible sequences lexicographically as a list is given.
Abstract: We represent a binary tree by the level numbers of its leaves from left to right Thus every binary tree of n leaves corresponds to a sequence of n numbers We first give the necessary and sufficient conditions for a sequence to represent a binary tree; then we give an algorithm for generating all the feasible sequences lexicographically as a list Also, algorithms are developed to determine the position of a given sequence, or to generate the sequence of a given position Finally, it is shown that the average time per sequence generated is constant (independent of the length of the sequence)
151 citations
26 Jun 2004
TL;DR: It is shown that randomized search heuristics find minimum spanning trees in expected polynomial time without employing the global technique of greedy algorithms.
Abstract: Randomized search heuristics, among them randomized local search and evolutionary algorithms, are applied to problems whose structure is not well understood, as well as to problems in combinatorial optimization The analysis of these randomized search heuristics has been started for some well-known problems, and this approach is followed here for the minimum spanning tree problem After motivating this line of research, it is shown that randomized search heuristics find minimum spanning trees in expected polynomial time without employing the global technique of greedy algorithms
137 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 2 |
| 2020 | 5 |
| 2019 | 9 |
| 2018 | 3 |
| 2017 | 3 |
| 2016 | 6 |