Related papers: Finding Distinct Subpalindromes Online
Online algorithms make decisions based on past inputs. In general, the decision may depend on the entire history of inputs. If many computers run the same online algorithm with the same input stream but are started at different times, they…
The authors recently gave an $n^{O(\log\log n)}$ time membership query algorithm for properly learning decision trees under the uniform distribution (Blanc et al., 2021). The previous fastest algorithm for this problem ran in $n^{O(\log…
DNA sequencing is the process of determining the exact order of the nucleotide bases of an individual's genome in order to catalogue sequence variation and understand its biological implications. Whole-genome sequencing techniques produce…
In this paper we present two algorithms for the following problem: given a string and a rational $e > 1$, detect in the online fashion the earliest occurrence of a repetition of exponent $\ge e$ in the string. 1. The first algorithm…
Many search engines such as Google, Bing & Yahoo! show search suggestions when users enter search phrases on their interfaces. These suggestions are meant to assist the user in finding what she wants quickly and also suggesting common…
We present an online algorithm to deal with pattern matching in strings. The problem we investigate is commonly known as string matching with mismatches in which the objective is to report the number of characters that match when a pattern…
Given $n$ intervals on a line $\ell$, we consider the problem of moving these intervals on $\ell$ such that no two intervals overlap and the maximum moving distance of the intervals is minimized. The difficulty for solving the problem lies…
We study the problem of supporting queries on a string $S$ of length $n$ within a space bounded by the size $\gamma$ of a string attractor for $S$. Recent works showed that random access on $S$ can be supported in optimal…
We study the problem of finding monotone subsequences in an array from the viewpoint of sublinear algorithms. For fixed $k \in \mathbb{N}$ and $\varepsilon > 0$, we show that the non-adaptive query complexity of finding a length-$k$…
In this paper we are dealing with the issue of finding possibly short synchronizing words in automata with weight assigned to each letter in the alphabet $\Sigma$. First we discuss some complexity problems, and then we present new…
We present a simple $O(n^4)$-time algorithm for computing optimal search trees with two-way comparisons. The only previous solution to this problem, by Anderson et al., has the same running time, but is significantly more complicated and is…
We introduce an asymptotically optimal representation of the Manacher array of a string that supports constant-time access. The approach relies on the combinatorial properties of palindromes, yielding a compact yet efficient structure. This…
Various grammar compression algorithms have been proposed in the last decade. A grammar compression is a restricted CFG deriving the string deterministically. An efficient grammar compression develops a smaller CFG by finding duplicated…
Simon's congruence $\sim_k$ is defined as follows: two words are $\sim_k$-equivalent if they have the same set of subsequences of length at most $k$. We propose an algorithm which computes, given two words $s$ and $t$, the largest $k$ for…
Online bipartite matching is a fundamental problem in online algorithms. The goal is to match two sets of vertices to maximize the sum of the edge weights, where for one set of vertices, each vertex and its corresponding edge weights appear…
In the well-known Minimum Linear Arrangement problem (MinLA), the goal is to arrange the nodes of an undirected graph into a permutation so that the total stretch of the edges is minimized. This paper studies an online (learning) variant of…
The method for analyzing algorithmic runtime complexity using decision trees is discussed using the sorting algorithm. This method is then extended to optimal algorithms which may find all cliques of size q in network N, or simply the first…
A string $S[1,n]$ is a power (or tandem repeat) of order $k$ and period $n/k$ if it can decomposed into $k$ consecutive equal-length blocks of letters. Powers and periods are fundamental to string processing, and algorithms for their…
We introduce data structures answering queries concerning the occurrences of patterns from a given dictionary $\mathcal{D}$ in fragments of a given string $T$ of length $n$. The dictionary is internal in the sense that each pattern in…
Searching for all occurrences of a pattern in a text is a fundamental problem in computer science with applications in many other fields, like natural language processing, information retrieval and computational biology. Sampled string…