We consider the -Canadian Traveller Problem, which asks for a shortest path between two nodes and in an undirected graph, where up to edges may be blocked. An online algorithm learns about a blocked edge when reaching...
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We consider the -Canadian Traveller Problem, which asks for a shortest path between two nodes and in an undirected graph, where up to edges may be blocked. An online algorithm learns about a blocked edge when reaching one of its endpoints. Recently, it has been shown that no randomized online algorithm can be better than -competitive, even if all --paths are node-disjoint. We show that the bound is tight by constructing a randomized online algorithm for this case that achieves the ratio against an oblivious adversary and is therefore best possible.
This paper deals with a two-machine open shop scheduling problem. The objective is to minimize the makespan. Jobs arrive over time. We study preemption-resume model, i.e., the currently processed job may be preempted ...
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This paper deals with a two-machine open shop scheduling problem. The objective is to minimize the makespan. Jobs arrive over time. We study preemption-resume model, i.e., the currently processed job may be preempted at any moment in necessary and be resumed some time later. Let p(1, j) and p(2, j) denote the processing time of a job J(j) on the two machines M-1 and M-2, respectively. Bounded processing times mean that 1 <= p(i, j) <= alpha (i = 1, 2) for each job J(j), where alpha >= 1 is a constant number. We propose an optimal online algorithm with a competitive ratio 5 alpha-1/4 alpha.
The intersection of N half Planes is a basic problem in computational geometry and computer graphics. The optimal offiine algorithm for this problem runs in time O(N log N). ln this paper, an optimal online algorithm ...
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The intersection of N half Planes is a basic problem in computational geometry and computer graphics. The optimal offiine algorithm for this problem runs in time O(N log N). ln this paper, an optimal online algorithm which runs also in time O(N log N) for this problem is presented. The main idea of the algorithm is to give a new definition for the left side of a given line, to assign the order for the points of a convex polygon, and then to use binary search method in an ordered vertex *** data structure used in the algorithm is no more complex than array.
Mobile edge Industrial Internet of Things (MEIIoT) is composed of Industrial Internet of Things (IIoT) and mobile edge computing, which is currently a new type of IIoT. MEIIoT has the characteristics of large scale an...
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Mobile edge Industrial Internet of Things (MEIIoT) is composed of Industrial Internet of Things (IIoT) and mobile edge computing, which is currently a new type of IIoT. MEIIoT has the characteristics of large scale and strong dynamics (e.g., network topology or number of IIoT devices would change from time to time). The placement of virtualized network functions (VNFs) in MEIIoT refers to placing multiple network functions (e.g., motion analyzer and video processor) on edge nodes in a form of software instances, so that IIoT devices can flexibly obtain services of these VNFs. However, an edge node can only be placed a small number of VNFs, because of its limited storage and computing resources. Therefore, if an IIoT device requires multiple VNFs, it needs to transmit its data to access several edge nodes, which would cause high delay. How to optimally place all the VNFs on edge nodes in MEIIoT, so that the whole access delay for all IIoT devices that requiring VNFs is minimized, is a challenging problem. In this article, we design an online placement algorithm. First, we decompose a long-term VNFs optimization problem into a series of one-shot optimization problems. Second, we formulate these one-shot problems into integer nonlinear programming problems, and prove that they are NP-hard. To overcome this hardness, we then propose a heuristic algorithm. Finally, we carried out extensive experiments with real-world datasets to validate the efficacy of our proposed solution.
The huge amount of energy consumed by the data centers around the world every year motivates the cloud service providers to operate data centers in a more energy efficient way. A promising solution is to turn off the ...
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The huge amount of energy consumed by the data centers around the world every year motivates the cloud service providers to operate data centers in a more energy efficient way. A promising solution is to turn off the idle servers, which, however, may be turned on later, incurring a significant startup cost. The problem turns to dynamically provisioning the workload, and cutting down the energy cost which includes the power to support the running of data center and the startup cost. Different from previous studies that usually consider the worst-case performance guarantee when designing online algorithms, this paper considers the average case which is more practical. We propose a simple online algorithm based on the expectation of job interval of workload, which is proven to be optimal for exponential and uniform distributions and achieves tight competitive ratio e/e-1 and 4/3, respectively, for them. Simulations using the synthetic data verify our theoretical analysis. Numerical results employing Google's data center workload trace demonstrate that the proposed algorithm outperforms the worst case-based algorithm in terms of operation cost reduction.
In this paper, we show that there is a 5/2 l .ln(1+ kappa)-competitive randomized algorithm for the kappa-sever problem on weighted Hierarchically Separated Trees (HSTs) with depth l when n = kappa + 1 where n is the ...
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In this paper, we show that there is a 5/2 l .ln(1+ kappa)-competitive randomized algorithm for the kappa-sever problem on weighted Hierarchically Separated Trees (HSTs) with depth l when n = kappa + 1 where n is the number of points in the metric space, which improved previous best competitive ratio 12l ln(1 + 4l (1 + k)) by Bansal et al. (FOCS, pp 267-276, 2011).
Software defined networking is increasingly prevalent in data center networks for it enables centralized network configuration and management. However, since switches are statically assigned to controllers and control...
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Software defined networking is increasingly prevalent in data center networks for it enables centralized network configuration and management. However, since switches are statically assigned to controllers and controllers are statically provisioned, traffic dynamics may cause long response time and incur high maintenance cost. To address these issues, we formulate the dynamic controller assignment problem (DCAP) as an online optimization to minimize the total cost caused by response time and maintenance on the cluster of controllers. By applying the randomized fixed horizon control framework, we decompose DCAP into a series of stable matching problems with transfers, guaranteeing a small loss in competitive ratio. Since the matching problem is NP-hard, we propose a hierarchical two-phase algorithm that integrates key concepts from both matching theory and coalitional games to solve it efficiently. Theoretical analysis proves that our algorithm converges to a near-optimal Nash stable solution within tens of iterations. Extensive simulations show that our online approach reduces total cost by about 46%, and achieves better load balancing among controllers compared with static assignment.
Built on top of virtualization technologies, network function virtualization (NFV) provides flexible and scalable software implementation of various network functions. Virtual network functions (VNFs), which are netwo...
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Built on top of virtualization technologies, network function virtualization (NFV) provides flexible and scalable software implementation of various network functions. Virtual network functions (VNFs), which are network functions implemented as virtual machines, are chained together to provide network services. Dynamic deployment of VNFs while satisfying incoming network traffic demand is the key to cost optimization of an NFV system. Besides considering server resource capacity and incoming traffic rates, an optimal scaling policy needs to strike a balance between VNF's operational costs, the costs for maintaining VNF instances, and VNF deployment costs, additional costs when setting up new VNF instances on a server. This paper targets dynamic scaling of VNF instances in a cloud data center where multiple VNF chains are running. We propose an online scaling algorithm to adjust the deployment of VNF instances according to time-varying traffic demand, ensuring a good competitive ratio. Through theoretical analysis and trace-driven simulation, we demonstrate effectiveness of the proposed online VNF scaling algorithm.
With the rapid development of economy and technology, large-scale integrated energy buildings account for an increasing proportion of urban load. However, the randomness of EV owner behaviors, electricity price and ou...
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With the rapid development of economy and technology, large-scale integrated energy buildings account for an increasing proportion of urban load. However, the randomness of EV owner behaviors, electricity price and outdoor temperature have brought challenges to the energy management of integrated energy buildings. This paper proposes a stochastic dynamic programming-based online algorithm to address the energy management of integrated energy buildings with electric vehicles and flexible thermal loads under multivariate uncertainties. First, an online energy management framework is established, which is further formulated as a multi-stage stochastic sequential decision-making problem. To address the complexities of the problem, a novel stochastic dynamic programming is employed to develop a distribution-free, computationally efficient, and scalable solution. By using extensive training samples, the algorithm is trained offline to learn how to deal with multivariate uncertainties and get the approximate optimal solution, which no longer depends on intraday forecast information. Numerical tests demonstrate the effectiveness of the proposed algorithm compared with other online algorithms in terms of optimality and computation efficiency.
We consider online scheduling with restarts in an unbounded parallel-batch processing system to minimize the makespan. By online we mean that jobs arrive over time and all the information on a job is unknown before it...
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We consider online scheduling with restarts in an unbounded parallel-batch processing system to minimize the makespan. By online we mean that jobs arrive over time and all the information on a job is unknown before its arrival time (release date) and restart means that a running batch may be interrupted, losing all the work done on it, and the jobs in the interrupted batch are released and become independently unscheduled jobs. It is known in the literature that the considered problem has no online algorithm with a competitive ratio less than (5 - root 5)/2. We give an online algorithm for the considered problem with a competitive ratio (5 - root 5)/2 approximate to 1.382.
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