Related papers: A New Algorithm for Building Alphabetic Minimax Tr…
Most of the attention in statistical compression is given to the space used by the compressed sequence, a problem completely solved with optimal prefix codes. However, in many applications, the storage space used to represent the prefix…
Tree path minimum query problem is a fundamental problem while processing trees, and is used widely in minimum spanning tree verification and randomized minimum spanning tree algorithms. In this paper, we study the possibility of building…
The palindromic tree (a.k.a. eertree) for a string $S$ of length $n$ is a tree-like data structure that represents the set of all distinct palindromic substrings of $S$, using $O(n)$ space [Rubinchik and Shur, 2018]. It is known that, when…
We propose new succinct representations of ordinal trees, which have been studied extensively. It is known that any $n$-node static tree can be represented in $2n + o(n)$ bits and a number of operations on the tree can be supported in…
We introduce the first index that can be built in $o(n)$ time for a text of length $n$, and can also be queried in $o(q)$ time for a pattern of length $q$. On an alphabet of size $\sigma$, our index uses $O(n\sqrt{\log n\log\sigma})$ bits,…
In this paper, we have developed a fully-dynamic algorithm for maintaining cardinality of maximum-matching in a tree using the construction of top-trees. The time complexities are as follows: 1. Initialization Time: $O(n(log(n)))$ to build…
Binary jumbled pattern matching asks to preprocess a binary string $S$ in order to answer queries $(i,j)$ which ask for a substring of $S$ that is of length $i$ and has exactly $j$ 1-bits. This problem naturally generalizes to…
We give the first algorithm for adaptive alphabetic prefix-free coding that is worst-case optimal in terms of time and compression when $\sigma \in o \left( \frac{n^{1 / 2}}{\log n} \right)$, where $\sigma$ is the size of the alphabet and…
Given two strings $T$ and $S$ and a set of strings $P$, for each string $p \in P$, consider the unique substrings of $T$ that have $p$ as their prefix and $S$ as their suffix. Two problems then come to mind; the first problem being the…
The problem of finding factors of a text string which are identical or similar to a given pattern string is a central problem in computer science. A generalised version of this problem consists in implementing an index over the text to…
We give the first data structure for the problem of maintaining a dynamic set of n elements drawn from a partially ordered universe described by a tree. We define the Line-Leaf Tree, a linear-sized data structure that supports the…
We consider the problem of augmenting an n-vertex graph embedded in a metric space, by inserting one additional edge in order to minimize the diameter of the resulting graph. We present exact algorithms for the cases when (i) the input…
Path partition problems on trees have found various applications. In this paper, we present an $O(n \log n)$ time algorithm for solving the following variant of path partition problem: given a rooted tree of $n$ nodes $1, \ldots, n$, where…
It is shown that for finding rational approximates to m'th root of any integer to any accuracy one only needs the ability to count and to distinguish between m different classes of objects. To every integer N can be associated a…
We present several results about position heaps, a relatively new alternative to suffix trees and suffix arrays. First, we show that, if we limit the maximum length of patterns to be sought, then we can also limit the height of the heap and…
We present a new algorithm for subsequence matching in grammar compressed strings. Given a grammar of size $n$ compressing a string of size $N$ and a pattern string of size $m$ over an alphabet of size $\sigma$, our algorithm uses…
A seed in a word is a relaxed version of a period in which the occurrences of the repeating subword may overlap. We show a linear-time algorithm computing a linear-size representation of all the seeds of a word (the number of seeds might be…
The block tree [Belazzougui et al., J. Comput. Syst. Sci. '21] is a compressed representation of a length-$n$ text that supports access, rank, and select queries while requiring only $O(z\log\frac{n}{z})$ words of space, where $z$ is the…
The problem of constructing optimal factoring automata arises in the context of unification factoring for the efficient execution of logic programs. Given an ordered set of $n$ strings of length $m$, the problem is to construct a trie-like…
In this paper we describe an algorithm for generating all the possible $PIW(m,n,k)$ - integer $m\times n$ Weighing matrices of weight $k$ up to Hadamard equivalence. Our method is efficient on a personal computer for small size matrices, up…