Distributed operating systems
On chromatic sums and distributed resource allocation
Information and Computation
Minimum color sum of bipartite graphs
Journal of Algorithms
Zero knowledge and the chromatic number
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
Probabilistic analysis for scheduling with conflicts
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
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Operating System Concepts
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ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
On Minimizing Average Weighted Completion Time: A PTAS for Scheduling General Multiprocessor Tasks
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
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Scheduling dependent jobs on multiple machines is modeled by the graph multi-coloring problem. In this paperweconsider the problem of minimizing the average completion time of all jobs. This is formalized as the sum multicoloring (SMC) problem: Given a graph and the number of colors required by each vertex, find a multi-coloring which minimizes the sum of the largest colors assigned to the vertices. It reduces to the known sum coloring (SC) problem in the special case of unit execution times.This paper reports a comprehensive study of the SMC problem, treating three models: with and without preemption allowed, as well as co-scheduling where tasks cannot start while others are running. We establish a linear relation between the approximability of the maximum independent set (IS) and SMC in all three models, via a link to the SC problem. Thus, for classes of graphs where IS is 驴-approximable, we obtain O(驴)-approximations for preemptive and coscheduling SMC, and O(驴 驴 log n) for non-preemptive SMC. In addition, we give constant-approximation algorithms for SMC under different models, on a number of fundamental classes of graphs, including bipartite, line, bounded degree, and planar graphs.