An introduction to chromatic sums
CSC '89 Proceedings of the 17th conference on ACM Annual Computer Science Conference
Theoretical Computer Science - Special issue on dynamic and on-line algorithms
On chromatic sums and distributed resource allocation
Information and Computation
Minimum color sum of bipartite graphs
Journal of Algorithms
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
Scheduling with conflicts, and applications to traffic signal control
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Probabilistic analysis for scheduling with conflicts
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Distributed Algorithms
Buffer sharing in rendezvous programs
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems - Special section on the ACM IEEE international conference on formal methods and models for codesign (MEMOCODE) 2009
The cinderella game on holes and anti-holes
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Cinderella versus the wicked stepmother
TCS'12 Proceedings of the 7th IFIP TC 1/WG 202 international conference on Theoretical Computer Science
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We consider the problem of scheduling a sequence of tasks in a multi-processor system with conflicts. Conflicting processors cannot process tasks at the same time. At certain times new tasks arrive in the system, where each task specifies the amount of work (processing time) added to each processor's workload. Each processor stores this workload in its input buffer. Our objective is to schedule task execution, obeying the conflict constraints, and minimizing the maximum buffer size of all processors. In the off-line case, we prove that, unless P = NP, the problem does not have a polynomial-time algorithm with a polynomial approximation ratio. In the on-line case, we provide the following results: (i) a competitive algorithm for general graphs, (ii) tight bounds on the competitive ratios for cliques and complete k-partite graphs, and (iii) a (Δ/2 + 1)-competitive algorithm for trees, where Δ is the diameter. We also provide some results for small graphs with up to 4 vertices.