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Finding an unknown acyclic orientation of a given graph
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Pikhurko, Oleg (2010) Finding an unknown acyclic orientation of a given graph. Combinatorics, Probability and Computing, Vol.19 (No.1). pp. 121-131. doi:10.1017/S0963548309990289 ISSN 0963-5483.
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Official URL: http://dx.doi.org/10.1017/S0963548309990289
Abstract
Let c(G) be the smallest number of edges we have to test in order to determine an unknown acyclic orientation of the given graph G in the worst case. For example, if G is the complete graph on n vertices, then c(G) is the smallest number of comparisons needed to sort n numbers.
We prove that c(G) ≤ (1/4 + o(1))n2 for any graph G on n vertices, answering in the affirmative a question of Aigner, Triesch and Tuza [Discrete Mathematics 144 (1995) 3–10]. Also, we show that, for every > 0, it is NP-hard to approximate the parameter c(G) within a multiplicative factor 74/73 − .
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Combinatorics, Probability and Computing | ||||
Publisher: | Cambridge University Press | ||||
ISSN: | 0963-5483 | ||||
Official Date: | 2010 | ||||
Dates: |
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Volume: | Vol.19 | ||||
Number: | No.1 | ||||
Page Range: | pp. 121-131 | ||||
DOI: | 10.1017/S0963548309990289 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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