Related papers: De Dictionariis Dynamicis Pauco Spatio Utentibus
Given a dynamic set $K$ of $k$ strings of total length $n$ whose characters are drawn from an alphabet of size $\sigma$, a keyword dictionary is a data structure built on $K$ that provides locate, prefix search, and update operations on…
A fully-dynamic dictionary is a data structure for maintaining sets that supports insertions, deletions and membership queries. A filter approximates membership queries with a one-sided error. We present two designs: 1. The first…
Two recent lower bounds on the compressibility of repetitive sequences, $\delta \le \gamma$, have received much attention. It has been shown that a length-$n$ string $S$ over an alphabet of size $\sigma$ can be represented within the…
We study the problem of constructing a dynamic fully indexable dictionary (FID) in the Word-RAM model using space close to the information-theoretic lower bound. A FID is a data-structure that encodes a bit-vector $B$ of length $u$ and…
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…
Continuous-time quantum walks can be used to solve the spatial search problem, which is an essential component for many quantum algorithms that run quadratically faster than their classical counterpart, in $\mathcal O(\sqrt n)$ time for $n$…
We solve an open problem related to an optimal encoding of a straight line program (SLP), a canonical form of grammar compression deriving a single string deterministically. We show that an information-theoretic lower bound for representing…
The rank and select operations over a string of length n from an alphabet of size $\sigma$ have been used widely in the design of succinct data structures. In many applications, the string itself need be maintained dynamically, allowing…
The representation of a dynamic ordered set of $n$ integer keys drawn from a universe of size $m$ is a fundamental data structuring problem. Many solutions to this problem achieve optimal time but take polynomial space, therefore preserving…
We introduce exponential search trees as a novel technique for converting static polynomial space search structures for ordered sets into fully-dynamic linear space data structures. This leads to an optimal bound of O(sqrt(log n/loglog n))…
Suffix arrays and LCP arrays are one of the most fundamental data structures widely used for various kinds of string processing. We consider two problems for a read-only string of length $N$ over an integer alphabet $[1, \dots, \sigma]$ for…
We describe algorithmic results for two crucial aspects of allocating resources on computational hardware devices with partial reconfigurability. By using methods from the field of computational geometry, we derive a method that allows…
In this paper we develop a new technique for proving lower bounds on the update time and query time of dynamic data structures in the cell probe model. With this technique, we prove the highest lower bound to date for any explicit problem,…
We consider the problem of maintaining a dynamic set of integers and answering queries of the form: report a point (equivalently, all points) in a given interval. Range searching is a natural and fundamental variant of integer search, and…
The ``state-of-the-art'' in Length Limited Huffman Coding algorithms is the $\Theta(ND)$-time, $\Theta(N)$-space one of Hirschberg and Larmore, where $D\le N$ is the length restriction on the code. This is a very clever, very problem…
Continuing the recent trend, in this article we design several space-efficient algorithms for two well-known graph search methods. Both these search methods share the same name {\it breadth-depth search} (henceforth {\sf BDS}), although…
While operations {\em rank} and {\em select} on static bitvectors can be supported in constant time, lower bounds show that supporting updates raises the cost per operation to $\Theta(\log n/ \log\log n)$ on bitvectors holding $n$ bits.…
In this work, we prove a $\tilde{\Omega}(\lg^{3/2} n )$ unconditional lower bound on the maximum of the query time and update time for dynamic data structures supporting reachability queries in $n$-node directed acyclic graphs under edge…
The membership problem asks to maintain a set $S\subseteq[u]$, supporting insertions and membership queries, i.e., testing if a given element is in the set. A data structure that computes exact answers is called a dictionary. When a (small)…
The monotone minimal perfect hash function (MMPHF) problem is the following indexing problem. Given a set $S= \{s_1,\ldots,s_n\}$ of $n$ distinct keys from a universe $U$ of size $u$, create a data structure $DS$ that answers the following…