Improved Range Minimum Queries

TL;DR: This paper considers that the objects can move freely and presents a new compressed data structure for storing their trajectories, called ContaCT, based on a combination of logs and snapshots, which outperforms the MVR-tree by orders of magnitude in space and also outperform the compressed representation in time performance.

TL;DR: Existing algorithms can be easily modified to satisfy conditions to answer a small batch of LCA queries and the presented experimental results highlight the practicality of this new scheme.

TL;DR: In this paper, the authors proposed a range minimum query (RMQ) algorithm for answering a small batch of Lowest Common Ancestor (LCA) queries, which can be easily modified to satisfy these conditions.

TL;DR: In this paper, the authors proposed a novel data structure and the algorithms to build, update and perform range query operations of transitive function, which takes O(log(n)) time, and the space required for operating data is also O(cn), where c=3 proving it to be efficient than other data structures such as segment tree and sparse table.

TL;DR: Data structures that represent static unlabeled trees and planar graphs are developed, and there is no other structure that encodes n-node trees with fewer bits per node, as N grows without bound.

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.

TL;DR: This paper presents a framework for experimentation with succinct data structures, providing a large set of configurable components, together with tests, benchmarks, and tools to analyze resource requirements.

TL;DR: This work builds a data structure that allows us to answer efficiently subsequent on-line queries of the form “what is the position of a minimum element in the subarray ranging from $i to $j$?”