Related papers: Common Permutation Problem
Minimizers sampling is one of the most widely-used mechanisms for sampling strings [Roberts et al., Bioinformatics 2004]. Let $S=S[1]\ldots S[n]$ be a string over a totally ordered alphabet $\Sigma$. Further let $w\geq 2$ and $k\geq 1$ be…
This paper addresses the online exact string matching problem which consists in finding all occurrences of a given pattern p in a text t. It is an extensively studied problem in computer science, mainly due to its direct applications to…
We prove NP-completeness of Yin-Yang / Shiromaru-Kuromaru pencil-and-paper puzzles. Viewed as a graph partitioning problem, we prove NP-completeness of partitioning a rectangular grid graph into two induced trees (normal Yin-Yang), or into…
The sequence a_1,...,a_m is a common subsequence in the set of permutations S = {p_1,...,p_k} on [n] if it is a subsequence of p_i(1),...,p_i(n) and p_j(1),...,p_j(n) for some distinct p_i, p_j in S. Recently, Beame and Huynh-Ngoc (2008)…
In this paper we propose a new approach for developing a proof that P=NP. We propose to use a polynomial-time reduction of a NP-complete problem to Linear Programming. Earlier such attempts used polynomial-time transformation which is a…
A pattern p (i.e., a string of variables and terminals) matches a word w, if w can be obtained by uniformly replacing the variables of p by terminal words. The respective matching problem, i.e., deciding whether or not a given pattern…
A $\lambda$-cover of a string $S$ is a set of strings $\{C_i\}_1^\lambda$ such that every index in $S$ is contained in an occurrence of at least one string $C_i$. The existence of a $1$-cover defines a well-known class of quasi-periodic…
The problem we consider is the following: Given an infinite word $w$ on an ordered alphabet, construct the sequence $\nu_w=(\nu[n])_n$, equidistributed on $[0,1]$ and such that $\nu[m]<\nu[n]$ if and only if $\sigma^m(w)<\sigma^n(w)$, where…
An automaton is monotonic if its states can be arranged in a linear order that is preserved by the action of every letter. We prove that the problem of deciding whether a given automaton is monotonic is NP-complete. The same result is…
We consider string matching with variable length gaps. Given a string $T$ and a pattern $P$ consisting of strings separated by variable length gaps (arbitrary strings of length in a specified range), the problem is to find all ending…
Let gamma be a (not necessarily finite) structure with a finite relational signature. We prove that deciding whether a given existential positive sentence holds in gamma is in Logspace or complete for the class CSP(gamma)_NP under…
We prove that persuasion is an NP-complete problem.
We study permutation (jumbled/Abelian) pattern matching over a general alphabet $\Sigma$. Given a pattern P of length m and a text T of length n, the classical task is to decide whether T contains a length-m substring whose Parikh vector…
The original knapsack problem is well known to be NP-complete. In a multidimensional version one have to decide whether a $p\in \N^k$ is in a sumset-sum of a set $X \subseteq \N^k$ or not. In this paper we are going to investigate a…
A consecutive pattern in a permutation $\pi$ is another permutation $\sigma$ determined by the relative order of a subsequence of contiguous entries of $\pi$. Traditional notions such as descents, runs and peaks can be viewed as particular…
There are at present two known string theories in $(2,2)$ dimensions. One of them is the well known $N=2$ string, and the other one is a more recently constructed $N=1$ spacetime supersymmetric string. They are both based on certain…
We characterize those strings whose suffix arrays are based on arithmetic progressions, in particular, arithmetically progressed permutations where all pairs of successive entries of the permutation have the same difference modulo the…
We define the ``shift-match number'' for a binary string and we compute the probability of occurrence of a given string as a subsequence in longer strings in terms of its shift-match number. We thus prove that the string matching…
In this paper we study the complexity of solving a problem when a solution of a similar instance is known. This problem is relevant whenever instances may change from time to time, and known solutions may not remain valid after the change.…
The regular number of a graph G denoted by reg(G) is the minimum number of subsets into which the edge set of G can be partitioned so that the subgraph induced by each subset is regular. In this work we answer to the problem posed as an…