On the 2-chain subgraph cover and related problems
Journal of Algorithms
On the fractional dimension of partially ordered sets
Discrete Mathematics - Special issue: trends in discrete mathematics
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
Some APX-completeness results for cubic graphs
Theoretical Computer Science
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
Partially-Ordered Knapsack and Applications to Scheduling
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Single-Machine Scheduling with Precedence Constraints
Mathematics of Operations Research
Single machine precedence constrained scheduling is a vertex cover problem
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
On the approximability of average completion time scheduling under precedence constraints
Discrete Applied Mathematics
Approximating precedence-constrained single machine scheduling by coloring
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Operations Research Letters
Vertex cover in graphs with locally few colors
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
On the Approximability of Single-Machine Scheduling with Precedence Constraints
Mathematics of Operations Research
Hardness of Precedence Constrained Scheduling on Identical Machines
SIAM Journal on Computing
The feedback arc set problem with triangle inequality is a vertex cover problem
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Vertex cover in graphs with locally few colors
Information and Computation
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We consider the single machine scheduling problem to minimize the average weighted completion time under precedence constrains. Improving on the various 2-approximation algorithms is considered one of the ten most prominent open problems in scheduling theory. Recently, research has focused on special cases of the problem, mostly by restricting the set of precedence constraints to special classes such as convex bipartite, two-dimensional, and interval orders.In this paper we extend our previous results by presenting a framework for obtaining (2 茂戮驴 2/d)-approximation algorithms provided that the set of precedence constraints has fractional dimension d. Our generalized approach yields the best known approximation ratios for all previously considered classes of precedence constraints, and it provides the first results for bounded degree and interval dimension 2 orders.As a negative result we show that the addressed problem remains NP-hard even when restricted to the special case of interval orders.