Mobile Crowdsensing Applications Research Articles

DWSP-MT: Discovery of workers sensing preferences to match tasks for improving data collection quality in MCS

Mobile CrowdSensing (MCS) is a new sensing paradigm that leverages the widespread use of mobile devices to collect data quickly and enable various key applications in the Internet of Things (IoT). Collecting high-quality data is essential for MCS to design and provide a high-quality service. However, it is difficult for the platform to detect dishonest workers who submit fake data. Therefore, MCS applications face a significant challenge. Although there are a number of studies on truth discovery, these studies mainly failed to consider the sensing preferences of workers, resulting in poor data quality enhancement. To overcome these issues, a Discovery of Workers Sensing Preferences to Match Tasks (DWSP-MT) scheme is proposed to improve the quality of MCS data collection. The DWSP-MT scheme primarily includes three components: 1) Unmanned Aerial Vehicles (UAVs) are employed to sense data as ground truth data and an unsupervised anomaly detection algorithm is adopted to identify the data truth of tasks submitted by unidentified workers. 2) The data truth of unidentified workers in historical tasks is evaluated to calculate their sensing preferences, which are used to identify trusted workers. 3) To improve the quality of data collection, a task assignment model based on the sensing preferences of trusted workers is proposed for the first time, which can ensure that tasks are assigned to their areas of most excellent expertise. At last, two open-access datasets were used to conduct experiments comparing the DWSP-MT scheme with existing truth discovery methods. The outcomes of these experiments indicate that our approach outperforms the state-of-the-art research and improves F1-score by 65.74 %, improves accuracy by 36.62 %, and reduces data bias by 60.61 %

MAB-RP: A Multi-Armed Bandit based workers selection scheme for accurate data collection in crowdsensing

Accurate data collection from workers is crucial for the success of Mobile Crowd Sensing (MCS) applications. However, Current studies exhibit several drawbacks. Firstly, the workers' sensing qualities remain unknown even after the platform acquires the data submitted by the workers, known as the Post Unknown Worker Selection (PUWS) problem. Secondly, systematic deviations between worker data and the Ground Truth Data (GTD) reduce the quality of MCS applications. Thirdly, the data collected by workers for different tasks may vary in accuracy, resulting in low-quality data collection. To address these challenges, we propose a novel Multi-armit-based worker selection scheme with reputation and preference (MAB-RP). The proposed scheme aims to select credible workers for high-quality data collection through trust identification, thus addressing the PUWS issue after worker recruitment. Additionally, the scheme employs a learning-based approach to identify and correct the gaps between the sensed data and the GTD, ultimately improving the accuracy of data collection. Lastly, a matching-based approach is used to identify workers' sensing qualities for different tasks, further enhancing the accuracy of data collection in MCS. Extensive simulations on real-world datasets demonstrate that the proposed MAB-RP scheme outperforms previous strategies in terms of both data quality and cost.

A UAV deployment strategy based on a probabilistic data coverage model for mobile CrowdSensing applications

Mobile CrowdSensing (MCS) is a computational paradigm designed to gather sensing data by using personal devices of MCS platform users. However, being the mobility of devices tightly correlated with mobility of their owners, the locations from which data are collected might be limited to specific sub-regions. We extend the data coverage capability of a traditional MCS platform by exploiting unmanned aerial vehicles (UAV) as mobile sensors gathering data from low covered locations. We present a probabilistic model designed to measure the coverage of a location. The model analyses the user’s trajectories and the detouring capability of users towards locations of interest. Our model provides a coverage probability for each of the target locations, so that to identify low-covered locations. In turn, these locations are used as targets for the StationPositioning algorithms which optimizes the deployment of k UAV stations. We analyze the performance of StationPositioning by comparing the ratio of the covered locations against Random, DBSCAN and KMeans deployment algorithm. We explore the performance by varying the time period, the deployment regions and the existence of areas where it is not possible to deploy any station. Our experimental results show that StationPositioning is able to optimize the selected target location for a number of UAV stations with a maximum covered ratio up to 60%.

Implementation of Secret Key Generation on Mobile Crowdsensing Application to Secure Tracking Location of Motorcyclists

Mobile crowdsensing is a method for collecting many data from sensors on smartphone. In this research, mobile crowdsensing application will be developed to display location of motorcyclits who connected in an Ad-Hoc network along with a security system using the Secret Key Generation (SKG) scheme to generate a secret key that will be used to encrypt and decrypt the data. From the results it can be concluded that the highest measurement correlation is 0.0398 and the lowest is 0.0018 but after randomness extraction proccess, the highest correlation is 0.996 and the lowest is 0.978. After encryption, information of Alice and Bob is stored as random character in database and decrypted as plaintext as shown as in application. In the attacking result, the data after encrypted just shown random character in traffic monitor. When the eavesdroppers manipulate its IP address like Alice's, they can’t connect to Bob.

Online Truthful Incentives for Heterogeneous and $K$-Submodular Crowdsensing

Recently, crowdsensing receives extensive attentions to solve complex sensing tasks. However, these existing works mainly focus on the incentive issues of traditional bidding model. In practice, solutions of the incentive issues of the posted-pricing model, are more important for some realistic mobile crowdsensing (MCS) applications. However, only few works focus on the homogeneous MCS applications (each user can perform only a single task). To this end, in this article we propose a posted-pricing incentive mechanism for heterogeneous MCS applications (different users have different limits of the number of assignments). Furthermore, considering more general MCS applications (satisfying <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K$</tex-math></inline-formula> -submodular function: the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K$</tex-math></inline-formula> -set functions that are submodular in every type <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k\in [K]$</tex-math></inline-formula> ), we define the weighted marginal utilities and explore two posted-pricing incentive mechanisms for heterogeneous and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K$</tex-math></inline-formula> -submodular MCS applications, respectively. Moreover, both of the two mechanisms are based not only on heterogeneous or <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K$</tex-math></inline-formula> -submodular sensing tasks, but also on heterogeneous sensing types. Finally, performance analysis shows that our mechanisms satisfy the desired properties, such as the truthfulness of acceptance decision, the individual rationality,budget feasibility,computational efficiency, and the regret minimization. Through extensive simulations, we evaluate the performance and validate the theoretical properties of our proposed mechanism.

A hybrid blockchain-based identity authentication scheme for Mobile Crowd Sensing

With the continuous innovative development and popularization of mobile smart devices, the application of Mobile Crowd Sensing (MCS) continues to be studied extensively. However, existing centralized MCS applications that use servers for task publishing and data collection exhibit common problems, such as single points of failure and security vulnerabilities. Accordingly, we proposed a hybrid blockchain-based identity authentication scheme for MCS called HBIA, which uses blockchain technology to resolve the single-point failure problem. HBIA builds a cluster structure based on factors such as geographical location and balance, and uses it to construct a hybrid blockchain, with the cluster head node and internal cluster node authenticating on the public and private chains, respectively. We also implemented zero-knowledge proof (ZKP) to ensure the privacy of participants’ identities, thus balancing the contradiction between blockchain transparency and security. In addition, HBIA uses the zero-knowledge succinct non-interactive argument of knowledge (zk-SNARK) technology to enable off-chain computing and on-chain verification, further reducing the blockchain’s workload. Finally,​ HBIA was evaluated based on the pavement crack detection task and tested on the Ethereum public test network known as Ropsten. The test results indicate that the identity authentication scheme proposed in this paper is superior to existing schemes in terms of authentication time.

P2SIM: Privacy-Preserving and Source-Reliable Incentive Mechanism for Mobile Crowdsensing

In mobile crowdsensing (MCS), providing appropriate rewards is a common and efficient way to motivate participants to participate in sensing tasks. However, the privacy of task participants is not protected well in most quality-aware incentive schemes. Moreover, these schemes are designed for general MCS application scenarios where data are collected by internal sensors embedded in participants’ smartphones, and not suitable for scenarios where additional sensors (ASs) except internal sensors are to collect data (e.g., household medical devices). In scenarios with ASs, malicious participants can fabricate sensing data instead of collecting data from ASs, i.e., the source reliability of sensing data cannot be ensured. To address these issues, we propose P2SIM, a privacy-preserving and the source-reliable incentive mechanism scheme for MCS with ASs. We combine redactable signature with private hash function to achieve the source reliability verification of sensing data without revealing the privacy of participants. Moreover, rewards are divided into two parts: 1) fixed rewards and 2) floating rewards, to enhance the flexibility of rewards distribution. Both formal theoretical analysis and extensive experimental evaluations on a real data set show that the proposed P2SIM is secure and efficient.

PSARE: A RL-Based Online Participant Selection Scheme Incorporating Area Coverage Ratio and Degree in Mobile Crowdsensing

Mobile crowdsensing (MCS) is a cost-effective paradigm for gathering real-time and location-related urban sensing data. To complete MCS tasks, MCS platform needs to exploit the trajectory of participants (vehicles or individuals, etc.) for effectively choosing participants. On one hand, the existing works usually assume that platform has possessed the abundant historical movement trajectory for participant selection, or can accurately predict the movement of participant before selection, but this assumption is impractical for many MCS applications, for some candidates have just arrived without sufficient mobility profiles, so-called trajectory from-scratch, or cold-trajectory issue. On the other hand, most of works only considers the coverage ratio of the sensing area, while some hotspots should be sensed frequently, so-called coverage degree of hotspots. To solve the issue, this paper proposes a reinforcement learning (RL) based, i.e., an improved Q-learning based online participant selection scheme to incorporate both coverage ratio and degree, PSARE. First, to solve the explosion of state-value table in traditional tabular Q-learning, an improved two-level Q-learning method is proposed to select participants in online way so as to achieve high long-term return. Specifically, in each selection round, PSARE dynamically compresses all the real participants (RPs) into several virtual participants (VPs) using the available historical trajectories of RPs, and the VP-based state-value table is constructed and constantly updated (i.e., the first level). Then, after selecting the VP through looking up the table, PARSE chooses the RP with the largest expected reward in this VP using epsilon-greedy way to balance the effect of exploration and exploitation (i.e., the second level). Moreover, the reward function is designed to measure the MCS coverage quality, including both coverage degree of hotspots and coverage ratio of target area. Thorough experiments on real-world mobility data set demonstrate that PSARE outperforms than other RL based online participant selection schemes (including deep Q-learning network) and traditional offline selection methods.

BETA: From Behavior Sequentializing to Task Mapping in Mobile Crowdsensing

Mobile crowdsensing (MCS) can be widely adopted for undertaking a variety of tasks for the smart city by recruiting distributed participants. With the rapid proliferation of MCS applications, tasks can be devised with different sensing scales. Hence, allocating the tasks to participants with variable spatiotemporal granularity would be urgent and challenging. To this end, we propose a behavior sequentializing and task mapping (BETA) framework, where MCS tasks can be flexibly mapped based on the moving behavior of a participant’s daily activities. A sequential behavior model is first proposed to describe the moving behavior of a participant’s daily activities. Specifically, the behavior of a daily activity is represented by the spatiotemporal trajectory distribution, and a sequential behavior graph is adopted to model the relationships among multiple activities. To extract the sequential behavior from historical trajectories, a projection-clustering (PC) algorithm and a behavior sequentializing approach are developed. Then, based on the extracted sequential behavior, a behavior-to-task mapping network is proposed to evaluate the fitness between tasks and a participant. Finally, extensive simulations are conducted to demonstrate the functionality and performance of BETA. The results show that our proposed method outperforms the state-of-the-art solutions in the mapping efficiency of tasks with different sensing scales.

Rational Task Assignment and Path Planning Based on Location and Task Characteristics in Mobile Crowdsensing

With the great development in smart devices, mobile crowdsensing (MCS) has been an innovative paradigm for data gathering. Task assignment is a fundamental problem in MCS systems and applications. Previous studies only focused on the assignment of individual tasks, neglecting planning the task processing from a higher level, e.g., making assignments between task locations and workers, which impacts the crowdsensing performance adversely. Furthermore, task characteristics, e.g., route distance, task similarity, and task priority, have a great impact on the rationality of a visiting order and the quality of crowdsensing services. In this article, we tackle the problem of rational task assignment and path planning for MCS, which aims to assign a set of task locations to a set of workers and generate location visiting sequences. We measure the assignment rationality by taking into account geographical information and task characteristics, i.e., route distance, task similarity, and task priority. We prove that the problem of computing the rationality maximization task assignment is NP-hard. For the single-worker scenario, we reduce the problem to a simpler problem with respect to only route distance and task priority criteria since the similarity measurement has a fixed value. We propose an effective greedy algorithm. For the multiple-worker scenario, we first extend the greedy idea by considering all three criteria and then propose an effective approach by reducing the computational complexity of similarity measurement. Extensive experiments show that our proposed approaches achieve promising results.

A Stackelberg Game Approach for Managing AI Sensing Tasks in Mobile Crowdsensing

Mobile Crowdsensing (MCS) is a new paradigm that leverages the collective sensing ability of a crowd so that a special task can be performed through the aggregation of information collected from personal mobile devices. While MCS brings several benefits, its application is prevented by challenges such as the efficient recruitment of users, effective mechanisms for rewarding users to encourage participation, and an effective and fast enough approach for managing the underlying resources that support large-scale MCS applications involving a large number of people in data collection. On the other hand, Artificial Intelligence (AI) applications, which are mostly based on Deep Neural Networks (DNN), are becoming pervasive today and are executed by the end users&#x2019; mobile devices, which are characterised by limited memory and computing power, and low battery level. This paper describes and evaluates an incentive mechanism for a mobile crowdsensing system with an AI sensing task based on a one-leader multi-follower Stackelberg game. The MCS platform, as a leader, provides an AI sensing task to be executed by a DNN, which can be deployed in two different ways: fully on the user device or partially on the device and partially on edge or cloud resources. The users, as followers, make their decisions regarding their participation to the MCS system and select their desired deployment given the energy and memory available on their device and the deployment reward proposed by the MCS platform. The goals of the MCS platform are: i) to motivate the users to participate in the system, ii) to maximize its profit, and iii) to identify the optimal resources supporting the sensing task that minimizes the cost and provide performance guarantees. This problem has been formulated as a mixed integer nonlinear program and propose an efficient algorithmic approach to solve it quickly. The proposed approach has been compared with some baseline methods and with BARON state-of-the-art solver. Results show that our approach converges to the optimal solution much faster than BARON (up to orders of magnitude) especially in large scale systems. Furthermore, the comparison to the baseline methods shows that our approach always beats the best baseline method under different scenarios providing up to 16% improvement for the MCS platform profit.

Mobile Crowd-sensing Applications: Data Redundancies, Challenges, and Solutions

Conventional data collection methods that use Wireless Sensor Networks (WSNs) suffer from disadvantages such as deployment location limitation, geographical distance, as well as high construction and deployment costs of WSNs. Recently, various efforts have been promoting mobile crowd-sensing (such as a community with people using mobile devices) as a way to collect data based on existing resources. A Mobile Crowd-Sensing System can be considered as a Cyber-Physical System (CPS), because it allows people with mobile devices to collect and supply data to CPSs’ centers. In practical mobile crowd-sensing applications, due to limited budgets for the different expenditure categories in the system, it is necessary to minimize the collection of redundant information to save more resources for the investor. We study the problem of selecting participants in Mobile Crowd-Sensing Systems without redundant information such that the number of users is minimized and the number of records (events) reported by users is maximized, also known as the Participant-Report-Incident Redundant Avoidance (PRIRA) problem. We propose a new approximation algorithm, called the Maximum-Participant-Report Algorithm (MPRA) to solve the PRIRA problem. Through rigorous theoretical analysis and experimentation, we demonstrate that our proposed method performs well within reasonable bounds of computational complexity.

Scale to measure usability in Mobile Crowd Sensing (MCS) applications

Mobile Crowd Sensing (MCS) applications are those where participants or users collect (through the different sensors on their mobile device - microphone, camera, GPS, among others) and share information in order to assist other users in making decisions (companies or government) or inform about the most diverse events. In this context, an important factor is the citizen / consumer adherence to this participatory process and studies have shown that usability is a crucial factor in this process. This article presents a scale to measure usability in MCS applications. The method employed made use of usability tests, development of a checklist with usability attributes in MCS and finally data analysis using Item Response Theory. As a result, a set of 30 items forms the usability measurement scale in MCS.

Framework for Integral Data Quality and Security Evaluation in Smartphones

Data quality (DQ) concept should play an important role in decision-making and engineering systems. Underestimation of DQ may lead to resource waste, wrong conclusions, or inefficient decisions. Unfortunately, current approaches to DQ incorporating into data management systems are limited to particular applications. This problem is aggravated by the DQ inequality of data sources. This is especially critical in mobile crowd-sensing applications where data may come from unverified data contributors using the smartphones and other mobile devices. To facilitate the expansion of DQ evaluation to a wider spectrum of applications, this article presents a framework for integral DQ and security evaluation in Android-based smartphones. The developed framework provides support for selecting the DQ metrics and implementing their calculus by integrating diverse sensor DQ and security metrics. We present multiple calculi for DQ and security evaluation such as hierarchical fuzzy rules expert system, neural networks, and algebraic functions. Case studies that demonstrate the framework's performance in addressing real-life tasks are presented and the achieved results are analyzed. The implementation results validate the framework's capability of performing comprehensive DQ evaluations.

Price Learning-based Incentive Mechanism for Mobile Crowd Sensing

Mobile crowd sensing (MCS) is an emerging sensing paradigm that can be applied to build various smart city and IoT applications. In an MCS application, the participation level of mobile users plays an essential role. Thus a great many incentive mechanisms have been proposed to motivate users. However, most of these works focus on the bidding behavior of users and overlook the feature of task requesters. Specifically, there exists a disparity between the low payment a requester would like to make and the high reward a user would like to receive. In this work, we address this issue by designing a group-buying-based online incentive mechanism, which contains two stages: In Stage I, a price learning algorithm is designed to select winning tasks for each group of sensing tasks and obtain a competitive total budget for recruiting users. In Stage II, an online auction is conducted between group agents and online users before a given recruitment deadline. Through theoretical analysis and extensive evaluations, we show that the proposed mechanisms possess computational efficiency, individual rationality, budget balance, truthfulness, and good performance.

RL-Recruiter+: Mobility-Predictability-Aware Participant Selection Learning for From-Scratch Mobile Crowdsensing

Participant selection is a fundamental research issue in Mobile Crowdsensing (MCS). Previous approaches commonly assume that adequately long periods of candidate participants’ historical mobility trajectories are available to model their patterns before the selection process, which is not realistic for some new MCS applications or platforms. The sparsity or even absence of mobility traces will incur inaccurate location prediction, thus undermining the deployment of new MCS applications. To this end, this paper investigates a novel problem called “From-Scratch MCS” (FS-MCS for short), in which we study how to intelligently select participants to minimize such a “cold-start” effect. Specifically, we propose a novel framework based on reinforcement learning, named RL-Recruiter+. With the gradual accumulation of mobility trajectories over time, RL-Recruiter+ is able to make a good sequence of participant selection decisions for each sensing slot. Compared to its previous version, RL-Recruiter, Re-Recruiter+ jointly considers both the previous coverage and current mobility predictability when training the participant selection decision model. We evaluate our approach experimentally based on two real-world mobility datasets. The results demonstrate that RL-Recruiter+ outperforms the baseline approaches, including RL-Recruiter under various settings.

Keeping Cell Selection Model Up-to-Date to Adapt to Time-Dependent Environment in Sparse Mobile Crowdsensing

Sparse mobile crowdsensing (MCS) requires participants to collect data from partial cells and then intelligently infer the data of the rest cells. Since collecting data from different cells will probably result in different data inference quality, cell selection (i.e., which cells need to be selected to collect data) is a critical issue in Sparse MCS. Currently, state-of-the-art cell selection algorithms are implemented based on reinforcement learning. These algorithms ignore the problem that the urban environment is usually time dependent, and the cell selection model needs to be kept up-to-date to adapt to the time-dependent environment. However, Sparse MCS applications require participants to collect data only in a few cells, which makes it hard to obtain suitable training data for continuous cell selection model learning. To solve this problem, we model the spatiotemporal correlations in the collected sparse data, and then design various methods to update training data based on it. Particularly, these methods make full use of the gradual changes of data in time and space, and reasonably transform and splice sparse data at different moments. Finally, updated training data is fed to the cell selection model to keep it up-to-date. We conduct experimental evaluations by performing several sensing tasks in air quality monitoring. The results show that our proposed methods can effectively update training data as well as the cell selection model. Compared with several baselines, our best method can reduce inference error by more than 10% on average.

Preserving Location Privacy for Outsourced Most-Frequent Item Query in Mobile Crowdsensing

The emergence of mobile crowdsensing (MCS) has provided us with unprecedented opportunities for both sensing coverage and data transmission. However, in many MCS applications, the MCS workers are usually required to report the location information of the assigned tasks, which inevitably reveals the workers' location information, even trajectories, and severely impedes the popularization of the MCS system. It is believed that the query on the most-frequent location, e.g., querying the most congested location over a period in a city, is one of the most popular statistics queries in the MCS system, but it may disclose workers' location information. To address the issue, in this article, we propose a location privacy-preserving scheme for outsourced most-frequent item query in the MCS system, where two noncollusive semi-trusted cloud servers cooperatively handle the most-frequent item query. Specifically, by employing our pseudonymization mechanism, transposition cipher, ciphertext packing technique, and order-preserving merge function, our proposed scheme can efficiently answer the most-frequent item query while ensuring the privacy of both workers' personal information and query results. Detailed security analysis shows that our proposed scheme is privacy-preserving. In addition, extensive experiments are conducted, and the results show that our proposed scheme outperforms alternative schemes in terms of computational costs and communication overhead.

Time-Constrained Task Allocation and Worker Routing in Mobile Crowd-Sensing Using a Decomposition Technique and Deep Q-Learning

Mobile crowd-sensing (MCS) is a data collection paradigm, which recruits mobile users with smart devices to perform sensing tasks on a city-wide scale. In MCS, a key challenge is task allocation, especially when MCS applications are time-sensitive, and the platform needs to consider task completion order (since a worker may perform multiple tasks and different task completion orders lead to different travel costs and response times, i.e., the times needed to arrive at the task venues), requirements of tasks (such as deadline and required sensor) and workers heterogeneity. In other words, the task allocation problem consists of multiple task completion order problems, which is challenging to solve due to the large solution space. Therefore, in this paper, we first formulate the considered problem into two related integer linear programming problems (i.e., assignment and task completion order problems) using a decomposition technique in order to reduce the problem size and enable the use of diverse searching strategies. Then, a deep Q-learning (DQN)-based algorithm, namely assignment DQN with a local search (A-DQN w/ LS), is proposed to determine the task-worker assignments, which iteratively employs an asymmetric traveling salesman (ATSP) heuristic to find the task completion orders of the workers. The local optimizer is applied at the end of the A-DQN algorithm to deal with the computation time and local optima. Simulation results show that the proposed method outperforms existing approaches under different sensing dynamics in terms of total cost.

Free Market of Multi-Leader Multi-Follower Mobile Crowdsensing: An Incentive Mechanism Design by Deep Reinforcement Learning

The explosive increase of mobile devices with built-in sensors such as GPS, accelerometer, gyroscope and camera has made the design of mobile crowdsensing (MCS) applications possible, which create a new interface between humans and their surroundings. Until now, various MCS applications have been designed, where the task initiators (TIs) recruit mobile users (MUs) to complete the required sensing tasks. In this paper, deep reinforcement learning (DRL) based techniques are investigated to address the problem of assigning satisfactory but profitable amount of incentives to multiple TIs and MUs as a MCS game. Specifically, we first formulate the problem as a multi-leader and multi-follower Stackelberg game, where TIs are the leaders and MUs are the followers. Then, the existence of the Stackelberg Equilibrium (SE) is proved. Considering the challenge to compute the SE, a DRL based Dynamic Incentive Mechanism (DDIM) is proposed. It enables the TIs to learn the optimal pricing strategies directly from game experiences without knowing the private information of MUs. Finally, numerical experiments are provided to illustrate the effectiveness of the proposed incentive mechanism compared with both state-of-the-art and baseline approaches.