We formulate and analyze a generic coverage optimization problem arising in wireless sensor networks with sensors of limited mobility. Given a set of targets to be covered and a set of mobile sensors, we seek a sensor dispatch algorithm maximizing the covered targets under the constraint that the maximal moving distance for each sensor is upper-bounded by a given threshold. We prove that the problem is NP-hard. Given its hardness, we devise four algorithms to solve it heuristically or approximately. Among the approximate algorithms, we first develop randomized (1−1/e)-optimal algorithm. We then employ a derandomization technique to devise a deterministic (1−1/e)-approximation algorithm. We also design a deterministic approximation algorithm with nearly ▵−1 approximation ratio by using a colouring technique, where ▵ denotes the maximal number of subsets covering the same target. Experiments are also conducted to validate the effectiveness of the algorithms in a variety of parameter settings.
Huge energy consumption of large-scale cloud data centers damages environments with excessive carbon emission. More and more data center operators are seeking to reduce carbon footprint via various types of renewable energy. However, the intermittent availability of renewable energy sources makes it quite challenging to cooperate with dynamically arriving workload.Meanwhile, the different natures (eg, price and carbon emission) of multiple energy sources also bring more challenges to achieve an optimal trade-off among carbon emission, power cost, and service level agreement (SLA). In this paper, we study the problem of reducing the long-term energy cost for geo-distributed cloud centers, where multiple sources of renewable energy are considered and SLA requirement and carbon budget are satisfied. To tackle the randomness of workload arrival, varying electricity price, and intermittent supply of renewable energy, we first formulate the cost minimization problem as a constraint stochastic optimization problem. Second, based on Lyapunov optimization technique, we propose an online control algorithm to solve it and provide the rigorous theory analysis to demonstrate its performance. By converting the long-term optimization problem to a mixed integer linear programming problem in each time slot, we analyze its inherent structure and propose an efficient algorithm to solve it based on Brenner's method.Our proposed algorithm makes online decisions rely only on the current system state and achieve [O( 1 ∕V), O(V)] cost emission trade-off. Finally, the effectiveness of our algorithm is evaluated by extensive simulations based on real-world data traces. KEYWORDS geo-distributed cloud center, green-aware, Lyapunov optimization, renewable energy INTRODUCTIONDriven by the exploding demand of enterprises and personal computation, the scale of cloud data centers has become increasingly large. As stated in the latest report, 1 some leading IT enterprises (eg, Facebook, Amazon, and Google) own their inter-continental data centers in different regions that contain thousands of servers. Thus, accompanied with the corresponding electricity cost is up to millions dollars per year. Meanwhile, large electricity consumption from "brown energy" (produce from oil or coal) brings a large amount of greenhouse gases (GHG) emissions which cause great damages to the fragile environment. Recent studies have shown that Information and Communications Technology (ICT) sector is responsible for 2% of global carbon emission, which places it on par with the aviation industry, and this is set to be doubled by 2020. 2,3 Therefore, it is significant for the large-scale data centers to reduce the net carbon footprint and power cost.Recently, reducing power consumption to make data centers green with renewable energy has received a lot of attention both in industry. 4 and academia. 5,6 Compared to brown energy, renewable energy (such as wind energy and solar energy) is more environmentally friendly with low carbon footprint. Google, Microsoft, and Faceboo...
As an important application of wireless sensor networks (WSNs), deployment of mobile sensors to periodically monitor (sweep cover) a set of points of interest (PoIs) arises in various applications, such as environmental monitoring and data collection. For a set of PoIs in an Eulerian graph, the point sweep coverage problem of deploying the fewest sensors to periodically cover a set of PoIs is known to be Non-deterministic Polynomial Hard (NP-hard), even if all sensors have the same velocity. In this paper, we consider the problem of finding the set of PoIs on a line periodically covered by a given set of mobile sensors that has the maximum sum of weight. The problem is first proven NP-hard when sensors are with different velocities in this paper. Optimal and approximate solutions are also presented for sensors with the same and different velocities, respectively. For M sensors and N PoIs, the optimal algorithm for the case when sensors are with the same velocity runs in O(MN) time; our polynomial-time approximation algorithm for the case when sensors have a constant number of velocities achieves approximation ratio 12; for the general case of arbitrary velocities, 12α and 12(1−1/e) approximation algorithms are presented, respectively, where integer α≥2 is the tradeoff factor between time complexity and approximation ratio.
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