Related papers: Cartesian Tree Matching and Indexing
Cartesian tree matching is the problem of finding all substrings of a given text which have the same Cartesian trees as that of a given pattern. So far there is one linear-time solution for Cartesian tree matching, which is based on the KMP…
Cartesian tree pattern matching consists of finding all the factors of a text that have the same Cartesian tree than a given pattern. There already exist theoretical and practical solutions for the exact case. In this paper, we propose the…
Cartesian tree pattern matching consists of finding all the factors of a text that have the same Cartesian tree than a given pattern. There already exist theoretical and practical solutions for the exact case. In this paper, we propose the…
The Cartesian tree of a sequence captures the relative order of the sequence's elements. In recent years, Cartesian tree matching has attracted considerable attention, particularly due to its applications in time series analysis. Consider a…
In this paper, we introduce the notion of Cartesian Forest, which generalizes Cartesian Trees, in order to deal with partially ordered sequences. We show that algorithms that solve both exact and approximate Cartesian Tree Matching can be…
Park et al. [TCS 2020] observed that the similarity between two (numerical) strings can be captured by the Cartesian trees: The Cartesian tree of a string is a binary tree recursively constructed by picking up the smallest value of the…
Cartesian tree matching is the problem of finding all substrings in a given text which have the same Cartesian trees as that of a given pattern. In this paper, we deal with Cartesian tree matching for the case of multiple patterns. We…
Two strings of the same length are said to Cartesian-tree match (CT-match) if their Cartesian-trees are isomorphic [Park et al., TCS 2020]. Cartesian-tree matching is a natural model that allows for capturing similarities of numerical…
The Cartesian-tree pattern matching is a recently introduced scheme of pattern matching that detects fragments in a sequential data stream which have a similar structure as a query pattern. Formally, Cartesian-tree pattern matching seeks…
Recently Kubica et al. (Inf. Process. Let., 2013) and Kim et al. (submitted to Theor. Comp. Sci.) introduced order-preserving pattern matching. In this problem we are looking for consecutive substrings of the text that have the same "shape"…
Packing several characters into one computer word is a simple and natural way to compress the representation of a string and to speed up its processing. Exploiting this idea, we propose an index for a packed string, based on a {\em sparse…
A central task in string processing is text indexing, where the goal is to preprocess a text (a string of length $n$) into an efficient index (a data structure) supporting queries about the text. Cole, Gottlieb, and Lewenstein (STOC 2004)…
We study the design of efficient algorithms for combinatorial pattern matching. More concretely, we study algorithms for tree matching, string matching, and string matching in compressed texts.
Pattern matching is a fundamental process in almost every scientific domain. The problem involves finding the positions of a given pattern (usually of short length) in a reference stream of data (usually of large length). The matching can…
We consider an index data structure for similar strings. The generalized suffix tree can be a solution for this. The generalized suffix tree of two strings $A$ and $B$ is a compacted trie representing all suffixes in $A$ and $B$. It has…
Cartesian tree matching is a form of generalized pattern matching where a substring of the text matches with the pattern if they share the same Cartesian tree. This form of matching finds application for time series of stock prices and can…
We suggest a new non-recursive algorithm for constructing a binary search tree given an array of numbers. The algorithm has $O(N)$ time and $O(1)$ memory complexity if the given array of $N$ numbers is sorted. The resulting tree is of…
We revisit a fundamental problem in string matching: given a pattern of length m and a text of length n, both over an alphabet of size $\sigma$, compute the Hamming distance between the pattern and the text at every location. Several…
We consider the well-studied pattern counting problem: given a permutation $\pi \in \mathbb{S}_n$ and an integer $k > 1$, count the number of order-isomorphic occurrences of every pattern $\tau \in \mathbb{S}_k$ in $\pi$. Our first result…
Error Tree is a novel tree structure that is mainly oriented to solve the approximate pattern matching problems, Hamming and edit distances, as well as the wildcards matching problem. The input is a text of length $n$ over a fixed alphabet…