Related papers: Faster Exponential Algorithm for Permutation Patte…
We describe the first self-indexes able to count and locate pattern occurrences in optimal time within a space bounded by the size of the most popular dictionary compressors. To achieve this result we combine several recent findings,…
Template matching is widely used for many applications in image and signal processing and usually is time-critical. Traditional methods usually focus on how to reduce the search locations by coarse-to-fine strategy or full search combined…
We study the complexity of the decision problem known as Permutation Pattern Matching, or PPM. The input of PPM consists of a pair of permutations $\tau$ (the `text') and $\pi$ (the `pattern'), and the goal is to decide whether $\tau$…
Significance testing -- especially the paired-permutation test -- has played a vital role in developing NLP systems to provide confidence that the difference in performance between two systems (i.e., the test statistic) is not due to luck.…
The classic string indexing problem is to preprocess a string S into a compact data structure that supports efficient pattern matching queries. Typical queries include existential queries (decide if the pattern occurs in S), reporting…
The worst-case fastest known algorithm for the Set Cover problem on universes with $n$ elements still essentially is the simple $O^*(2^n)$-time dynamic programming algorithm, and no non-trivial consequences of an $O^*(1.01^n)$-time…
A family of comparison-based exact pattern matching algorithms is described. They utilize multi-dimensional arrays in order to process more than one adjacent text window in each iteration of the search cycle. This approach leads to a lower…
In this paper, we develop new tools and connections for exponential time approximation. In this setting, we are given a problem instance and a parameter $\alpha>1$, and the goal is to design an $\alpha$-approximation algorithm with the…
Given a set of pattern strings $\mathcal{P}=\{P_1, P_2,\ldots P_k\}$ and a text string $S$, the classic dictionary matching problem is to report all occurrences of each pattern in $S$. We study the dictionary problem in the compressed…
Two recent lower bounds on the compressibility of repetitive sequences, $\delta \le \gamma$, have received much attention. It has been shown that a length-$n$ string $S$ over an alphabet of size $\sigma$ can be represented within the…
Repeat finding in strings has important applications in subfields such as computational biology. The challenge of finding the longest repeats covering particular string positions was recently proposed and solved by \.{I}leri et al., using a…
We consider the algorithm by Ferson et al. (Reliable computing 11(3), p. 207-233, 2005) designed for solving the NP-hard problem of computing the maximal sample variance over interval data, motivated by robust statistics (in fact, the…
We consider the problem of encoding a string of length $n$ from an integer alphabet of size $\sigma$ so that access and substring equality queries (that is, determining the equality of any two substrings) can be answered efficiently. Any…
We present two new deterministic algorithms for the Feedback Vertex Set problem parameterized by the solution size. We begin with a simple algorithm, which runs in O*((2 + \phi)^k) time, where \phi < 1.619 is the golden ratio. It already…
In this paper we suggest analytical methods and associated algorithms for determining the sum of the subsets $X_m$ of the set $X_n$ (subset sum problem). Our algorithm has time complexity $T=O(C_{n}^{k})$ ($k=[m/2]$, which significantly…
We present parallel algorithms for exact and approximate pattern matching with suffix arrays, using a CREW-PRAM with $p$ processors. Given a static text of length $n$, we first show how to compute the suffix array interval of a given…
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"…
The $k$-mappability problem has two integers parameters $m$ and $k$. For every subword of size $m$ in a text $S$, we wish to report the number of indices in $S$ in which the word occurs with at most $k$ mismatches. The problem was lately…
Let $S_1, S_2 \in \Sigma^*$ strings, we say that $S_1$ {\em jumble match} $S_2$ if they are permutations of each other. Given a text $T$ of size $N$ and a string $S \in \Sigma^*$, the problem of \emph{Jumbled Pattern Matching} (JPM) is to…
We show new algorithms and constructions over linear delta-matroids. We observe an alternative representation for linear delta-matroids, as a contraction representation over a skew-symmetric matrix. This is equivalent to the more standard…