On minimizing jumps for ordered sets
โ Scribed by Ahmad H. Sharary; Nejib Zaguia
- Publisher
- Springer Netherlands
- Year
- 1991
- Tongue
- English
- Weight
- 383 KB
- Volume
- 7
- Category
- Article
- ISSN
- 0167-8094
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โฆ Synopsis
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.
AMS subject classifications (1980). 06Al& &X15.
๐ SIMILAR VOLUMES
A linear extension x1x2. . . x, of a partially or&red set P has a bump whenever Xi <xi+1 in P. The bump number problem is to find a linear extension of P with the smallest possible number of bumps. We present a basic decomposition theorem for this problem. This leads to simple formulae for the bump
A simply polynomial time algorithm is given for computing the setup number, or jump number, of an ordered set with fixed width. This arises as an interesting application of a polynomial time algorithm for solving a more general weighted problem in precedence constrained scheduling.
A linear extension x,x2xs ... of a partially ordered set (X, <) has a bump whenever xi < xi+l. We examine the problem of determining linear extensions with as few bumps as possible. Heuristic algorithms for approximate bump minimization are considered. AhfS (MOS) subject classifications (1980). Prim
The maximum size of a jump-critical ordered set with jump-number m is at most (m + l)! AMS (MOS) subject classifications (1980). Primary 06AlO; secondary 68C25.