A unified approach to approximating resource allocation and scheduling
Journal of the ACM (JACM)
Approximating the Throughput of Multiple Machines in Real-Time Scheduling
SIAM Journal on Computing
Tight approximation algorithms for maximum general assignment problems
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
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
A (1-1/e)-approximation algorithm for the generalized assignment problem
Operations Research Letters
| Hi-index | 0.00 |
We consider the Generalized Scheduling Within Intervals (GSWI) problem: given a set J of jobs and a set I of intervals, where each job j ∈ J has in interval I ∈ I length (processing time) lj,I and profit pj,I, find the highest-profit feasible schedule. The best approximation ratio known for GSWI is (1/2-Ɛ). We give a (1-1/e-Ɛ)-approximation scheme for GSWI with bounded profits, based on the work by Chuzhoy, Rabani, and Ostrovsky [4] for the {0, 1}-profit case. We also consider the Scheduling Within Intervals (SWI) problem, which is a particular case of GSWI where for every j ∈ J there is a unique interval I = Ij ∈ I with pj,I 0. We prove that SWI is (weakly) NP-hard even if the stretch factor (the maximum ratio of job's interval size to its processing time) is arbitrarily small, and give a polynomial-time algorithm for bounded profits and stretch factor