Related papers: A Suffix Tree Or Not A Suffix Tree?
We deal with the problem of maintaining the suffix tree indexing structure for a fully-online collection of multiple strings, where a new character can be prepended to any string in the collection at any time. The only previously known…
We solve the problem of finding interspersed maximal repeats using a suffix array construction. As it is well known, all the functionality of suffix trees can be handled by suffix arrays, gaining practicality. Our solution improves the…
The precise formulation of derivation for tree-adjoining grammars has important ramifications for a wide variety of uses of the formalism, from syntactic analysis to semantic interpretation and statistical language modeling. We argue that…
This paper presents a tree-to-tree transduction method for sentence compression. Our model is based on synchronous tree substitution grammar, a formalism that allows local distortion of the tree topology and can thus naturally capture…
A closed-form formula is derived for the number of occurrences of matches of a multiset of patterns among all ordered (plane-planted) trees with a given number of edges. A pattern looks like a tree, with internal nodes and leaves, but also…
Let $\Sigma$ and $\Pi$ be disjoint alphabets, respectively called the static alphabet and the parameterized alphabet. Two strings $x$ and $y$ over $\Sigma \cup \Pi$ of equal length are said to parameterized match (p-match) if there exists a…
The computational complexity of the isomorphism problem for regular trees, regular linear orders, and regular words is analyzed. A tree is regular if it is isomorphic to the prefix order on a regular language. In case regular languages are…
Given a set $F$ of words, one associates to each word $w$ in $F$ an undirected graph, called its extension graph, and which describes the possible extensions of $w$ on the left and on the right. We investigate the family of sets of words…
We present the first solution to $\tau$-majorities on tree paths. Given a tree of $n$ nodes, each with a label from $[1..\sigma]$, and a fixed threshold $0<\tau<1$, such a query gives two nodes $u$ and $v$ and asks for all the labels that…
The signature of a spanning tree $T$ of the $n$-cube $Q_n$ is the $n$-tuple $\mathrm{sig}(T)=(a_1,a_2,\dots,a_n)$ such that $a_i$ is the number of edges of $T$ in the $i$th direction. We characterise the $n$-tuples that can occur as the…
We study a class of combinatorial objects that we call "decorated trees". These consist of vertices, arrows and edges, where each edge is decorated by two integers (one near each of its endpoints), each arrow is decorated by an integer, and…
The Subtree Isomorphism problem asks whether a given tree is contained in another given tree. The problem is of fundamental importance and has been studied since the 1960s. For some variants, e.g., ordered trees, near-linear time algorithms…
Tree-structured neural networks encode a particular tree geometry for a sentence in the network design. However, these models have at best only slightly outperformed simpler sequence-based models. We hypothesize that neural sequence models…
Tree-width is an invaluable tool for computational problems on graphs. But often one would like to compute on other kinds of objects (e.g. decorated graphs or even algebraic structures) where there is no known tree-width analogue. Here we…
We study the following substring suffix selection problem: given a substring of a string T of length n, compute its k-th lexicographically smallest suffix. This a natural generalization of the well-known question of computing the maximal…
A spectral faux tree with respect to a given matrix is a graph which is not a tree but is cospectral with a tree for the given matrix. We consider the existence of spectral faux trees for several matrices, with emphasis on constructions.…
We give a short and direct proof of a remarkable identity that arises in the enumeration of labeled trees with respect to their indegree sequence, where all edges are oriented from the vertex with lower label towards the vertex with higher…
We introduce a new metric of match, called Cartesian tree matching, which means that two strings match if they have the same Cartesian trees. Based on Cartesian tree matching, we define single pattern matching for a text of length n and a…
We show that equivalence of deterministic top-down tree-to-string transducers is decidable, thus solving a long standing open problem in formal language theory. We also present efficient algorithms for subclasses: polynomial time for total…
The weighted ancestor problem on a rooted node-weighted tree $T$ is a generalization of the classic predecessor problem: construct a data structure for a set of integers that supports fast predecessor queries. Both problems are known to…