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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. doi:10.1007/11786986_5 ISSN 0302-9743.

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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:
DateEvent
2006Published
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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