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On counting homomorphisms to directed acyclic graphs
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Dyer, Martin, Goldberg, Leslie Ann and Paterson, Michael S. (2006) On counting homomorphisms to directed acyclic graphs. In: 33rd International Colloquium on Automata, Languages and Programming, Venice, Italy, 10-14 Jul 2006. Published in: Lecture Notes in Computer Science, Volume 4051 pp. 38-49. ISBN 3-540-35904-4. ISSN 0302-9743. doi:10.1007/11786986_5
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Abstract
We give a dichotomy theorem for the problem of counting homomorphisms to directed acyclic graphs. H is a fixed directed acyclic graph. The problem is, given an input digraph G, to determine how many homomorphisms there are from G to H. We give a graph-theoretic classification, showing that for some digraphs H, the problem is in P and for the rest of the digraphs H the problem is #P-complete. An interesting feature of the dichotomy, absent from related dichotomy results, is the rich supply of tractable graphs H with complex structure.
| Item Type: | Conference Item (Paper) | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||
| Series Name: | LECTURE NOTES IN COMPUTER SCIENCE | ||||
| Journal or Publication Title: | Lecture Notes in Computer Science | ||||
| Publisher: | Springer | ||||
| ISBN: | 3-540-35904-4 | ||||
| ISSN: | 0302-9743 | ||||
| Editor: | Bugliesi, M and Preneel, B and Sassone, V and Wegener, I | ||||
| Official Date: | 2006 | ||||
| Dates: |
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| Volume: | Volume 4051 | ||||
| Number of Pages: | 12 | ||||
| Page Range: | pp. 38-49 | ||||
| DOI: | 10.1007/11786986_5 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Conference Paper Type: | Paper | ||||
| Title of Event: | 33rd International Colloquium on Automata, Languages and Programming | ||||
| Type of Event: | Other | ||||
| Location of Event: | Venice, Italy | ||||
| Date(s) of Event: | 10-14 Jul 2006 |
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