Bibliographic Details
| Title: |
Parameterised and Fine-Grained Subgraph Counting, Modulo 2. |
| Authors: |
Goldberg, Leslie Ann1 (AUTHOR), Roth, Marc1 (AUTHOR) marc.roth.cs@gmail.com |
| Superior Title: |
Algorithmica. Apr2024, Vol. 86 Issue 4, p944-1005. 62p. |
| Subject Terms: |
*DISCRETE mathematics, *MATHEMATICAL simplification, *SUBGRAPHS, *BIPARTITE graphs |
| Company/Entity: |
DELL Technologies Inc. |
| Abstract: |
Given a class of graphs H , the problem ⊕ Sub (H) is defined as follows. The input is a graph H ∈ H together with an arbitrary graph G. The problem is to compute, modulo 2, the number of subgraphs of G that are isomorphic to H. The goal of this research is to determine for which classes H the problem ⊕ Sub (H) is fixed-parameter tractable (FPT), i.e., solvable in time f (| H |) · | G | O (1) . Curticapean, Dell, and Husfeldt (ESA 2021) conjectured that ⊕ Sub (H) is FPT if and only if the class of allowed patterns H is matching splittable, which means that for some fixed B, every H ∈ H can be turned into a matching (a graph in which every vertex has degree at most 1) by removing at most B vertices. Assuming the randomised Exponential Time Hypothesis, we prove their conjecture for (I) all hereditary pattern classes H , and (II) all tree pattern classes, i.e., all classes H such that every H ∈ H is a tree. We also establish almost tight fine-grained upper and lower bounds for the case of hereditary patterns (I). [ABSTRACT FROM AUTHOR] |
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| Database: |
Academic Search Premier |
