A primal-dual approximation algorithm for the k-prize-collecting minimum power cover problem

Liu, Xiaofei; Li, Weidong; Xie, Runtao

doi:10.1007/s11590-021-01831-z

Cited by 21 publications

(4 citation statements)

References 26 publications

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“…In [26], Liu et al considered a k-prize-collecting cover problem, in which at least k points are covered. The k-prize-collecting scheduling problem with release times and rejection penalties, which can be viewed as another generalization of the P|r j , reject|C max + π(R), deserves to be explored.…”

Section: Discussionmentioning

confidence: 99%

A Combinatorial 2-Approximation Algorithm for the Parallel-Machine Scheduling with Release Times and Submodular Penalties

Wang

Liu

2021

Mathematics

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In this paper, we consider parallel-machine scheduling with release times and submodular penalties (P|rj,reject|Cmax+π(R)), in which each job can be accepted and processed on one of m identical parallel machines or rejected, but a penalty must paid if a job is rejected. Each job has a release time and a processing time, and the job can not be processed before its release time. The objective of P|rj,reject|Cmax+π(R) is to minimize the makespan of the accepted jobs plus the penalty of the rejected jobs, where the penalty is determined by a submodular function. This problem generalizes a multiprocessor scheduling problem with rejection, the parallel-machine scheduling with submodular penalties, and the single machine scheduling problem with release dates and submodular rejection penalties. In this paper, inspired by the primal-dual method, we present a combinatorial 2-approximation algorithm to P|rj,reject|Cmax+π(R). This ratio coincides with the best known ratio for the parallel-machine scheduling with submodular penalties and the single machine scheduling problem with release dates and submodular rejection penalties.

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Section: Discussionmentioning

confidence: 99%

A Combinatorial 2-Approximation Algorithm for the Parallel-Machine Scheduling with Release Times and Submodular Penalties

Wang

Liu

2021

Mathematics

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“…In this section, based on the primal-dual method devised in [9,43] and the disk structure proposed in this paper, we design a primal-dual cloud-edge collaborative task offloading algorithm for minimizing system energy consumption.…”

Section: Primal-dual Algorithm For Cloud-edge Collaborative Task Offl...mentioning

confidence: 99%

Energy-Aware Cloud-Edge Collaborative Task Offloading with Adjustable Base Station Radii in Smart Cities

Zhang

2022

Mathematics

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In smart cities, the computing power and battery life of terminal devices (TDs) can be effectively enhanced by offloading tasks to nearby base stations (BSs) with richer resources. With the goal of TDs being fully served and achieving low-carbon energy savings for the system, this paper investigates task offloading in cloud-edge collaborative heterogeneous scenarios with multiple BSs and TDs. According to the proportional relationship between the energy and coverage radii of BSs, a complete coverage task offloading model with adjustable BS radii is proposed. The task offloading problem is formulated as an integer linear program with multidimensional resource constraints to minimize the sum of energy consumption of BS coverage, offloading tasks to BSs and the cloud data center (CC). Since this task offloading problem is NP-hard, two approximate algorithms with polynomial time complexity are designed based on the greedy strategy of seeking the most energy-effective disk and the primal–dual method of constructing primal feasible solutions according to dual feasible solutions. Experimental results show that both the greedy and primal–dual algorithms can achieve good approximation performance, but each of them has its own advantages due to different design principles. The former is superior in execution time and energy consumption, while the latter has advantages in balancing loads among BSs and alleviating core network bandwidth pressure.

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“…Considering weight, Varadarajan [19] presented a clever quasi-uniform sampling technique that was improved by Chan et al [4], yielding a constant approximation for the minimum weight disk cover problem. About partial cover problem, Liu et al [15] introduced the 𝑘-prize-collecting minimum power cover problem (𝑘-PCPC), and present a novel two-phase primal-dual algorithm and got an approximation ratio of at most 3 𝛼 . The author then introduced the minimum power cover problem with submodular and linear penalties in [14] and presented a combinatorial primal-dual (3 𝛼 + 1)-approximation algorithm.…”

Section: Introductionmentioning

confidence: 99%

A Local-Ratio-Based Power Control Approach for Capacitated Access Points in Mobile Edge Computing

Li¹,

Zhang

2022

Proceedings of the 6th International Conference on High Performance Compilation, Computing and Communications

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Terminal devices (TDs) connect to networks through access points (APs) integrated into the edge server. This provides a prerequisite for TDs to upload tasks to cloud data centers or offload them to edge servers for execution. In this process, signal coverage, data transmission, and task execution consume energy, and the energy consumption of signal coverage increases sharply as the radius increases. Lower power leads to less energy consumption in a given time segment. Thus, power control for APs is essential for reducing energy consumption. Our objective is to determine the power assignment for each AP with same capacity constraints such that all TDs are covered, and the total power is minimized. We define this problem as a minimum power capacitated cover (MPCC) problem and present a minimum local ratio (MLR) power control approach for this problem to obtain accurate results in polynomial time. Power assignments are chosen in a sequence of rounds. In each round, we choose the power assignment that minimizes the ratio of its power to the number of currently uncovered TDs it contains. In the event of a tie, we pick an arbitrary power assignment that achieves the minimum ratio. We continue choosing power assignments until all TDs are covered. Finally, various experiments verify that this method can outperform another greedy-based way.CCS Concepts: • Networks → Wireless access networks; • Theory of computation → Design and analysis of algorithms.

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A primal-dual approximation algorithm for the k-prize-collecting minimum power cover problem

Cited by 21 publications

References 26 publications

A Combinatorial 2-Approximation Algorithm for the Parallel-Machine Scheduling with Release Times and Submodular Penalties

A Combinatorial 2-Approximation Algorithm for the Parallel-Machine Scheduling with Release Times and Submodular Penalties

Energy-Aware Cloud-Edge Collaborative Task Offloading with Adjustable Base Station Radii in Smart Cities

A Local-Ratio-Based Power Control Approach for Capacitated Access Points in Mobile Edge Computing

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