Related papers: Exhaustive Generation of Pattern-Avoiding s-Words
We present a new algorithm for iterating over all permutations of a sequence. The algorithm leverages elementary~$O(1)$ operations on recursive lists. As a result, no new nodes are allocated during the computation. Instead, all elements are…
Shaping gain is attained in schemes where a shaped subcode is chosen from a larger codebook by a codeword selection process. This includes the popular method of Trellis Shaping (TS), originally proposed by Forney for average power…
In the problem of $\texttt{Generalised Pattern Matching}\ (\texttt{GPM})$ [STOC'94, Muthukrishnan and Palem], we are given a text $T$ of length $n$ over an alphabet $\Sigma_T$, a pattern $P$ of length $m$ over an alphabet $\Sigma_P$, and a…
We revisit skip-gram negative sampling (SGNS), one of the most popular neural-network based approaches to learning distributed word representation. We first point out the ambiguity issue undermining the SGNS model, in the sense that the…
A Gray code for a combinatorial class is a method for listing the objects in the class so that successive objects differ in some prespecified, small way, typically expressed as a bounded Hamming distance. In a previous work, the authors of…
Pattern-avoiding permutations are a central object of study in both combinatorics and theoretical computer science. In this paper we design a data structure that can store any size-$n$ permutation $\tau$ that avoids an arbitrary (and…
We present S-Path-RAG, a semantic-aware shortest-path Retrieval-Augmented Generation framework designed to improve multi-hop question answering over large knowledge graphs. S-Path-RAG departs from one-shot, text-heavy retrieval by…
Random number generators are imperfect due to manufacturing bias and technological imperfections. These imperfections are removed using post-processing algorithms that in general compress the data and do not work in every scenario. In this…
We present a novel algorithm, Westfall-Young light, for detecting patterns, such as itemsets and subgraphs, which are statistically significantly enriched in one of two classes. Our method corrects rigorously for multiple hypothesis testing…
We consider the problem of comparison-sorting an $n$-permutation $S$ that avoids some $k$-permutation $\pi$. Chalermsook, Goswami, Kozma, Mehlhorn, and Saranurak prove that when $S$ is sorted by inserting the elements into the GreedyFuture…
Sentence formation is a highly structured, history-dependent, and sample-space reducing (SSR) process. While the first word in a sentence can be chosen from the entire vocabulary, typically, the freedom of choosing subsequent words gets…
Genome rearrangements are events in which large blocks of DNA exchange pieces during evolution. The analysis of such events is a tool for understanding evolutionary genomics, based on finding the minimum number of rearrangements to…
In this paper, we study grant-free random access with massive multiple input multiple output (MIMO) systems. We first show that the performance of massive MIMO based grant-free random access is mainly decided by the probability of preamble…
The stack sort algorithm has been the subject of extensive study over the years. In this paper we explore a generalized version of this algorithm where instead of avoiding a single decrease, the stack avoids a set $T$ of permutations. We…
Reordering poses a major challenge in machine translation (MT) between two languages with significant differences in word order. In this paper, we present a novel reordering approach utilizing sparse features based on dependency word pairs.…
Geometric grid classes and the substitution decomposition have both been shown to be fundamental in the understanding of the structure of permutation classes. In particular, these are the two main tools in the recent classification of…
Math word problems (MWPs) is a task that automatically derives solution expression from a giving math problems in text. The previous studies suffer from spurious correlations between input text and output expression. To mitigate this issue,…
We consider a random permutation drawn from the set of 321-avoiding permutations of length $n$ and show that the number of occurrences of another pattern $\sigma$ has a limit distribution, after scaling by $n^{m+\ell}$ where $m$ is the…
The generation of random graphs using edge swaps provides a reliable method to draw uniformly random samples of sets of graphs respecting some simple constraints, e.g. degree distributions. However, in general, it is not necessarily…
Motivated by the recent proof of the Stanley-Wilf conjecture, we study the asymptotic behavior of the number of permutations avoiding a generalized pattern. Generalized patterns allow the requirement that some pairs of letters must be…