# The Parameterized Space Complexity of Embedding Along a Path

The Parameterized Space Complexity of Embedding Along a Path The embedding problem is to decide, given an ordered pair of structures, whether or not there is an injective homomorphism from the first structure to the second. We study this problem using an established perspective in parameterized complexity theory: the universe size of the first structure is taken to be the parameter, and we define the embedding problem relative to a class 𝓐 ${\mathcal {A}}$ of structures to be the restricted version of the general problem where the first structure must come from 𝓐 ${\mathcal {A}}$ . We initiate a systematic complexity study of this problem family, by considering classes whose structures are what we call rooted path structures; these structures have paths as Gaifman graphs. Our main theorem is a dichotomy theorem on classes of rooted path structures. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Theory of Computing Systems Springer Journals

# The Parameterized Space Complexity of Embedding Along a Path

, Volume 61 (3) – Dec 3, 2016
20 pages

/lp/springer_journal/the-parameterized-space-complexity-of-embedding-along-a-path-gJIa6TXft4
Publisher
Springer US
Subject
Computer Science; Theory of Computation
ISSN
1432-4350
eISSN
1433-0490
D.O.I.
10.1007/s00224-016-9728-7
Publisher site
See Article on Publisher Site

### Abstract

The embedding problem is to decide, given an ordered pair of structures, whether or not there is an injective homomorphism from the first structure to the second. We study this problem using an established perspective in parameterized complexity theory: the universe size of the first structure is taken to be the parameter, and we define the embedding problem relative to a class 𝓐 ${\mathcal {A}}$ of structures to be the restricted version of the general problem where the first structure must come from 𝓐 ${\mathcal {A}}$ . We initiate a systematic complexity study of this problem family, by considering classes whose structures are what we call rooted path structures; these structures have paths as Gaifman graphs. Our main theorem is a dichotomy theorem on classes of rooted path structures.

### Journal

Theory of Computing SystemsSpringer Journals

Published: Dec 3, 2016

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