Related papers: Wavelet Trees Meet Suffix Trees
We propose a dynamic programming algorithm for projection onto wavelet tree structures. In contrast to other recently proposed algorithms which only give approximate tree projections for a given sparsity, our algorithm is guaranteed to…
This paper studies the performances of BERT combined with tree structure in short sentence ranking task. In retrieval-based question answering system, we retrieve the most similar question of the query question by ranking all the questions…
Given a pattern $P$ and a text $T$, both strings over a binary alphabet, the binary jumbled string matching problem consists in telling whether any permutation of $P$ occurs in $T$. The indexed version of this problem, i.e., preprocessing a…
In this paper, we provide algorithms to rank and unrank certain degree-restricted classes of Cayley trees (spanning trees of the n-vertex complete graph). Specifically, we consider classes of trees that have a given set of leaves or a fixed…
We consider partitions of a point set into two parts, and the lengths of the minimum spanning trees of the original set and of the two parts. If $w(P)$ denotes the length of a minimum spanning tree of $P$, we show that every set $P$ of $n…
In this work, we study the limits of compressed data structures, i.e., structures that support various queries on an input text $T\in\Sigma^n$ using space proportional to the size of $T$ in compressed form. Nearly all fundamental queries…
The tree edit distance is a natural dissimilarity measure between rooted ordered trees whose nodes are labeled over an alphabet $\Sigma$. It is defined as the minimum number of node edits (insertions, deletions, and relabelings) required to…
Palindromes are strings that read the same forward and backward. Problems of computing palindromic structures in strings have been studied for many years with a motivation of their application to biology. The longest palindrome problem is…
In the field of algorithmic analysis, one of the more well-known exercises is the subset sum problem. That is, given a set of integers, determine whether one or more integers in the set can sum to a target value. Aside from the brute-force…
In this paper we present an algorithm to compute the Lyndon array of a string $T$ of length $n$ as a byproduct of the inversion of the Burrows-Wheeler transform of $T$. Our algorithm runs in linear time using only a stack in addition to the…
We investigate the complexity of several fundamental polynomial-time solvable problems on graphs and on matrices, when the given instance has low treewidth; in the case of matrices, we consider the treewidth of the graph formed by non-zero…
A decision tree recursively splits a feature space $\mathbb{R}^{d}$ and then assigns class labels based on the resulting partition. Decision trees have been part of the basic machine-learning toolkit for decades. A large body of work treats…
We consider a sliding window $W$ over a stream of characters from some alphabet of constant size. The user wants to perform deterministic substring matching on the current sliding window content and obtain positions of the matches. We…
This paper shows the weighted matching problem on general graphs can be solved in time $O(n(m + n\log n))$ for $n$ and $m$ the number of vertices and edges, respectively. This was previously known only for bipartite graphs. The crux is a…
In this work, we study the relative hardness of fundamental problems with state-of-the-art word RAM algorithms that take $O(n\sqrt{\log n})$ time for instances described in $\Theta(n)$ machine words ($\Theta(n\log n)$ bits). This complexity…
Several methods are known for parsing languages generated by Tree Adjoining Grammars (TAGs) in O(n^6) worst case running time. In this paper we investigate which restrictions on TAGs and TAG derivations are needed in order to lower this…
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…
In phylogenetics, a central problem is to infer the evolutionary relationships between a set of species $X$; these relationships are often depicted via a phylogenetic tree -- a tree having its leaves univocally labeled by elements of $X$…
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…
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…