Routing Protocol For Low-Power Research Articles

Advancing Healthcare Networks: Optimizing Multi-Objective RPL for Diverse Traffic in Low-Power, Lossy Environments

RPL: Powering modern healthcare IoT Networks. The Routing Protocol for Low Power and Lossy Networks(RPL) is a protocol specifically designed for routing in networks characterized by low power and lossy connections built on IPv6. It is specifically designed for the growing use of Instantaneous IoT (Internet of Things) applications. These networks cater to the specialized requirements of Low Power (resource-constrained) and Lossy Networks(unstable networks), also known as LLNs, where routing data smoothly and prioritizing traffic types are the significant challenges. Studies have shown that standard RPL, which makes use of a set of routing rules, struggles to provide the level of performance that many IoT applications in modern-day healthcare demand. This limits RPL’s potential in scenarios where we have a mix of data traffic, which is very common in healthcare settings. To handle the diverse data traffic found in healthcare settings, our method involves distributing several instances of RPL settings throughout the network. The main objective of this strategy is to improve the effectiveness of important and critical healthcare applications. We have developed and thoroughly tested our system using Contiki, which is an open-source IoT operating system. We have three instances in our MultiInstance RPL setup, each of which is intended to handle different kinds of network traffic and provide varying Quality of Service (QoS) measures. Different sets of Objective Function (OF) rules are used by each instance to decide which route is optimal for the data it processes. We have made use of OF0 (Objective Function 0) and MRHOF (Minimum Rank with Hysteresis Objective Function). We have rigorously tested our solution. Our focus has been on metrics like delay, average energy consumption and Packet Delivery Ratio (PDR). Compared to standard RPL, our approach improved packet delivery rates and significantly reduced delays for high priority data packets. This research shows how to better address the complex data traffic needs of real-time healthcare IoT networks.

An Intrusion Detection System against RPL-based Routing Attacks for IoT Networks

<span lang="EN-US">The significant improvement in the Internet, Internet of Things (IoT), communication, and cloud computing have created considerable challenges in providing security for data and devices.  In IoT networks, “Routing Protocol for Low power and Lossy networks”- (RPL) is a communication protocol that enables devices to exchange information and communicate with limited resources like low processing capabilities, less memory and energy. Through the Internet, unauthorised users can access RPL-based IoT networks, making these networks susceptible to routing attacks. Therefore, it is crucial to design Intrusion Detection System-(IDS) to address attacks from IoT communication devices. In this paper, we have proposed GCNConv, a Graph Neural Network (GNN) method that allows capturing the edge and node features of a graph to identify routing attacks. The proposed   system   has experimented on the RADAR dataset and experimental findings proved that, our approach performs well compared to state-of-the-art method with reference to precision, F1-score, accuracy and recall.</span>

Design of a load balancing Objective Function for RPL

Routing protocols for Internet of Things (IoT) play a major role in the performance of the network. The standard Routing Protocol for Low-Power and Lossy Networks (RPL) suffers from a number of limitations including congestion of higher-level nodes and unbalanced topology. This paper proposes a novel Objective Function called Load Balanced Minimum Rank with Hysteresis Objective Function (LB_MRHOF), which assigns child nodes to the most suitable parent in the topology. The Objective Function utilizes a weight of the Expected Transmission Count (ETX) and number of children to calculate the Composite ETX and Number of Children (CENOC) which estimates the load on each node. The attained CENOC is used to select the optimum parent for each node in the topology, where nodes with high CENOC are avoided in the parent selection process. The proposed Objective Function has been evaluated under random and hierarchical network topologies. In addition, the evaluation has investigated the influence of the number of nodes by testing for small, medium and large-scale networks. Results have shown that the proposed Objective Function outperforms MRHOF, OF_FUZZY and OF-EC in terms of Packet Delivery Ratio (PDR) and reduces nodal hop-count under all tested scenarios, with no compromise in energy consumption. They have also revealed that the best performance achieved by LB_MRHOF is attained under large-scale networks. The resulting network topology which is formed by the proposed Objective Function has shown improved balance and more depth.

Trust-Based Optimized Reporting for Detection and Prevention of Black Hole Attacks in Low-Power and Lossy Green IoT Networks.

The Internet of Things (IoT) is empowering various sectors and aspects of daily life. Green IoT systems typically involve Low-Power and Lossy Networks (LLNs) with resource-constrained nodes. Lightweight routing protocols, such as the Routing Protocol for Low-Power and Lossy Networks (RPL), are increasingly being applied for efficient communication in LLNs. However, RPL is susceptible to various attacks, such as the black hole attack, which compromises network security. The existing black hole attack detection methods in Green IoT rely on static thresholds and unreliable metrics to compute trust scores. This results in increasing false positive rates, especially in resource-constrained IoT environments. To overcome these limitations, we propose a delta-threshold-based trust model called the Optimized Reporting Module (ORM) to mitigate black hole attacks in Green IoT systems. The proposed scheme comprises both direct trust and indirect trust and utilizes a forgetting curve. Direct trust is derived from performance metrics, including honesty, dishonesty, energy, and unselfishness. Indirect trust requires the use of similarity. The forgetting curve provides a mechanism to consider the most significant and recent feedback from direct and indirect trust. To assess the efficacy of the proposed scheme, we compare it with the well-known trust-based attack detection scheme. Simulation results demonstrate that the proposed scheme has a higher detection rate and low false positive alarms compared to the existing scheme, confirming the applicability of the proposed scheme in green IoT systems.

Towards an IoT based secured framework for smart cities

<p>Cities are evolving into smart urban environments, where various devices, technologies, services, connections, blocks, and storage systems are transforming to embrace smart solutions, departing from traditional counterparts. This intricate network of interconnected devices collectively constitutes the Internet of Things (IoT), promising users a life of enhanced convenience. However, this transformation also introduces challenges, particularly in managing loosely linked devices and transmitting information across networks. This study conducts a comprehensive review of the various components contributing to the formation of a smart city, scrutinizing the challenges and factors that influence them. The overarching objective is to identify specific areas within smart cities grappling with cybersecurity challenges and ascertain the relative significance of each area. Data for this research is gathered through questionnaires, expert opinions, and paired comparisons drawn from previous studies, and employs the Fuzzy Analytic Hierarchy Process approach to determine the weight of each factor and sub-factor, subsequently ranking them. Among the nine identified factors, the "Smart Security" factor is the most critical, with a weight of 0.198, signifying its paramount importance. To overcome the security challenges in smart cities, we introduce an advanced secure framework (ARPL) for detecting security threats, using the Routing Protocol for Low Power and Lossy Networks (RPL) as its foundation. The advanced framework is adept at identifying a variety of attacks. Performance assessments of the proposed framework encompass several key parameters, such as ADA, TPR, FPR, and end-to-end delay. The positive outcomes observed strongly endorse the effectiveness of the proposed framework, positioning it as an optimal solution for RPL-based smart environments.</p>

RT-Ranked: Towards Network Resiliency by Anticipating Demand in TSCH/RPL Communication Environments

Time-slotted Channel Hopping (TSCH) Media Access Control (MAC) was specified to target the Industrial Internet of Things needs. This MAC balances energy, bandwidth, and latency for deterministic communications in unreliable wireless environments. Building a distributed or autonomous TSCH schedule is arduous because the node negotiates cells with its neighbours based on queue occupancy, latency, and consumption metrics. The Minimal TSCH Configuration defined by RFC 8180 was specified for bootstrapping a 6TiSCH network and detailed configurations necessary to be supported. In particular, it adopts Routing Protocol for Low Power and Lossy networks (RPL) Non-Storing mode, which reduces the node’s network awareness. Dealing with unpredicted traffic far from the forwarding node is difficult due to limited network information. Anticipating this unexpected flow from multiple network regions is essential because it can turn the forwarding node into a network bottleneck leading to high latency, packet discard or disconnection rates, forcing RPL to change the topology. To cope with that, this work proposes a new mechanism that implements an RPL control message option for passing forward the node’s cell demand, allowing the node to anticipate the proper cell allocation for supporting the traffic originating by nodes far from the forwarding point embedded in Destination-Oriented Directed Acyclic Graph (DODAG) Information Object (DIO) and Destination Advertisement Object (DAO) RPL control messages. Implementing this mechanism in a distributed TSCH Scheduling developed in Contiki-NG yielded promising results in supporting unforeseen traffic bursts and has the potential to significantly improve the performance and reliability of TSCH schedules in challenging network environments.

Evaluation of 6LoWPAN Generic Header Compression in the Context of a RPL Network.

The Internet of Things (IoT) facilitates the integration of diverse devices, leading to the formation of networks such as Low-power Wireless Personal Area Networks (LoWPANs). These networks have inherent constraints that make header and payload compression an attractive solution to optimise communication. In this work, we evaluate the performance of Generic Header Compression (6LoWPAN-GHC), defined in RFC 7400, for IEEE 802.15.4-based networks running the IPv6 Routing Protocol for Low-Power and Lossy Networks (RPL). Through simulation and real-device experiments, we study the impact of 6LoWPAN-GHC on energy consumption and delays and investigate for which scenarios 6LoWPAN-GHC is beneficial. We show that all RPL control packets are compressible by 6LoWPAN-GHC, which reduces their transmission delay and as such their vulnerability to interference. However, for the devices under study transmitting at 250 kbit/s, the energy gain obtained from sending a compressed packet is outweighed by the energy needed to compress it. The use of 6LoWPAN-GHC causes an energy increase of between 2% and 26%, depending on the RPL packet type. When the range is more important than the bandwidth and a sub-GHz band is used at 10 kbit/s, an energy gain of 11% to 29% can be obtained, depending on the type of RPL control packet.

Prediction Of Compromised Iot Infrastructure Using Machine Learning

The rapid growth of the Internet of Things (IoT) has led to big advancements in Fog Computing, Smart Cities, and Industry 4.0. These areas handle complex data and need strong protection against cyberattacks. To make IoT devices use power more efficiently, the IETF created the RPL protocol (Routing Protocol for Low-Power and Lossy Networks). However, due to its sophisticated design it is vulnerable to attacks. One of the most successful attacks against this protocol is flooding attacks, which leads to resource exhaustion in nodes. Consequently, there is a pressing need for new security methods. Nonetheless, there is a scarcity of readily accessible, comprehensive, and organized datasets specifically tailored for IoT, as well as benchmark datasets, to train and assess machine learning models. Therefore, the primary focus of this research is on creating new labeled IoT-specific datasets with the COOJA simulator and processing these packets with machine learning algorithms. Decision Tree, Random Forest, K-Nearest Neighbor and Artificial Neural Network algorithms were compared for identifying the Flooding Attacks. The average accuracy obtained for each of the above algorithm is 89.24%, 91.128%, 89.25% and 89.73% respectively.

Priority RPL for IOT Based Smart Manufacturing Industries

A routing protocol used in heterogeneous transport networks for low-power, lossy networks. This is a routing protocol for wireless networks. This protocol follows the same specifications as Zigbee, 6 lopan is IEEE 802.15. 4 Enables both many-to-one and one-to-one communication. To address the need for enhancing in this study proposes a novel methodology called RPL-PG (Routing Protocol for Low-Power and Lossy Networks Priority Generation). Initially sensors like Temperature, Humidity, Vibration, Proximity, Gas and Current Monitoring Sensors are used for smart manufacturing. Consequently, Destination Oriented Directed Acyclic Graph (DODAG) is used for RPL configuration. Based on selected RPL configuration the priority is generated using assign priority count and priority-based queuing. Finally, Fuzzy rules are used to select the RPL path and then update the DODAG finally reached the destination. The study involves setting up a simulated environment using appropriate tools, such as MATLAB. Experimental findings evaluate and compares performance measures, such as Energy Consumption, Network Life Time, Packet Loss Ratio, Packet Delivery Ratio (PDR), E2E Delay, and Network Throughput. The Energy Consumption of the proposed RPL-PG method achieves 43.6 % lower than 38 % and 35.8 % in terms of OMC-RPL and RMA-RP respectively.

Review of routing protocol for low power and lossy network in the internet of things

The growth of internet of things (IoT) devices and apps has caused disruptions in key sectors such as smart environment, healthcare, and mission-critical tool. Security of IoT devices, networks, and infrastructure is the biggest challenge. RPL, a routing protocol optimised for low-power and lossy networks, is applied by the IoT to offer seamless information transfer among the myriad of interconnected entities. So, the paper delves into the nuts and bolts of RPL, covering its protocol settings, trickle timer, and objective function, as well as the IoT’s architecture and applications. This article also provides a framework for categorising past research on the effects of RPL-IoT on energy consumption, transportation, service quality, traffic congestion, and safety. The future of energy efficiency, congestion, objective function, mobility, stability, security, collaborative intrusion detection systems, active learning, and Key Management are all considered in this analysis.

Comparative Study of Routing Protocols for IoT Networks

Abstract: The Internet of things (IoT) is widely used for communication between portable and intelligent heterogeneous devices, like laptops, smartphones, computers, etc. IoT networks are popular in the modern era because they allow data to be exchanged anywhere when connected to the internet. IoT networks have several challenges, including those related to routing, connectivity, privacy, security, and other issues. The major challenge is routing in terms of choosing the best route for sharing data in IoT networks; IoT routing algorithms use more time and energy. In this paper, we review relevent literature and patents and also various routing approaches are categorized into groups, like multicast, clustering, emergency application, traffic, location, tree, and residual energy based approach, and they are compared based on several parameters, like energy consumption, network lifetime, path length, packet delivery ratio, and network latency. In terms of performance metrics, like energy consumption, network lifetime, reliability, efficiency, and packet delivery ratio, the comparison shows that Routing Protocol for Low Power and Lossy Networks (RPL), Efficient Tree-based Self-organizing Protocol (ETSP), Collection Tree Protocol (CTP), and Fast Multi-constrained Multicast Routing Algorithms (FAMOUS) are the best protocols. The best approach is a tree-based one since it solves the larger problem in the hierarchy with the least amount of time complexity.

CERP: Cooperative and Efficient Routing Protocol for Wireless Sensor Networks.

Wireless sensor networks (WSNs), constrained by limited resources, demand routing strategies that prioritize energy efficiency. The tactic of cooperative routing, which leverages the broadcast nature of wireless channels, has garnered attention for its capability to amplify routing efficacy. This manuscript introduces a power-conscious routing approach, tailored for resource-restricted WSNs. By exploiting cooperative communications, we introduce an innovative relay node selection technique within clustered networks, aiming to curtail energy usage while safeguarding data dependability. This inventive methodology has been amalgamated into the Routing Protocol for Low-Power and Lossy Networks (RPL), giving rise to the cooperative and efficient routing protocol (CERP). The devised CERP protocol pinpoints and selects the most efficacious relay node, ensuring that packet transmission is both energy-minimal and reliable. Performance evaluations were executed to substantiate the proposed strategy, and its practicality was examined using an Arduino-based sensor node and the Contiki operating system in real-world scenarios. The outcomes affirm the efficacy of the proposed strategy, outshining the standard RPL concerning reliability and energy conservation, enhancing RPL reliability by 10% and energy savings by 18%. This paper is posited to contribute to the evolution of power-conscious routing strategies for WSNs, crucial for prolonging sensor node battery longevity while sustaining dependable communication.

An ensemble learning framework for the detection of RPL attacks in IoT networks based on the genetic feature selection approach

The rapid proliferation of Internet of Things (IoT) devices has raised critical concerns regarding the security of corresponding IoT networks. The Routing Protocol for Low-Power and Lossy Networks (RPL), a foundational element in IoT communication, is susceptible to diverse routing attacks due to IoT nodes’ constrained resources and open nature. This underscores the necessity for an Intrusion Detection System (IDS) to safeguard RPL-based IoT networks. Existing anomaly-based IDS suffer from high false alarm rates (FAR). In response to these challenges, this paper presents the Ensemble Learning-based Intrusion Detection System (ELG-IDS), which employs stacking and extreme parameter optimization to detect three RPL internal attacks: version number, decreased rank, and DIS flooding attacks. ELG-IDS employs enhanced feature extraction and genetic algorithm (GA)-based feature selection. Experimental results on a dedicated dataset demonstrate ELG-IDS's remarkable accuracy: 99.18%, 99.38%, 99.66%, and 97.90% for version number, rank attack, DIS flooding, and an average accuracy of 97.90% in multi-classification mode, respectively. This study advances IoT network security through ELG-IDS, enhancing protection against evolving security challenges.

A Lightweight Mitigation Approach against a New Inundation Attack in RPL-Based IoT Networks

Internet of Things (IoT) networks are being widely deployed for a broad range of critical applications. Without effective security support, such a trend would open the doors to notable security challenges. Due to their inherent constrained characteristics, IoT networks are highly vulnerable to the adverse impacts of a wide scope of IoT attacks. Among these, flooding attacks would cause great damage given the limited computational and energy capacity of IoT devices. However, IETF-standardized IoT routing protocols, such as the IPv6 Routing Protocol for Low Power and Lossy Networks (RPL), have no relevant security-provision mechanism. Different variants of the flooding attack can be easily initiated in RPL networks to exhaust network resources and degrade overall network performance. In this paper, a novel variant referred to as the Destination Information Object Flooding (DIOF) attack is introduced. The DIOF attack involves an internal malicious node disseminating falsified information to instigate excessive transmissions of DIO control messages. The results of the experimental evaluation demonstrated the significant adverse impact of DIOF attacks on control overhead and energy consumption, which increased by more than 500% and 210%, respectively. A reduction of more than 32% in Packet Delivery Ratio (PDR) and an increase of more than 192% in latency were also experienced. These were more evident in cases in which the malicious node was in close proximity to the sink node. To effectively address the DIOF attack, we propose a new lightweight approach based on a collaborative and distributed security scheme referred to as DIOF-Secure RPL (DSRPL). It provides an effective solution, enhancing RPL network resilience against DIOF attacks with only simple in-protocol modifications. As the experimental results indicated, DSRPL guaranteed responsive detection and mitigation of the DIOF attacks in a matter of a few seconds. Compared to RPL attack scenarios, it also succeeded in reducing network overhead and energy consumption by more than 80% while maintaining QoS performance at satisfactory levels.

An Investigation Schoolwork of IoT Systems In Interior Routing Outbreak

Internet of Things (IoT) deployments mostly relies on the establishment of Low-Power and Lossy Networks (LLNs) among a large number of constraint devices. The Internet Engineering Task Force (IETF) provides an effective IPv6-based LLN routing protocol, namely the IPv6 Routing Protocol for Low Power and Lossy Network (RPL). RPL provides adequate protection against external security attacks but stays vulnerable to internal routing attacks such as a rank attack. Malicious RPL nodes can carry out a rank attack in different forms and cause serious network performance degradation. An experimental study of the impact of the decreased rank attack on the overall network performance is presented in this paper. In also besides, it is important to understand the main influencing factors in this context. In this study, several some many network scenarios were considered with varying network sizes, attacker properties, and topological setups. The experimental results indicate a noticeable adverse effect of the rank attack on the average PDR, delay, ETX, and beacon interval. However, such impact was varied according to network size, attacker position, attacker neighbor count, number of attack-affected nodes, and overall hops increase. The results give a practical reference to the overall performance of RPL networks under rank attacks.

Dynamic-RPL: Enhancing RPL-Based IoT Networks with Effective Support of Dynamic Topology Management

The inherent characteristics and limitations of Internet of Things networks make it hard to avoid facing adverse network conditions. Addressing high performance in extreme situations still remains a challenge even for a standardized routing protocol like the IPv6 Routing Protocol for Low Power and Lossy Networks (RPL). No effective support is provided by the design of RPL to guarantee high network performance in the presence of such challenging conditions. To address such a compelling need, an innovative approach referred to as Dynamic-RPL is proposed in this research paper. With only limited in-protocol modifications to RPL, Dynamic-RPL provides effective support of dynamic topology management in a distributed manner. Seamless optimization of network topology is realized with dynamic topological adjustments to sustain high network performance and stability. It incorporates modified RPL topology establishment, customized RPL objective function and parent selection, a new dynamic topology management algorithm, and additional inter-routing support. The evaluation results demonstrated the ability of Dynamic-RPL to maintain high overall network performance irrespective of the adversity of ongoing network conditions. Considering varying-scale experimental setups, high QoS performance and low energy consumption were achieved without much increase in network overhead. Dynamic-RPL succeeded in adapting responsively with little time required to have the network performance successfully restored and network topology completely converged.

A Subjective Logical Framework-Based Trust Model for Wormhole Attack Detection and Mitigation in Low-Power and Lossy (RPL) IoT-Networks

The increasing use of wireless communication and IoT devices has raised concerns about security, particularly with regard to attacks on the Routing Protocol for Low-Power and Lossy Networks (RPL), such as the wormhole attack. In this study, the authors have used the trust concept called PCC-RPL (Parental Change Control RPL) over communicating nodes on IoT networks which prevents unsolicited parent changes by utilizing the trust concept. The aim of this study is to make the RPL protocol more secure by using a Subjective Logic Framework-based trust model to detect and mitigate a wormhole attack. The study evaluates the trust-based designed framework known as SLF-RPL (Subjective Logical Framework-Routing Protocol for Low-Power and Lossy Networks) over various key parameters, i.e., low energy consumption, packet loss ratio and attack detection rate. The achieved results were conducted using a Contiki OS-based Cooja Network simulator with 30, 60, and 90 nodes with respect to a 1:10 malicious node ratio and compared with the existing PCC-RPL protocol. The results show that the proposed SLF-RPL framework demonstrates higher efficiency (0.0504 J to 0.0728 J out of 1 J) than PCC-RPL (0.065 J to 0.0963 J out of 1 J) in terms of energy consumption at the node level, a decreased packet loss ratio of 16% at the node level, and an increased attack detection rate at network level from 0.42 to 0.55 in comparison with PCC-RPL.

A Novel Approach for Enhanced Network Formation in 6TiSCH-based IoT Low-Power and Lossy Networks

The Internet of Things – Low-Power and Lossy Networks (IoT-LLN) can operate with low power consumption and support reliable communication even in noisy and congested environments. Minimal 6TiSCH Configuration (6TiSCH-MC) and Routing Protocol for Low-Power and Lossy Networks (RPL) protocols bootstrap the IoT-LLN with minimum resources. The 6TiSCH and RPL protocols transmit different control messages for network bootstrapping and maintenance. The 6TiSCH-MC allows only a single minimal cell in each slotframe for transferring and receiving control messages. All network-associated nodes transmit their control messages simultaneously, using the same channel, which leads to collisions. Due to these control message collisions, new nodes waiting to associate with the network are not receiving the required control messages. It delays network formation, and nodes consume more energy. This research work proposes Two Minimal Cells with Dynamic ChannelOffset (TMDC) to overcome the bootstrapping issue of the 6TiSCH-MC. The TMDC increases the minimal cell count to two and provides mutual synchronization between parent and child nodes for transmitting and receiving control messages. The Contiki-NG's COOJA simulator was used for extensive simulation analysis. The TMDC bootstraps networks quicker with less energy and associates more nodes into the network than the 6TiSCH-MC.

Incremental hybrid intrusion detection for 6LoWPAN

IPv6 over Low-powered Wireless Personal Area Networks (6LoWPAN) has grown in importance in recent years, with the Routing Protocol for Low Power and Lossy Networks (RPL) emerging as a major enabler. However, RPL can be subject to attack, with severe consequences. Most proposed IDSs have been limited to specific RPL attacks and typically assume a stationary environment. In this article, we propose the first adaptive hybrid IDS to efficiently detect and identify a wide range of RPL attacks (including DIO Suppression, Increase Rank, and Worst Parent attacks, which have been overlooked in the literature) in evolving data environments. We apply our framework to networks under various levels of node mobility and maliciousness. We experiment with several incremental machine learning (ML) approaches and various ‘concept-drift detection’ mechanisms (e.g. ADWIN, DDM, and EDDM) to determine the best underlying settings for the proposed scheme.

Securing Low-Power Blockchain-enabled IoT Devices against Energy Depletion Attack

Blockchain-enabled Internet of Things (IoT) envisions a world with rapid development and implementations to change our everyday lives based on smart devices. These devices are attached to the internet that can communicate with each other without human interference. A well-known wireless network in blockchain-enabled IoT frameworks is the Low Power and Lossy Network (LLN) that uses a novel protocol known as Routing protocol for low power and lossy networks (RPL) to provide effective and energy-efficient routing. LLNs that run on RPL are inherently prone to multiple Denial of Service (DoS) attacks due to the low cost, shared medium, and resource-constrained nature of blockchain-enabled IoT devices. A Spam DODAG Information Solicitation (DIS) attack is one of the novel attacks that drains the energy source of legitimate nodes and ends up causing the legitimate nodes to suffer from DoS. To address this problem, a mitigation scheme named DIS Spam Attack Mitigation (DISAM) is proposed. The proposed scheme effectively mitigates the effects of the Spam DIS attack on the network’s performance. The experimental results show that DISAM detects and mitigates the attack quickly and efficiently.