====== Acyclic networks ====== ===== Dilworth's theorem ===== * wikipedia: [[http://en.wikipedia.org/wiki/Dilworth's_theorem|Dilworth's theorem]] * Theorem of the Day:[[http://www.theoremoftheday.org/CombinatorialTheory/Dilworth/TotDDilworth.pdf|Dilworth's theorem]] * Wim Pijls, Rob Potharst: Dilworth's theorem revisited, an algorithmic proof [[http://repub.eur.nl/pub/23112/EI2011-13.pdf|report EI2011-13]]; [[http://www.hindawi.com/journals/jdm/2013/692645/|Hindawi]] * L. Haskins, S. Gudder: [[http://www.sciencedirect.com/science/article/pii/0012365X72900143/|Height on posets and graphs.]] Discrete Mathematics, Volume 2, Issue 4, July 1972, Pages 357–382 * Anne Kaldewaij: [[http://www.sciencedirect.com/science/article/pii/0167642387900268#|Some algorithms based on the dual of Dilworth's theorem.]] Science of Computer Programming, Volume 9, Issue 1, August 1987, Pages 85–89 * wikipedia: [[http://en.wikipedia.org/wiki/Mirsky's_theorem|Mirsky's theorem]] ===== Transitivity reduction / skeleton ===== * [[http://en.wikipedia.org/wiki/Transitive_reduction|wikipedia]] * Aho, A.V., Garey, M.R., Ullman, J.D.: [[http://dept-info.labri.fr/~thibault/tmp/0201008.pdf|The transitive reduction of a directed graph.]] SIAM Journal on Computing 1(1972)2: 131–137 * Goralčíková, A., Koubek, V.: [[http://link.springer.com/chapter/10.1007%2F3-540-09526-8_27|A reduct-and-closure algorithm for graphs.]] Mathematical Foundations of Computer Science 1979, Lecture Notes in Computer Science Volume 74, 1979, pp 301-307 * Klaus Simon: [[http://link.springer.com/chapter/10.1007%2F3-540-16761-7_87|An improved algorithm for transitive closure on acyclic digraphs.]] Automata, Languages and Programming. Lecture Notes in Computer Science Volume, 226, 1986, pp 376-386 * Habib, M., Morvan, M., Rampon, J.-X.: [[http://www.sciencedirect.com/science/article/pii/0012365X9390164O|On the calculation of transitive reduction—closure of orders.]] Discrete Mathematics, Volume 111, Issues 1–3, 22 February 1993, Pages 289–303 ===== Acyclic ===== * Hummon, N.P., Doreian, P.: [[http://garfield.library.upenn.edu/papers/hummondoreian1989.pdf|Connectivity in a citation network:The development of DNA.]] Social Networks 11 (1989), 39--63 ===== CPM ===== * http://www.cs.sandia.gov/~rbbrigh/papers/ncp-southern.pdf * https://en.wikipedia.org/wiki/Critical_path_method