Related papers: Heapable Sequences and Subsequences

Accessibility percolation is a new type of percolation problem inspired by evolutionary biology. To each vertex of a graph a random number is assigned and a path through the graph is called accessible if all numbers along the path are in…

A superpermutation is a sequence that contains every permutation of $n$ distinct symbols as a contiguous substring. For instance, a valid example for three symbols is a sequence that contains all six permutations. This paper introduces a…

We study the problem of generating interesting integer sequences with a combinatorial interpretation. For this we introduce a two-step approach. In the first step, we generate first-order logic sentences which define some combinatorial…

This paper describes new, simple, recursive methods of construction for orientable sequences, i.e. periodic binary sequences in which any n-tuple occurs at most once in a period in either direction. As has been previously described, such…

We consider the longest common subsequence (LCS) problem with the restriction that the common subsequence is required to consist of at least $k$ length substrings. First, we show an $O(mn)$ time algorithm for the problem which gives a…

For many online problems, it is known that the uniform arrival order enables the design of algorithms with much better performance guarantees than under worst-case. The quintessential example is the secretary problem. If the sequence of…

We consider the problem of identifying tandem scattered subsequences within a string. Our algorithm identifies a longest subsequence which occurs twice without overlap in a string. This algorithm is based on the Hunt-Szymanski algorithm,…

A longest repeat query on a string, motivated by its applications in many subfields including computational biology, asks for the longest repetitive substring(s) covering a particular string position (point query). In this paper, we extend…

A special case of the satisfiability problem, in which the clauses have a hierarchical structure, is shown to be solvable in linear time, assuming that the clauses have been represented in a convenient way.

We consider the offline sorting buffer problem. The input is a sequence of items of different types. All items must be processed one by one by a server. The server is equipped with a random-access buffer of limited capacity which can be…

Let $S_n$ denote the set of permutations of $[n]$ and let $\sigma=\sigma_1\cdots\sigma_n\in S_n$. For a subsequence $\{\sigma_{i_j}\}_{j=1}^k$ of $\{\sigma_i\}_{i=1}^n$ of length $k\ge2$, construct the ``up/down'' sequence $V_1\cdots…

Binary jumbled pattern matching asks to preprocess a binary string $S$ in order to answer queries $(i,j)$ which ask for a substring of $S$ that is of length $i$ and has exactly $j$ 1-bits. This problem naturally generalizes to…

Encoding long sequences in Natural Language Processing (NLP) is a challenging problem. Though recent pretraining language models achieve satisfying performances in many NLP tasks, they are still restricted by a pre-defined maximum length,…

We consider the learning and communication complexity of subsequence containment. In the learning problem, we seek to learn a classifier that positively labels a binary string $x$ if it contains a fixed binary string $y$ as a subsequence.…

The merit factor problem is of practical importance to manifold domains, such as digital communications engineering, radars, system modulation, system testing, information theory, physics, chemistry. However, the merit factor problem is…

A permutation is $k$-coverable if it can be partitioned into $k$ monotone subsequences. Barber conjectured that, for any given permutation, if every subsequence of length $k+2 \choose 2$ is $k$-coverable then the permutation itself is…

Longest Increasing Subsequence (LIS) is a fundamental problem in combinatorics and computer science. Previously, there have been numerous works on both upper bounds and lower bounds of the time complexity of computing and approximating LIS,…

We consider here the problem of chaining seeds in ordered trees. Seeds are mappings between two trees Q and T and a chain is a subset of non overlapping seeds that is consistent with respect to postfix order and ancestrality. This problem…

In this paper we initiate the study of computing a maximal (not necessarily maximum) repeating pattern in a single input string, where the corresponding problems have been studied (e.g., a maximal common subsequence) only in two or more…

An extension to a recently introduced architecture of clique-based neural networks is presented. This extension makes it possible to store sequences with high efficiency. To obtain this property, network connections are provided with…