Related papers: Dynamic "Succincter"
In [SPAA2007], Bender et al. define a streaming B-tree (or index) as one that supports updates in amortized $o(1)$ IOs, and present a structure achieving amortized $O((\log N)/B)$ IOs and queries in $O(\log N)$ IOs. We extend their result…
We consider the problem of designing a succinct data structure for {\it path graphs} (which are a proper subclass of chordal graphs and a proper superclass of interval graphs) on $n$ vertices while supporting degree, adjacency, and…
In a dynamic retrieval system, documents must be ingested as they arrive, and be immediately findable by queries. Our purpose in this paper is to describe an index structure and processing regime that accommodates that requirement for…
We give the first non-trivial fully dynamic probabilistic tree embedding algorithm for weighted graphs undergoing edge insertions and deletions. We obtain a trade-off between amortized update time and expected stretch against an oblivious…
A retrieval data structure stores a static function f : S -> {0,1}^r . For all x in S, it returns the r-bit value f(x), while for other inputs it may return an arbitrary result. The structure cannot answer membership queries, so it does not…
We introduce the zip tree, a form of randomized binary search tree that integrates previous ideas into one practical, performant, and pleasant-to-implement package. A zip tree is a binary search tree in which each node has a numeric rank…
In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…
Rapidly-exploring Random Tree star (RRT*) has recently gained immense popularity in the motion planning community as it provides a probabilistically complete and asymptotically optimal solution without requiring the complete information of…
Dynamic graphs model many real-world applications, and as their sizes grow, efficiently storing and updating them becomes critical. We present RadixGraph, a fast and memory-efficient data structure for dynamic graph storage. RadixGraph…
It is widely assumed that $O(m+\lg \sigma)$ is the best one can do for finding a pattern of length $m$ in a compacted trie storing strings over an alphabet of size $\sigma$, if one insists on linear-size data structures and deterministic…
Binary search trees (BSTs) with rotations can adapt to various kinds of structure in search sequences, achieving amortized access times substantially better than the Theta(log n) worst-case guarantee. Classical examples of structural…
A dynamic dictionary is a data structure that maintains sets of cardinality at most $n$ from a given universe and supports insertions, deletions, and membership queries. A filter approximates membership queries with a one-sided error that…
In this paper we propose a dynamic data structure that supports efficient algorithms for updating and querying singly connected Bayesian networks (causal trees and polytrees). In the conventional algorithms, new evidence in absorbed in time…
We observe that a standard transformation between \emph{ordinal} trees (arbitrary rooted trees with ordered children) and binary trees leads to interesting succinct binary tree representations. There are four symmetric versions of these…
We present a deterministic algorithm for solving a wide range of dynamic programming problems in trees in $O(\log D)$ rounds in the massively parallel computation model (MPC), with $O(n^\delta)$ words of local memory per machine, for any…
Succinct trees, such as wavelet trees and those based on, for instance, range Min-Max trees (RMMTs), are a family of practical data structures that store information close to their information-theoretic space lower bound. These structures…
The rank problem in succinct data structures asks to preprocess an array A[1..n] of bits into a data structure using as close to n bits as possible, and answer queries of the form rank(k) = Sum_{i=1}^k A[i]. The problem has been intensely…
Suffix trees are one of the most versatile data structures in stringology, with many applications in bioinformatics. Their main drawback is their size, which can be tens of times larger than the input sequence. Much effort has been put into…
Retrieval data structures are data structures that answer key-value queries without paying the space overhead of explicitly storing keys. The problem can be formulated in four settings (static, value-dynamic, incremental, or dynamic), each…
Suffix trees and suffix arrays are two of the most widely used data structures for text indexing. Each uses linear space and can be constructed in linear time for polynomially sized alphabets. However, when it comes to answering queries…