Exploiting the Lattice of ideals representation of a poset

Fundamenta Informaticae

Volumn 71, Issue 2-3, 2006, Pages 309-321

  De Loof, Karel ^a   De Meyer, Hans ^a   De Baets, Bernard ^a  

^a GHENT UNIVERSITY   (Belgium)

Author keywords

Ideal lattice; Mutual rank probabilities; Number of linear extensions; Poset; Random linear extension; Rank probability distribution

Indexed keywords

ALGORITHMS; COMPUTATION THEORY; COMPUTATIONAL COMPLEXITY; DECISION THEORY; GRAPH THEORY; LINEAR SYSTEMS; PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES;

IDEAL LATTICE; MUTUAL RANK PROBABILITIES; NUMBER OF LINEAR EXTENSIONS; POSET; RANDOM LINEAR EXTENSION; RANK PROBABILITY DISTRIBUTION;

LATTICE CONSTANTS;

EID: 33745149303     PISSN: 01692968     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. G. Brightwell and P. Winkler. Counting linear extensions. Order, 8(3):225-242, 1991.
2. R. Brüggemann, D. Lerche, and P.B. Sørensen. First attempts to relate structures of Hasse diagrams with mutual probabilities. Technical Report 479, The 5th workshop held at the National Environmental Research Institute (NERI), Roskilde, Denmark, 2003.
3. R. Bubley and M. Dyer. Faster random generation of linear extensions. Discrete Mathematics, 20:81-88, 1999.
4. B.A. Davey and H.A. Priestley. Introduction to Lattices and Order. Cambridge University Press, Cambridge, 2003.
5. M. Dyer, L.A. Goldberg, C. Greenhill, and M. Jerrum. On the relative complexity of approximate counting problems. Algorithmica, 38(3):471-500, 2003.
6. M. Habib, R. Medina, L. Nourine, and G. Steiner. Efficient algorithms on distributive lattices. Discrete Applied Mathematics, 110:169-187, 2001.
7. M. Habib and L. Nourine. Tree structure for distributive lattices and its applications. Theoretical Computer Science, 165:391-405, 1996.
8. Y. Koda and F. Ruskey. A gray code for the ideals of a forest poset. Journal of Algorithms, 15(2):324-340, 1993.
9. D. Lerche and P.B. Sørensen. Evaluation of the ranking probabilities for partial orders based on random linear extensions. Chemosphere, 53:981-992, 2004.
10. H. Mannila and C. Meek. Global partial orders from sequential data. Proceedings of the Sixth ACM SIGKDD Intern. Conf. on Knowledge Discovery and Data Mining, Boston, MA, USA, 161-168, 2000.
11. M. Peczarski. New results in minimum-comparison sorting. Algorithmica, 40:133-145, 2004.
12. G. Pruesse and F. Ruskey. Gray codes from antimatroids. Order, 10:239-252, 1993.
13. G. Pruesse and F. Ruskey. Generating linear extensions fast. SIAM Journal on Computing, 23:373-386, 1994.
14. U. Simon, R. Brüggeman, and S. Pudenz. Aspects of decision support in water management - example Berlin and Potsdam (Germany)I - spatially differentiated evaluation. Water Research, 38:1809-1816, 2004.
15. U. Simon, R. Brüggeman, and S. Pudenz. Aspects of decision support in water management - example Berlin and Potsdam (Germany)II - improvement of management strategies. Water Research, 38:4085-4092, 2004.
16. M.B. Squire. Enumerating the ideals of a poset, North Carolina State University, 1995. http://citeseer.ist.psu.edu/465417.html.
17. L.G. Valiant. The complexity of enumeration and reliability problems. SIAM Journal on Computing, 8:410-421, 1979.