Maximum κ-chains in planar point sets: Combinatorial structure and algorithms

SIAM Journal on Computing

Volumn 28, Issue 1, 1998, Pages 192-209

  Felsner, Stefan ^a   Wernisch, Lorenz ^a  

^a FREIE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Algorithms; Antichains; Chains; Orders; Point sets; Skeletons; Young tableaux

Indexed keywords

ALGORITHMS; COMBINATORIAL MATHEMATICS; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL GEOMETRY;

GREENE-KLEITMAN THEORY;

SET THEORY;

EID: 0032057912     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539794266171     Document Type: Article

References (15)

1. S. EVEN, A. PNUELI, AND A. LEMPEL, Permutation graphs and transitive graphs, J. Assoc. Comput. Mach., 19 (1972), pp. 400-410.
2. A. FRANK, On chain and antichain families of partially ordered sets, J. Combin. Theory Ser. B, 29 (1980), pp. 176-184.
3. M. L. FREDMAN, On computing the length of longest increasing subsequences, Discrete Math., 11 (1975), pp. 29-35.
4. F. GAVRIL, Algorithms for maximum κ-colorings and maximum κ-coverings of transitive graphs, Networks, 17 (1987), pp. 465-470.
5. C. GREENE, An extension of Schensted's theorem, Adv. Math., 14 (1974), pp. 254-265.
6. C. GREENE, Some partitions associated with a partially ordered set, J. Combin. Theory Ser. A, 20 (1976), pp. 69-79.
7. C. GREENE AND D. J. KLEITMAN, The structure of Sperner κ-families, J. Combin. Theory Ser. A, 20 (1976), pp. 41-68.
8. D. E. KNUTH, The Art of Computer Programming III. Sorting and Searching, Vol. 3, Addison-Wesley, Reading, MA, 1973.
9. R. D. Lou AND M. SARRAFZADEH, An optimal algorithm for the maximum 3-chain problem, SIAM J. Comput., 22 (1993), pp. 976-993.
10. R. D. Lou, M. SARRAFZADEH, AND D. T. LEE, An optimal algorithm for the maximum two-chain problem, SIAM J. Discrete. Math., 5 (1992), pp. 285-304.
11. J. MATOUŠEK AND E. WELZL, Good splitters for counting points in triangles, J. Algorithms, 13 (1992), pp. 307-319.
12. M. SARRAFZADEH AND R. D. Lou, Maximum κ-covering of weighted transitive graphs with applications, Algorithmica, 9 (1993), pp. 84-100.
13. G. VIENNOT, Une forme géométrique de la correspondance de Robinson-Schensted, in Combinatoire et Représentation du Groupe Symétrique, D. Foata, ed., Lecture Notes in Math. 579, Springer, New York, 1977, pp. 29-58.
14. G. VIENNOT, Chain and antichain families, grids and young tableaux, in Orders; Description and Roles, Math. Stud. 99, North-Holland, Amsterdam, 1984, pp. 409-463.
15. L. WERNISCH, Dominance Relation on Point Sets and Aligned Rectangles, Dissertation, Freie Universität Berlin, 1994.