7,673 research outputs found

    New complexity results for parallel identical machine scheduling problems with preemption, release dates and regular criteria

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    In this paper, we are interested in parallel identical machine scheduling problems with preemption and release dates in case of a regular criterion to be minimized. We show that solutions having a permutation flow shop structure are dominant if there exists an optimal solution with completion times scheduled in the same order as the release dates, or if there is no release date. We also prove that, for a subclass of these problems, the completion times of all jobs can be ordered in an optimal solution. Using these two results, we provide new results on polynomially solvable problems and hence refine the boundary between P and NP for these problems

    Dagstuhl Reports : Volume 1, Issue 2, February 2011

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    Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn

    Cross-Sender Bit-Mixing Coding

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    Scheduling to avoid packet collisions is a long-standing challenge in networking, and has become even trickier in wireless networks with multiple senders and multiple receivers. In fact, researchers have proved that even {\em perfect} scheduling can only achieve R=O(1lnN)\mathbf{R} = O(\frac{1}{\ln N}). Here NN is the number of nodes in the network, and R\mathbf{R} is the {\em medium utilization rate}. Ideally, one would hope to achieve R=Θ(1)\mathbf{R} = \Theta(1), while avoiding all the complexities in scheduling. To this end, this paper proposes {\em cross-sender bit-mixing coding} ({\em BMC}), which does not rely on scheduling. Instead, users transmit simultaneously on suitably-chosen slots, and the amount of overlap in different user's slots is controlled via coding. We prove that in all possible network topologies, using BMC enables us to achieve R=Θ(1)\mathbf{R}=\Theta(1). We also prove that the space and time complexities of BMC encoding/decoding are all low-order polynomials.Comment: Published in the International Conference on Information Processing in Sensor Networks (IPSN), 201

    Scheduling MapReduce Jobs under Multi-Round Precedences

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    We consider non-preemptive scheduling of MapReduce jobs with multiple tasks in the practical scenario where each job requires several map-reduce rounds. We seek to minimize the average weighted completion time and consider scheduling on identical and unrelated parallel processors. For identical processors, we present LP-based O(1)-approximation algorithms. For unrelated processors, the approximation ratio naturally depends on the maximum number of rounds of any job. Since the number of rounds per job in typical MapReduce algorithms is a small constant, our scheduling algorithms achieve a small approximation ratio in practice. For the single-round case, we substantially improve on previously best known approximation guarantees for both identical and unrelated processors. Moreover, we conduct an experimental analysis and compare the performance of our algorithms against a fast heuristic and a lower bound on the optimal solution, thus demonstrating their promising practical performance
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