惯性聚合 高效追踪和阅读你感兴趣的博客、新闻、科技资讯
阅读原文 在惯性聚合中打开

推荐订阅源

雷峰网
雷峰网
MongoDB | Blog
MongoDB | Blog
D
Docker
Martin Fowler
Martin Fowler
人人都是产品经理
人人都是产品经理
GbyAI
GbyAI
Jina AI
Jina AI
酷 壳 – CoolShell
酷 壳 – CoolShell
M
MIT News - Artificial intelligence
腾讯CDC
阮一峰的网络日志
阮一峰的网络日志
H
Hackread – Cybersecurity News, Data Breaches, AI and More
N
Netflix TechBlog - Medium
B
Blog RSS Feed
云风的 BLOG
云风的 BLOG
Blog — PlanetScale
Blog — PlanetScale
Vercel News
Vercel News
The Cloudflare Blog
freeCodeCamp Programming Tutorials: Python, JavaScript, Git & More
有赞技术团队
有赞技术团队
G
Google Developers Blog
Stack Overflow Blog
Stack Overflow Blog
I
InfoQ
U
Unit 42

math.CO updates on arXiv.org

Complement Submodular Information Measures for Balanced and Robust Data Selection A Proof of a Conjecture on Positive and Negative Square Energies of Unicyclic Graphs Laplacian Spectrum of the Weakly Zero-Divisor Graph of a Finite Commutative Ring An identity for second Eulerian numbers via lattice-point counting $t$-tone edge coloring of graphs Constructing Maximal Bumpless Pipedreams for Double Grothendieck Polynomials Mubayi's Polynomial-Ideal Conjecture and Cover-Ideal Turán Methods Implicit Binarization via Complex Phase Dynamics in Combinatorial Optimization The limits of Schur multipliers in Pólya conversion problems for the $q$-permanent function Universality theorems for generalized splines Framing Triangulations for Arbitrary Integer Flow Polytopes On the Common Generalization of Gentle Algebras and Framed Directed Acyclic Graphs The complexity of frugal digraph homomorphisms Chaotic and periodic behavior of jeu de taquin on infinite Young tableaux Enumerating Pattern Avoiding Parking Functions Incidence toric ideals and three-point functions Unique Winning Opening Move in Three-Row Chomp Strong majority colorings of graphs A Balancing Theorem for Spanning Trees of Rectangular Grid Graphs Spectral radius and edge-disjoint connected factors of graphs New invariants for rank metric codes, with applications to the classification of rank two semifields of order 256 Flexible DP-4-coloring of planar graphs without 4-cycles and intersecting triangles Balanced intersection size distributions in projective planes List Reconstruction Problem with List Size Two Is Dimensionality a Barrier for Retrieval Models? The INIEP: Irreducible and Positive Realizations The number of Pfaffian orientations on punctured polygonally cellulated surfaces Explicit Construction of Polytopes whose Ehrhart Polynomials Realize any Given Sign Pattern Finite-state enumeration of adjacency-constrained 132-avoiding permutations AMDS and quantum AMDS Constacyclic codes of length $4p^ς$ over $\mathbb{F}_{{p}^{m}}$
Parameterized complexity of isometric path partition: tre...
Dibyayan Chakraborty, Oscar Defrain, Florent Foucaud, Mathieu Ma · 2025-08-07 · via math.CO updates on arXiv.org

We investigate the parameterized complexity of the Isometric Path Partition problem when parameterized by the treewidth ($\mathrm{tw}$) of the input graph, arguably one of the most widely studied parameters. Courcelle's theorem shows that graph problems that are expressible as MSO formulas of constant size admit FPT algorithms parameterized by the treewidth of the input graph. This encompasses many natural graph problems. However, many metric-based graph problems, where the solution is defined using some metric-based property of the graph (often the distance) are not expressible as MSO formulas of constant size. These types of problems, Isometric Path Partition being one of them, require individual attention and often draw the boundary for the success story of parameterization by treewidth. We prove that Isometric Path Partition is $W[1]$-hard when parameterized by treewidth (in fact, even pathwidth), answering the question by Dumas et al. [SIDMA, 2024], Fernau et al. [CIAC, 2023], and confirming the aforementioned tendency. We complement this hardness result by designing a tailored dynamic programming algorithm running in $n^{O(\mathrm{tw})}$ time. This dynamic programming approach also results in an algorithm running in time $\textrm{diam}^{O(\mathrm{tw}^2)} \cdot n^{O(1)}$, where $\textrm{diam}$ is the diameter of the graph. Note that the dependency on treewidth is unusually high, as most problems admit algorithms running in time $2^{O(\mathrm{tw})}\cdot n^{O(1)}$ or $2^{O(\mathrm{tw} \log (\mathrm{tw}))}\cdot n^{O(1)}$. However, we rule out the possibility of a significantly faster algorithm by proving that Isometric Path Partition does not admit an algorithm running in time $\textrm{diam}^{o(\mathrm{tw}^2/(\log^3(\mathrm{tw})))} \cdot n^{O(1)}$, unless the Randomized-ETH fails.