The maximum k-colorable subgraph problem for chordal graphs
Information Processing Letters
On chromatic sums and distributed resource allocation
Information and Computation
Minimum color sum of bipartite graphs
Journal of Algorithms
Journal of Algorithms
Scheduling to Minimize the Average Completion Time of Dedicated Tasks
FST TCS 2000 Proceedings of the 20th Conference on Foundations of Software Technology and Theoretical Computer Science
Multicoloring Planar Graphs and Partial k-Trees
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
The Optimum Cost Chromatic Partition Problem
CIAC '97 Proceedings of the Third Italian Conference on Algorithms and Complexity
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Minimum Cost Homomorphism Dichotomy for Oriented Cycles
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
Minimum cost homomorphisms to oriented cycles with some loops
CATS '09 Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94
Approximation of minimum cost homomorphisms
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
On the approximation of minimum cost homomorphism to bipartite graphs
Discrete Applied Mathematics
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Scheduling dependent jobs on multiple machines is modeled as a graph (multi)coloring problem. The focus of this work is on the sum of completion times measure. This is known as the sum (multi)coloring of the conflict graph. We also initiate the study of the waiting time and the robust throughput of colorings. For uniform-length tasks we give an algorithm which simultaneously approximates these two measures, as well as sum coloring and the chromatic number, within constant factor, for any graph in which the k-colorable subgraph problem is polynomially solvable. In particular, this improves the best approximation ratio known for sum coloring interval graphs from 2 to 1.665. We then consider the problem of scheduling non-preemptively tasks (of non-uniform lengths) that require exclusive use of dedicated processors. The objective is to minimize the sum of completion times. We obtain the first constant factor approximations for this problem, when each task uses a constant number of processors.