26,325 research outputs found
Approximation algorithms for min-max resource sharing and malleable tasks scheduling
This thesis deals with approximation algorithms for problems in mathematical programming, combinatorial optimization, and their applications. We first study the min-max resource-sharing problem (the packing problem as the linear case) with nonnegative convex constraints on a convex set , which is a class of convex programming. In general block solvers are required for solving the problems. We generalize the algorithm by Grigoriadis et al. to the case with only weak approximate block solvers. In this way we present an approximation algorithm that needs at most calls to the block solver for any given relative accuracy . It is the first bound independent of the data and the approximation ratio of the block solver. As applications of the min-max resource-sharing problem, we study the multicast congestion problem in communication networks and the range assignment problem in arbitrary ad-hoc networks. We present improved approximation algorithms for these problems. We also study the problem of scheduling malleable tasks with precedence constraints. We are given identical processors and tasks. For each task the processing time is a discrete function of the number of processors allotted to it. In addition, the tasks must be processed according to the precedence constraints. The goal is to minimize the makespan (maximum completion time) of the resulting schedule. We improve the previous best approximation algorithm with a ratio to . Finally, we propose a new model for malleable tasks and develop an approximation algorithm for the scheduling problem with a ratio . We also show that our results are very close to the best asymptotic one
Joint Data compression and Computation offloading in Hierarchical Fog-Cloud Systems
Data compression has the potential to significantly improve the computation
offloading performance in hierarchical fog-cloud systems. However, it remains
unknown how to optimally determine the compression ratio jointly with the
computation offloading decisions and the resource allocation. This joint
optimization problem is studied in the current paper where we aim to minimize
the maximum weighted energy and service delay cost (WEDC) of all users. First,
we consider a scenario where data compression is performed only at the mobile
users. We prove that the optimal offloading decisions have a threshold
structure. Moreover, a novel three-step approach employing convexification
techniques is developed to optimize the compression ratios and the resource
allocation. Then, we address the more general design where data compression is
performed at both the mobile users and the fog server. We propose three
efficient algorithms to overcome the strong coupling between the offloading
decisions and resource allocation. We show that the proposed optimal algorithm
for data compression at only the mobile users can reduce the WEDC by a few
hundred percent compared to computation offloading strategies that do not
leverage data compression or use sub-optimal optimization approaches. Besides,
the proposed algorithms for additional data compression at the fog server can
further reduce the WEDC
Optimizing egalitarian performance in the side-effects model of colocation for data center resource management
In data centers, up to dozens of tasks are colocated on a single physical
machine. Machines are used more efficiently, but tasks' performance
deteriorates, as colocated tasks compete for shared resources. As tasks are
heterogeneous, the resulting performance dependencies are complex. In our
previous work [18] we proposed a new combinatorial optimization model that uses
two parameters of a task - its size and its type - to characterize how a task
influences the performance of other tasks allocated to the same machine.
In this paper, we study the egalitarian optimization goal: maximizing the
worst-off performance. This problem generalizes the classic makespan
minimization on multiple processors (P||Cmax). We prove that
polynomially-solvable variants of multiprocessor scheduling are NP-hard and
hard to approximate when the number of types is not constant. For a constant
number of types, we propose a PTAS, a fast approximation algorithm, and a
series of heuristics. We simulate the algorithms on instances derived from a
trace of one of Google clusters. Algorithms aware of jobs' types lead to better
performance compared with algorithms solving P||Cmax.
The notion of type enables us to model degeneration of performance caused by
using standard combinatorial optimization methods. Types add a layer of
additional complexity. However, our results - approximation algorithms and good
average-case performance - show that types can be handled efficiently.Comment: Author's version of a paper published in Euro-Par 2017 Proceedings,
extends the published paper with addtional results and proof
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