On the approximability of average completion time scheduling under precedence constraints

Authors:
Gerhard J. Woeginger
Affiliations:
Institut für Mathematik, Technische Universität Graz, Steyrergasse 30, 8010 Graz, Austria and Department of Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, Netherlands
Venue:
Discrete Applied Mathematics - Special issue: The second international colloquium, "journées de l'informatique messine"
Year:
2003

Citing 7
Cited 0

Bipartite permutation graphs

Discrete Applied Mathematics
Formulating the single machine sequencing problem with release dates as a mixed integer program

Discrete Applied Mathematics - Southampton conference on combinatorial optimization, April 1987
Knapsack problems: algorithms and computer implementations

Knapsack problems: algorithms and computer implementations
Scheduling to minimize average completion time: off-line and on-line approximation algorithms

Mathematics of Operations Research
Precedence constrained scheduling to minimize sum of weighted completion times on a single machine

Discrete Applied Mathematics
Two-Dimensional Gantt Charts and a Scheduling Algorithm of Lawler

SIAM Journal on Discrete Mathematics
A half-integral linear programming relaxation for scheduling precedence-constrained jobs on a single machine

Operations Research Letters

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider the scheduling problem of minimizing the average weighted job completion time on a single machine under precedence constraints. We show that this problem with arbitrary job weights, the special case of the problem where all job weights are one, and several other special cases of the problem all have the same approximability threshold with respect to polynomial time approximation algorithms. Moreover, for the special case of interval order precedence constraints and for the special case of convex bipartite precedence constraints, we give a polynomial time approximation algorithm with worst case performance guarantee arbitrarily close to the golden ratio ½(1 + √5) ≈ 1.61803.