Abstract
This paper considers the problem of maximizing the throughput of jobs wherein each job consists of multiple tasks. Consider a system offering a uniform capacity of a resource (say unit bandwidth). We are given a set of jobs, each consisting of a sequence of at most r tasks. Each task is associated with a window (specified by a release time and a deadline) within which it can be scheduled; each task also has a processing time and a bandwidth requirement. Each job has a profit associated with it. A feasible solution must choose a subset of jobs and schedule all the tasks for these jobs such that at any point of time, the total bandwidth requirement does not exceed the capacity of the resource; furthermore, the schedule must obey the precedence constraints (tasks of a job must be scheduled in order of the input sequence). The goal is to compute the feasible solution having maximum profit.
Prior work has studied the problem without the notion of windows; furthermore, the algorithms presented therein require that the bandwidths of all the tasks of a job are uniform. Under these two restrictions, O(r)-approximation algorithms are known. Our main result presents an O(r)-approximation algorithm for the general case wherein tasks can have windows and bandwidths of tasks within the same job may be non-uniform.
Chapter PDF
Similar content being viewed by others
Keywords
- Feasible Solution
- Approximation Algorithm
- Precedence Constraint
- Bandwidth Requirement
- Bandwidth Constraint
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Bafna, V., Narayanan, B., Ravi, R.: Nonoverlapping local alignments (weighted independent sets of axis-parallel rectangles). Discrete Applied Math. 71(1-3), 41–53 (1996)
Bar-Noy, A., Bar-Yehuda, R., Freund, A., Naor, J., Schieber, B.: A unified approach to approximating resource allocation and scheduling. J. of the ACM 48(5), 1069–1090 (2001)
Bar-Yehuda, R., Halldórsson, M., Naor, J., Shachnai, H., Shapira, I.: Scheduling split intervals. SIAM Journal of Computing 36(1), 1–15 (2006)
Bar-Yehuda, R., Rawitz, D.: Using fractional primal-dual to schedule split intervals with demands. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 714–725. Springer, Heidelberg (2005)
Berman, P., DasGupta, B., Muthukrishnan, S.: Simple approximation algorithm for nonoverlapping local alignments. In: SODA (2002)
Bonsma, P., Schulz, J., Wiese, A.: A constant factor approximation algorithm for unsplittable flow on paths. In: FOCS (2011)
Calinescu, G., Chakrabarti, A., Karloff, H., Rabani, Y.: Improved approximation algorithms for resource allocation. In: Cook, W.J., Schulz, A.S. (eds.) IPCO 2002. LNCS, vol. 2337, pp. 401–414. Springer, Heidelberg (2002)
Chakrabarti, A., Chekuri, C., Gupta, A., Kumar, A.: Approximation algorithms for the unsplittable flow problem. Algorithmica 47(1), 53–78 (2007)
Chekuri, C., Khanna, S.: On multidimensional packing problems. SIAM J. Comput. 33(4), 837–851 (2004)
Grötschel, M., Lovász, L., Schrijver, A.: Geometric Algorithms And Combinatorial Optimization. Springer (1993)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chakaravarthy, V.T., Roy Choudhury, A., Roy, S., Sabharwal, Y. (2013). Scheduling Jobs with Multiple Non-uniform Tasks. In: Wolf, F., Mohr, B., an Mey, D. (eds) Euro-Par 2013 Parallel Processing. Euro-Par 2013. Lecture Notes in Computer Science, vol 8097. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40047-6_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-40047-6_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40046-9
Online ISBN: 978-3-642-40047-6
eBook Packages: Computer ScienceComputer Science (R0)