The maximum k-colorable subgraph problem for chordal graphs
Information Processing Letters
SIAM Journal on Discrete Mathematics
On chromatic sums and distributed resource allocation
Information and Computation
Journal of Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Scheduling Algorithms
Approximating Min Sum Set Cover
Algorithmica
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
The pipelined set cover problem
ICDT'05 Proceedings of the 10th international conference on Database Theory
Improved bounds for sum multicoloring and scheduling dependent jobs with minsum criteria
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
"Rent-or-buy" scheduling and cost coloring problems
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
Minimum weighted sum bin packing
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
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Motivated by applications in batch scheduling of interval jobs, processes in manufacturing systems and distributed computing, we study two related problems. Given is a set of jobs { J1,...,Jn}, where Jj has the processing time pj, and an undirected intersection graph G =({ 1,2,...,n},E); there is an edge (i,j) ∈E if the pair of jobs Ji and Jj cannot be processed in the same batch. At any period of time, we can process a batch of jobs that forms an independent set in G. The batch completes its processing when the last job in the batch completes its execution. The goal is to minimize the sum of job completion times. Our two problems differ in the definition of completion time of a job within a given batch. In the first variant, a job completes its execution when its batch is completed, whereas in the second variant, a job completes execution when its own processing is completed. For the first variant, we show that an adaptation of the greedy set cover algorithm gives a 4-approximation for perfect graphs. For the second variant, we give new or improved approximations for a number of different classes of graphs. The algorithms are of widely different genres (LP, greedy, subgraph covering), yet they curiously share a common feature in their use of randomized geometric partitioning.