Abstract
An ordered set P is called K-free if it does not contain a four-element subset {a, b, c, d} such that a < b is the only comparability among these elements. In this paper we present a polynomial algorithm to find the jump number of K-free ordered sets.
Similar content being viewed by others
References
V.Bouchitté and M.Habib (1987) Some NP-completeness properties about linear extensions, Order 4, 143–154.
M.Chein and M.Habib (1984) Jump number of dags having Dilworth number 2, Discrete Applied Math. 7, 243–250.
O.Cogis and M.Habib (1979) Nombre de sauts et graphes séries-parallèles, RAIRO Inf. Th. 13 (1), 3–18.
C. J.Colbourn and W. R.Pulleyblank (1985) Minimizing setup in ordered sets of fixed width, Order 1, 225–229.
D.Duffus, I.Rival, and P.Winkler (1982) Minimizing setups for cycle-free ordered sets, Proc. Amer. Math. Soc. 85, 509–513.
S.Felsner (1990) A 3/2-approximation algorithm for the jump number of interval orders, Order 4, 325–334.
I.Rival (1983) Optimal linear extensions by interchanging chains, Proc. Amer. Math. Soc. 83, 387–394.
I. Rival (1989) Problem 2.2, in Algorithms and Order (I. Rival, ed.), Kluwer Acad. Pub., p. 475.
I.Rival and N.Zaguia (1986) Constructing greedy linear extensions by interchanging chains, Order 3, 107–121.
A. Sharary and N. Zaguia (1990) On a setup optimization problem for interval orders, preprint.
G.Steiner and L. K.Stewart (1987) A linear algorithm to find the jump number of 2-dimensional bipartite partial orders, Order 3, 359–367.
Author information
Authors and Affiliations
Additional information
Communicated by R. H. Möhring
Rights and permissions
About this article
Cite this article
Sharary, A.H., Zaguia, N. On minimizing jumps for ordered sets. Order 7, 353–359 (1990). https://doi.org/10.1007/BF00383200
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00383200