Parity Permutation Pattern Matching

IF 0.9 4区计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Algorithmica Pub Date : 2024-05-22 DOI:10.1007/s00453-024-01237-0

Virginia Ardévol Martínez, Florian Sikora, Stéphane Vialette

引用次数: 0

Abstract

Given two permutations, a pattern \(\sigma \) and a text \(\pi \), Parity Permutation Pattern Matching asks whether there exists a parity and order preserving embedding of \(\sigma \) into \(\pi \). While it is known that Permutation Pattern Matching is in \(\textsc {FPT}\), we show that adding the parity constraint to the problem makes it \(\textsc {W}[1]\)-hard, even for alternating permutations or for 4321-avoiding patterns. However, the problem remains in \(\textsc {FPT}\) if \(\pi \) avoids a fixed permutation, thanks to a recent meta-theorem on twin-width. On the other hand, as for the classical version, Parity Permutation Pattern Matching remains polynomial-time solvable when the pattern is separable, or if both permutations are 321-avoiding, but NP-hard if \(\sigma \) is 321-avoiding and \(\pi \) is 4321-avoiding.

Abstract Image

查看原文本刊更多论文

奇偶校验模式匹配

给定两种排列，一种是模式（pattern \sigma \），另一种是文本（text \pi \），奇偶性排列模式匹配（Parity Permutation Pattern Matching）询问是否存在奇偶性和秩保存的将（\sigma \）嵌入到（\pi \）中。虽然我们知道排列组合模式匹配是在（textsc {FPT}\）中的，但我们证明在这个问题中加入奇偶性约束会使（textsc {W}[1]\）这个问题变得很困难，甚至对于交替排列组合或4321-avoiding模式也是如此。然而，如果（\pi \）避免了一个固定的排列组合，那么这个问题仍然是（\textsc {FPT}\）困难的，这要归功于最近一个关于孪生宽度的元定理。另一方面，与经典版本一样，当模式是可分离的，或者两种排列都是 321 避开的时候，奇偶性排列模式匹配仍然是多项式时间可解的，但是如果 \(\sigma \) 是 321 避开的，而 \(\pi \) 是 4321 避开的，那么这个问题就是 NP 难的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Algorithmica 工程技术-计算机：软件工程

CiteScore

2.80

自引率

9.10%

发文量

158

审稿时长

12 months

期刊介绍： Algorithmica is an international journal which publishes theoretical papers on algorithms that address problems arising in practical areas, and experimental papers of general appeal for practical importance or techniques. The development of algorithms is an integral part of computer science. The increasing complexity and scope of computer applications makes the design of efficient algorithms essential. Algorithmica covers algorithms in applied areas such as: VLSI, distributed computing, parallel processing, automated design, robotics, graphics, data base design, software tools, as well as algorithms in fundamental areas such as sorting, searching, data structures, computational geometry, and linear programming. In addition, the journal features two special sections: Application Experience, presenting findings obtained from applications of theoretical results to practical situations, and Problems, offering short papers presenting problems on selected topics of computer science.