Worst case bound of an LRF schedule for the mean weighted flow-time problem
SIAM Journal on Computing
A PTAS for minimizing the weighted sum of job completion times on parallel machines
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Algorithms for Scheduling Independent Tasks
Journal of the ACM (JACM)
Scheduling independent tasks to reduce mean finishing time
Communications of the ACM
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
Approximation Schemes for Minimizing Average Weighted Completion Time with Release Dates
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Order Scheduling in an Environment with Dedicated Resources in Parallel
Journal of Scheduling
An improved approximation algorithm for combinatorial auctions with submodular bidders
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A note on the complexity of the concurrent open shop problem
Journal of Scheduling
Approximation algorithms for allocation problems: Improving the factor of 1 - 1/e
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Tight information-theoretic lower bounds for welfare maximization in combinatorial auctions
Proceedings of the 9th ACM conference on Electronic commerce
Order scheduling models: hardness and algorithms
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
Minimizing the sum of weighted completion times in a concurrent open shop
Operations Research Letters
| Hi-index | 5.23 |
We consider the total weighted completion time minimization in the following scheduling problem. There are m identical resources available at each time unit, and n jobs. Each job requires a number s"i of resources and one resource can only be assigned to one job at each time unit. Each job is also called fully parallel such that the job is satisfied once it receives enough resources no matter how the resources distribute. The objective is to find a schedule that minimizes @?w"iC"i, where w"i is the weight of job J"i and C"i is the time when job J"i receives s"i resources. We show that the total weighted completion time minimization is NP-hard when m is an input of the problem. We then give a simple greedy algorithm with an approximation ratio 2. Finally, we present a polynomial time algorithm with complexity O(n^d^+^1) to solve this problem when the number of different resource requirements that are not multiples of m is at most d.