Nonoverlapping local alignments (weighted independent sets of axis-parallel rectangles)
Discrete Applied Mathematics - Special volume on computational molecular biology
A unified approach to approximating resource allocation and scheduling
Journal of the ACM (JACM)
Simple approximation algorithm for nonoverlapping local alignments
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Improved Approximation Algorithms for Resource Allocation
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
On Multidimensional Packing Problems
SIAM Journal on Computing
SIAM Journal on Computing
A Constant Factor Approximation Algorithm for Unsplittable Flow on Paths
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Using fractional primal-dual to schedule split intervals with demands
ESA'05 Proceedings of the 13th annual European conference on Algorithms
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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.