Related papers: Permutation patterns in streams
Permutation Pattern Matching (PPM) is the problem of deciding for a given pair of permutations P and T whether the pattern P is contained in the text T. Bose, Buss and Lubiw showed that PPM is NP-complete. In view of this result, it is…
Given permutations $\sigma \in S_k$ and $\pi \in S_n$ with $k<n$, the \emph{pattern matching} problem is to decide whether $\pi$ matches $\sigma$ as an order-isomorphic subsequence. We give a linear-time algorithm in case both $\pi$ and…
Pattern matching is a fundamental process in almost every scientific domain. The problem involves finding the positions of a given pattern (usually of short length) in a reference stream of data (usually of large length). The matching can…
Frequency estimation in data streams is one of the classical problems in streaming algorithms. Following much research, there are now almost matching upper and lower bounds for the trade-off needed between the number of samples and the…
We study the longest increasing subsequence problem for random permutations avoiding the pattern $312$ and another pattern $\tau$ under the uniform probability distribution. We determine the exact and asymptotic formulas for the average…
A permutation $\pi$ contains a pattern $\sigma$ if and only if there is a subsequence in $\pi$ with its letters are in the same relative order as those in $\sigma$. Partially ordered patterns (POPs) provide a convenient way to denote…
The turnstile continual release model of differential privacy captures scenarios where a privacy-preserving real-time analysis is sought for a dataset evolving through additions and deletions. In typical applications of real-time data…
Multiparty computation is raising importance because it's primary objective is to replace any trusted third party in the distributed computation. This work presents two multiparty shuffling protocols where each party, possesses a private…
Big data streams are possibly one of the most essential underlying notions. However, data streams are often challenging to handle owing to their rapid pace and limited information lifetime. It is difficult to collect and communicate stream…
Recently, B\'ona and Smith defined strong pattern avoidance, saying that a permutation $\pi$ strongly avoids a pattern $\tau$ if $\pi$ and $\pi^2$ both avoid $\tau$. They conjectured that for every positive integer $k$, there is a…
We introduce a notion of pattern occurrence that generalizes both classical permutation patterns as well as poset containment. Many questions about pattern statistics and avoidance generalize naturally to this setting, and we focus on…
Adversarially robust streaming algorithms are required to process a stream of elements and produce correct outputs, even when each stream element can be chosen as a function of earlier algorithm outputs. As with classic streaming…
In this work, we tackle a natural variation of the String Matching Problem on the case of a dynamic pattern, that is, given a static text $T$ and a pattern $P$, we want to support character additions and deletions to the pattern, and after…
Space complexity is a critical factor in various computational models, including streaming, parallel/distributed computing, and communication complexity. We study the space complexity of the minimum-cost flow problem, a generalization of…
A permutation $\pi$ strongly avoids the pattern $\tau$ if both $\pi$ and $\pi^2$ avoid $\tau$. In this paper, we enumerate permutations of size $n$ that strongly avoid the pattern 132. This enumeration allows us to prove a conjecture that…
We study relationships between permutation statistics and pattern-functions, counting the number of times particular patterns occur in a permutation. This allows us to write several familiar statistics as linear combinations of pattern…
While there has been a lot of work on finding frequent itemsets in transaction data streams, none of these solve the problem of finding similar pairs according to standard similarity measures. This paper is a first attempt at dealing with…
In this paper we consider several variants of the pattern matching problem. In particular, we investigate the following problems: 1) Pattern matching with k mismatches; 2) Approximate counting of mismatches; and 3) Pattern matching with…
The Gap-Hamming-Distance problem arose in the context of proving space lower bounds for a number of key problems in the data stream model. In this problem, Alice and Bob have to decide whether the Hamming distance between their $n$-bit…
An occurrence of a classical pattern p in a permutation \pi is a subsequence of \pi whose letters are in the same relative order (of size) as those in p. In an occurrence of a generalized pattern, some letters of that subsequence may be…