Abstract
Minor Containment is a fundamental problem in Algorithmic Graph Theory used as a subroutine in numerous graph algorithms. A model of a graph H in a graph G is a set of disjoint connected subgraphs of G indexed by the vertices of H, such that if {u,v} is an edge of H, then there is an edge of G between components C u and C v . A graph H is a minor of G if G contains a model of H as a subgraph. We give an algorithm that, given a planar n-vertex graph G and an h-vertex graph H, either finds in time O(2 O(h) · n+n 2·log n) a model of H in G, or correctly concludes that G does not contain H as a minor. Our algorithm is the first single-exponential algorithm for this problem and improves all previous minor testing algorithms in planar graphs. Our technique is based on a novel approach called partially embedded dynamic programming.
Original language | English (US) |
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Pages (from-to) | 69-84 |
Number of pages | 16 |
Journal | Algorithmica |
Volume | 64 |
Issue number | 1 |
DOIs | |
State | Published - Sep 2012 |
Keywords
- Branchwidth
- Dynamic programming
- Graph minors
- Parameterized complexity
- Planar graphs
ASJC Scopus subject areas
- General Computer Science
- Computer Science Applications
- Applied Mathematics