An Algorithmic Framework for Locally Constrained Homomorphisms

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-04-18 DOI:10.1137/22m1513290

Laurent Bulteau, Konrad K. Dabrowski, Noleen Köhler, Sebastian Ordyniak, Daniël Paulusma

引用次数: 0

Abstract

SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1315-1350, June 2024.
Abstract. A homomorphism [math] from a guest graph [math] to a host graph [math] is locally bijective, injective, or surjective if for every [math], the restriction of [math] to the neighbourhood of [math] is bijective, injective, or surjective, respectively. We prove a number of new FPT (fixed-parameter tractable), W[1]-hard, and paraNP-complete results for the corresponding decision problems LBHom, LIHom, and LSHom by considering a hierarchy of parameters of the guest graph [math]. In this way we strengthen several existing results. For our FPT results, we develop a new algorithmic framework that involves a general ILP (integer linear program) model. We also use our framework to prove FPT results for the Role Assignment problem, which originates from social network theory and is closely related to locally surjective homomorphisms.

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局部受限同态的算法框架

SIAM 离散数学杂志》，第 38 卷第 2 期，第 1315-1350 页，2024 年 6 月。摘要如果对于每一个[math]，[math]对[math]邻域的限制分别是双射、注入或射出的，那么从客图[math]到主图[math]的同态[math]就是局部双射、注入或射出的。通过考虑客体图 [math] 的参数层次，我们证明了相应决策问题 LBHom、LIHom 和 LSHom 的一系列新的 FPT（固定参数可处理）、W[1]-困难和 paraNP-完备结果。通过这种方法，我们加强了几个已有的结果。对于我们的 FPT 结果，我们开发了一个新的算法框架，涉及一般的 ILP（整数线性规划）模型。我们还利用我们的框架证明了角色分配问题的 FPT 结果，该问题源于社交网络理论，与局部投射同构密切相关。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Discrete Mathematics 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution. Topics include but are not limited to: properties of and extremal problems for discrete structures combinatorial optimization, including approximation algorithms algebraic and enumerative combinatorics coding and information theory additive, analytic combinatorics and number theory combinatorial matrix theory and spectral graph theory design and analysis of algorithms for discrete structures discrete problems in computational complexity discrete and computational geometry discrete methods in computational biology, and bioinformatics probabilistic methods and randomized algorithms.