Optimizing Movement for Maximizing Lifetime of Mobile Sensors for Covering Targets on a Line

Given a set of sensors distributed on the plane and a set of Point of Interests (POIs) on a line segment, a primary task of the mobile wireless sensor network is to schedule covering the POIs by the sensors, such that each POI is monitored by at least one sensor. For balancing the energy consumption, we study the min-max line barrier target coverage (LBTC) problem which aims to minimize the maximum movement of the sensors from their original positions to their final positions at which the coverage is composed. We first proved that when the radius of the sensors are non-uniform integers, even 1-dimensional LBTC (1D-LBTC), a special case of LBTC in which the sensors are distributed on the line segment instead of the plane, is NP -hard. The hardness result is interesting, since the continuous version of LBTC to cover a given line segment instead of the POIs is known polynomial solvable. Then we present an exact algorithm for LBTC with uniform radius and sensors distributed on the plane, via solving the decision version of LBTC. We argue that our algorithm runs in time O ( n 2 log n ) and produces an optimal solution to LBTC. The time complexity compares favorably to the state-of-art runtime O ( n 3 log n ) of the continuous version which aims to cover a line barrier instead of the targets. Last but not the least, we carry out numerical experiments to evaluate the practical performance of the algorithms, which demonstrates a practical runtime gain comparing with an optimal algorithm based on integer linear programming.

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Fast Filtering of Search Results Sorted by Attribute

ACM Transactions on Information Systems ◽

10.1145/3477982 ◽

2022 ◽

Vol 40 (2) ◽

pp. 1-24

Author(s):

Franco Maria Nardini ◽

Roberto Trani ◽

Rossano Venturini

Keyword(s):

Heuristic Algorithms ◽

State Of The Art ◽

Optimal Algorithm ◽

Computational Cost ◽

Approximation Error ◽

Optimal Solution ◽

Exact Algorithm ◽

Performance Bounds ◽

Search Results ◽

Filtering Problem

Modern search services often provide multiple options to rank the search results, e.g., sort “by relevance”, “by price” or “by discount” in e-commerce. While the traditional rank by relevance effectively places the relevant results in the top positions of the results list, the rank by attribute could place many marginally relevant results in the head of the results list leading to poor user experience. In the past, this issue has been addressed by investigating the relevance-aware filtering problem, which asks to select the subset of results maximizing the relevance of the attribute-sorted list. Recently, an exact algorithm has been proposed to solve this problem optimally. However, the high computational cost of the algorithm makes it impractical for the Web search scenario, which is characterized by huge lists of results and strict time constraints. For this reason, the problem is often solved using efficient yet inaccurate heuristic algorithms. In this article, we first prove the performance bounds of the existing heuristics. We then propose two efficient and effective algorithms to solve the relevance-aware filtering problem. First, we propose OPT-Filtering, a novel exact algorithm that is faster than the existing state-of-the-art optimal algorithm. Second, we propose an approximate and even more efficient algorithm, ϵ-Filtering, which, given an allowed approximation error ϵ, finds a (1-ϵ)–optimal filtering, i.e., the relevance of its solution is at least (1-ϵ) times the optimum. We conduct a comprehensive evaluation of the two proposed algorithms against state-of-the-art competitors on two real-world public datasets. Experimental results show that OPT-Filtering achieves a significant speedup of up to two orders of magnitude with respect to the existing optimal solution, while ϵ-Filtering further improves this result by trading effectiveness for efficiency. In particular, experiments show that ϵ-Filtering can achieve quasi-optimal solutions while being faster than all state-of-the-art competitors in most of the tested configurations.

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Maximum Target Coverage Problem in Mobile Wireless Sensor Networks

Sensors ◽

10.3390/s21010184 ◽

2020 ◽

Vol 21 (1) ◽

pp. 184

Author(s):

Dieyan Liang ◽

Hong Shen ◽

Lin Chen

Keyword(s):

Wireless Sensor Networks ◽

Sensor Networks ◽

Approximation Algorithm ◽

Optimization Problem ◽

Optimal Algorithm ◽

Wireless Sensor ◽

Coverage Problem ◽

Mobile Wireless ◽

Limited Mobility ◽

Mobile Wireless Sensor

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.

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