Structure of a simple scheduling polyhedron
Mathematical Programming: Series A and B
Scheduling to minimize average completion time: off-line and on-line approximation algorithms
Mathematics of Operations Research
On chromatic sums and distributed resource allocation
Information and Computation
Minimum color sum of bipartite graphs
Journal of Algorithms
Scheduling to minimize average completion time: off-line and on-line algorithms
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Algorithms for compile-time memory optimization
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Journal of Algorithms
Data migration to minimize the average completion time
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
Improved Scheduling Algorithms for Minsum Criteria
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
Approximating Min-sum Set Cover
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
A 27/26-Approximation Algorithm for the Chromatic Sum Coloring of Bipartite Graphs
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
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
The Optimum Cost Chromatic Partition Problem
CIAC '97 Proceedings of the Third Italian Conference on Algorithms and Complexity
Information and Computation
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Weighted sum coloring in batch scheduling of conflicting jobs
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
Combinatorial algorithms for data migration to minimize average completion time
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
A reliability optimization method for RAID-structured storage systems based on active data migration
Journal of Systems and Software
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We consider a general class of scheduling problems where a set of dependent jobs needs to be scheduled (preemptively or non-preemptively) on a set of machines so as to minimize the weighted sum of completion times. The dependencies among the jobs are formed as an arbitrary conflict graph. An input to our problems can be modeled as an instance of the sum multicoloring (SMC) problem: Given a graph and the number of colors required by each vertex, find a proper multicoloring which minimizes the sum over all vertices of the largest color assigned to each vertex. In the preemptive case (pSMC), each vertex can receive an arbitrary subset of colors; in the non-preemptive case (npSMC), the colors assigned to each vertex need to be contiguous. SMC is known to be no easier than classic graph coloring, even in the case of unit color requirements. Building on the framework of Queyranne and Sviridenko (J. of Scheduling, 5:287-305, 2002), we present a general technique for reducing the sum multicoloring problem to classical graph multicoloring. Using the technique, we improve the best known results for pSMC and npSMC on several fundamental classes of graphs, including line graphs, (k + 1)-claw free graphs and perfect graphs. In particular, we obtain the first constant factor approximation ratio for npSMC on interval graphs, on which our problems have numerous applications. We also improve the results of Kim (SODA 2003, 97–98) for npSMC of line graphs and for resource-constrained scheduling.