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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
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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 | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of 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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