66 results about "Communication complexity" patented technology

The invention relates to the technical field of underwater robot cooperative control, and provides an elastic consistency control method and system of a multi-underwater robot system. The elastic consistency control method for the multi-AUV system comprises the following steps: discretizing and linearizing the multi-AUV system, introducing a performance index to describe the influence of communication topology on the dynamic behavior of the system, and calculating the elastic consistency of the multi-AUV system on the basis of a centralized optimal control method of a local decoupling system and a robust stability theory. And designing an elastic consistency controller and obtaining controller gain by solving a local algebraic Riccati equation so as to realize consistency control of multiple AUV system states. According to a sparse mode matrix spectrum of a distributed controller, a system stability condition is given, and efficient cooperation and stable operation of a multi-AUV system in a complex underwater environment are ensured. According to the method, the calculation and communication complexity is remarkably reduced, the method is suitable for a multi-AUV cooperative working environment, and a new technical solution is provided for cooperative control of the underwater unmanned system.

The invention discloses a distributed urban and rural planning decision support method and system, and relates to the technical field of data analysis, and the method comprises the following steps: S100, drawing a planar graph of a to-be-planned region, dividing the planar graph of the region according to a Morse decomposition method, and constructing a region matrix, S200, calculating the coverage rate of the region matrix, and S300, calculating the coverage rate of the region matrix. And planning the surveying and mapping path. According to the method, planning units and surveying and mapping grids are unified into the same quadrilateral matrix through Morse complex, repeated zoning and edge matching errors are effectively avoided, the edge weight is inversely proportional to the building coverage rate, an unmanned aerial vehicle and a surveying and mapping vehicle automatically and preferentially encrypt a high built-up area, field working hours are saved, the data precision of a core construction area is guaranteed, and the construction efficiency is improved. The regional matrix naturally corresponds to edge nodes, and each node only communicates with an adjacent unit, so that the MST and the local route can be locally solved, the communication complexity is reduced, and the method is suitable for large-scale regional surveying and mapping.

The invention provides an Internet of Vehicles data sharing and storage model based on a double-layer block chain, and aims to solve the problems of low data interaction efficiency, poor expansibility, insufficient security and the like in the traditional Internet of Vehicles. According to the model, road side units are grouped geographically, an optimized Raft protocol is adopted in each group to realize rapid consensus, and an improved PBFT protocol is adopted among the groups to ensure global consistency. Self-adaptive leader election, batch processing and assembly line mechanisms are introduced into the Raft protocol, so that the throughput and response speed of the system are improved; a reputation value-based VRF main node election mechanism and a BLS aggregation signature technology are introduced into the PBFT protocol, so that the communication complexity is reduced, and the system security and fault-tolerant capability are enhanced. According to the method, the fault-tolerant rate and the message complexity of the system are analyzed theoretically, the advantages of the system in the aspects of throughput, time delay and fault-tolerant performance are verified through simulation experiments, and the method is suitable for large-scale and high-concurrency car networking application scenes.

The invention discloses a multi-type resource participation power grid frequency modulation method based on a consistency algorithm, and the method comprises the steps: firstly constructing an improved frequency response model fusing distributed optical storage equipment, hydrogen storage and energy storage equipment and a DC flexible load, identifying system parameters, solving a multi-resource comprehensive adjustment coefficient, constructing a directed graph model, employing a grouping consistency algorithm, and obtaining a multi-type resource participation power grid frequency modulation model; the optimal adjustment coefficient of each resource is solved through distributed optimization of an augmented Lagrange function and a consistency index, and primary frequency modulation of a multi-type resource collaborative response system is driven. According to the multi-type resource participation power grid frequency modulation method based on the consistency algorithm, by driving a multi-type resource collaborative response system to perform primary frequency modulation, collaborative regulation and control of light storage, hydrogen storage and flexible load are realized, economy and operation constraints are considered through distributed optimization, and communication complexity is reduced through a clustering iteration mechanism; and the frequency stability of the high-proportion new energy power grid is obviously improved.

The invention relates to a practical consensus algorithm for file resource sharing, which comprises reputation-driven task allocation: according to reputation values calculated in real time, nodes with high reputation values are preferentially selected by the algorithm to form a core consensus group to execute the most critical consensus task, and the number of nodes participating in core communication is remarkably reduced. And protocol flow optimization: fundamentally reducing the communication complexity to O (n) level by limiting the scale of the core consensus group and reconstructing a message transmission path. And node state dynamic autonomy: the algorithm has real-time evaluation and dynamic adjustment capabilities on node types. The reputation model continuously monitors node behaviors, can automatically perform degradation processing on low-reputation or fault nodes, and can timely discover and safely isolate or delete bad nodes through a specific mechanism without restarting the system. Through test verification, the reliability, safety, higher throughput and lower delay of the consensus algorithm are verified.

The invention discloses a multi-IP motion controller, industrial equipment and a control method, and relates to the technical field of virtual controllers. A plurality of virtual controls; a multi-IP binding module; an IP mapping module; wherein the virtual controller receives a data packet to generate a control instruction, and sends the control instruction to the corresponding execution terminal through the physical network interface, so as to control the operation of the execution terminal. According to the multi-IP motion controller provided by the invention, the independent IP address is allocated to each internal virtual controller and bound to the same physical network interface, and accurate data addressing and distribution based on the target IP address are realized in combination with an IP mapping mechanism, so that the problems of resource coupling and communication mixing of a traditional single IP architecture are effectively solved, the system integration and use process is simplified, and the system reliability is improved. And a high-performance, high-reliability and flexible solution is provided for complex multi-station cooperative control.

The invention discloses a privacy protection Transform reasoning method based on function secret sharing, which is characterized in that homomorphic encryption is adopted to encrypt an input token sequence, nonlinear operation is processed through a secure multi-party computing protocol, a distributed interval function key is generated by using function secret sharing, and secure comparison and dynamic token pruning are realized. The privacy protection reasoning specifically comprises the steps of an initialization stage, an input encryption stage, a cooperative calculation stage, a safety pruning stage, a result recovery stage and the like. Compared with the prior art, the method has the advantages that the online communication complexity of security comparison is reduced to a constant level from a quadratic level through a function secret sharing technology, the communication bottleneck problem of token pruning in the prior art is effectively solved, and the security comparison efficiency is improved on the premise of protecting client input data and server model parameter privacy. The reasoning efficiency of the Transform model in the privacy sensitive scene is remarkably improved, the method is particularly suitable for the scene where Transform model reasoning needs to be carried out on sensitive data and the privacy requirement is high, and the application prospect is good.

The invention discloses a block chain consensus method and system based on dynamic Byzantine consensus, which are applied to a distributed system on a block chain, and the method comprises the following steps: in a preparation stage, after a leader node receives a proposal, proposing a new block, and broadcasting a preparation message; after the replica node receives the preparation message and successfully verifies the validity of the block in the preparation message, the replica node sends preparation information of a local signature to the leader node; in the pre-commitment stage, the leader node broadcasts a pre-commitment message; when the replica node belongs to the previous system configuration and does not belong to the current system configuration, the replica node leaves the distributed system after receiving the pre-commitment message and submitting all blocks of the previous period; in the decision stage, the leader node broadcasts a decision message; and when the replica node belongs to the current system configuration, submitting the block according to a preset submitting mode. According to the method, the performance of the system cannot be reduced when the member joining / leaving instruction is processed, and the linear communication complexity is met.

The invention discloses a hybrid protocol-based efficient hierarchical parallel Byzantine consensus method, which comprises the following steps of: constructing network nodes into a plurality of consensus groups capable of processing transactions in parallel and a verification group responsible for sequencing and confirming global transactions of a system, and introducing a self-adaptive hybrid consensus protocol mechanism into each consensus group, dynamically switching between a two-stage protocol and a three-stage protocol according to a network state; an efficient protocol switching and state fallback algorithm under parallel fragmentation is designed, when a protocol is switched from a two-stage to a three-stage, the safety fallback and data consistency of a consensus state can be ensured, and the robustness of system operation is ensured; each consensus group submits the transaction batch subjected to intra-group consensus preliminary processing to a verification group; the verification group globally sorts and verifies the transaction batches from all the consensus groups, and blocks are finally generated in sequence; and the block is broadcasted and distributed to all consensus groups, and each consensus group performs final verification and state submission on the block to complete a round of complete global consensus. According to the method, the problems of high communication complexity and insufficient expansibility are solved, and the consensus process parallelism and the overall operation efficiency are improved under Byzantine fault tolerance.

The invention discloses a lightweight non-repudiation model fingerprint efficient traceability method, and belongs to the related technical fields of cryptography application, digital content traceability and the like. The method comprises the following specific steps: inputting an original image data set into a computer system; training and learning a lightweight encoder and a decoder, wherein the encoder maps a binary fingerprint and an image to generate a residual error; the residual error is constrained through a Sigmoid function to generate a fingerprint-containing image, and the model is optimized through dual loss; generating metadata of a PIT parameter binding salt value and a commitment value, and embedding the fingerprint into the image; during detection, a decoder is loaded to extract a decoded fingerprint, binaryzation is carried out through a threshold function, and dual verification is realized through fingerprint polynomial comparison and commitment value verification. According to the method, a fingerprint verification mode is converted into polynomial verification through a polynomial equivalent detection technology, the communication complexity is reduced to sub-linear overhead, lightweight efficient verification is realized, and the method is suitable for efficient traceability and authenticity verification of deep forged images.

The invention discloses a distributed particle filtering algorithm based on Gaussian mixture and Gossip fusion, which relates to the technical field of distributed state estimation and comprises the following steps: acquiring local posteriori distribution by a sensor node through local particle filtering, exchanging sufficient statistics of GMM between the node and a randomly selected neighbor node based on a Gossip protocol, and obtaining a distributed state estimation result. Iterative fusion of the GMM is realized through weighted mixed importance sampling; and finally, optimizing a global state estimation result through a posterior correction step. According to the method, only full statistics such as a mixed coefficient, a mean vector and a covariance matrix of a Gaussian mixture model (GMM) are exchanged among nodes, original particle transmission is replaced, the communication overhead is remarkably reduced, and the communication complexity is linearly increased along with the network scale; meanwhile, an adaptive GMM component adjustment, a regularization weighting EM algorithm and an iteration updating strategy of random weight matrix control are adopted, the calculation process is simplified on the premise that the estimation precision is guaranteed, the single-node calculation burden is reduced, and large-scale sensor network deployment with limited adaptive resources is achieved.

The invention discloses a data access method. The method can be applied to an integration platform. When a user wants to access a first application program deployed in an intranet through an extranet, a proxy server deployed in the extranet obtains a data access request, and the data access request is used for requesting to access application data in the first application program. The proxy server packages the data access request to obtain a first message, and the first message is a transport layer message and comprises the data access request. And then, the proxy server sends the first message to a proxy client deployed in an intranet, so that the proxy client parses the first message and then sends the obtained data access request to the first application program. Visibly, through the scheme, the proxy server side and the proxy client side can interact through the transmission layer, the proxy client side does not need to pay attention to an application layer protocol, the communication complexity between the extranet and the intranet is simplified, and therefore the convenience that the extranet accesses the intranet is improved.

The invention provides a communication method and device, communication equipment, a communication system and a storage medium. The method comprises the following steps: sending a first instruction to second equipment; the second equipment is environment Internet of Things equipment, and the first instruction is used for inventory of the second equipment; receiving first information and / or a first identifier sent by the second equipment; the first information is a random number generated by the second equipment, and the first identifier is used for identifying the second equipment; and determining second information based on the first information and / or the first identifier, wherein the second information is used for performing communication authentication between the first equipment and the second equipment. According to the method disclosed by the invention, the communication complexity is greatly reduced, meanwhile, the implementation complexity of the environment Internet of Things equipment is also reduced, the communication time and communication resources are saved, and the communication efficiency is improved.

The invention belongs to the technical field of medical scene consensus, provides a medical alliance block chain grouping consensus method and system based on leader group decision, and aims to solve the practical problems of high communication complexity, power concentration and main node failure of a traditional PBFT in a large-scale node scene. Through hierarchical design of leader group decision, a grouping strategy is adopted to prevent a power concentration phenomenon, and through leader group parallel decision, post quantum security is guaranteed, communication overhead is reduced, consensus efficiency is improved, and the power concentration phenomenon is avoided.

The invention belongs to the technical field of network communication, and discloses a multi-party cooperative vehicle-road communication security guarantee system and method based on a block chain. The method comprises the following steps: adding a mine card, an RSU and a control center into a block chain network, matching the mine card with a sensor, generating an identity certificate containing public key hash and the like by using an ECC, generating an initial weight according to historical operation data, and selecting a high-weight mine card to endow the network with consensus qualification. And after the operation is completed, collecting physical data, generating workload proof through zero-knowledge proof and hash, and calculating weight distribution communication authority. Grouping is carried out according to geographic areas, RSUs are used as leaders, the RSUs with high weights are preferentially submitted to blocks, and lightweight PBF variants are verified; if the smart contract monitors abnormity, triggering verification, and adjusting the weight according to the communication task; the problem that the identity of physical equipment is difficult to verify in a traditional scheme is solved, the communication safety is improved, the communication complexity is reduced, the method adapts to frequent moving scenes of mine cards, and the consensus efficiency is improved.

This application relates to an interaction method, apparatus, device, and medium supporting a service-oriented software architecture. The method includes: obtaining a list of SOME / IP services for a vehicle; configuring a corresponding configuration file for each SOME / IP service according to the SOME / IP service list; creating at least one processing cluster based on the configuration file to process message input from the SOME / IP services; and monitoring the activity status of SOME / IP service topics using a pre-defined message middleware; and subscribing to topics published by the SOME / IP services and / or publishing topics subscribed to by the SOME / IP services based on the activity status. Thus, by mapping the vehicle's SOME / IP services to topics, the problem of numerous, separate communication between each SOME / IP service, which makes one-to-many message fusion communication difficult, is solved, simplifying communication complexity and improving convenience.

The present application relates to the technical field of unmanned aerial vehicle swarm technology and blockchain technology, and particularly relates to a chain BFT consensus method for unmanned aerial vehicle ad hoc network. The present application selects a plurality of unmanned aerial vehicles for network authentication, constructs an unmanned aerial vehicle ad hoc network, constructs an ad hoc network topology structure, selects consensus nodes based on flight requirements, constructs a consensus network topology structure, assembles a consensus network based on a chain BFT protocol, divides the consensus nodes into a plurality of chain nodes and a plurality of backup chain nodes, optimizes the consensus network using a PSO algorithm to determine the chain sequence of each chain node in the consensus network, transmits information according to the chain sequence, and updates the topology structure in the consensus network based on a sudden situation to redetermine the chain sequence of each chain node. The present application guarantees the timing of information transmission, effectively determines the optimal chain sequence quickly and accurately, effectively guarantees the data transmission efficiency, effectively reduces the communication complexity, and effectively improves the consensus efficiency of the unmanned aerial vehicle group in the consensus network.

The invention discloses a fine-grained distributed training method and system based on gradient quantization sparse compression, proposes a dynamic tensor fusion technology, automatically searches an optimal tensor fusion buffer threshold by using a binary search method, merges gradient tensors of a plurality of layers into a larger buffer for transmission, does not need manual adjustment and optimization, and improves the training efficiency. And the optimal balance between the communication delay and the bandwidth utilization rate is realized. A fine-grained pipeline scheduling mechanism for communication decoupling is provided, a gradient synchronization process is decoupled into a sparse communication task in a back propagation stage and a quantitative communication task in a forward propagation stage, fine-grained overlapping with forward and backward calculation tasks is realized, the utilization rate of calculation resources is maximized, and communication delay is completely masked. In the back propagation stage, a fragmentation Top-k sparsification and AlltoAll routing strategy is adopted, transmission of a large number of zero values is avoided, and the communication complexity of back propagation is reduced; in the forward propagation stage, a low-bit sparse quantization and AllGather strategy is adopted, and the bandwidth bottleneck problem caused by the fact that a traditional sparse method becomes dense back in the parameter synchronization stage is solved.

This invention discloses a privacy-preserving method for federated learning based on adaptive quantization and sparse secret sharing: the server generates a globally random seed and broadcasts it to the clients. Each client locally generates a sparse neighbor set and negotiates a shared key, reducing communication complexity to logarithmic levels. After training gradients, the clients adaptively quantize to an integer ring, using their private seed and shared key to generate private masks and pairwise masks, which are then superimposed and uploaded. Simultaneously, the seed and key are split into secret shares and distributed to neighbors. The server directly sums these to obtain a preliminary aggregation result. After the window expires, it requests secret fragments to reconstruct the private seed and shared key, eliminating private masks and pairwise mask remnants caused by disconnected clients. After dequantization, the global model is updated. This invention reduces communication and computational overhead, eliminates the need for homomorphic encryption, has strong anti-disconnection capabilities, supports large-scale IoT devices, and achieves efficient and robust federated learning aggregation while ensuring information-theoretic security.

The invention discloses an underwater wireless optical communication method and system, and the method comprises the steps: controlling a second transmitting module in a second communication terminal to generate a second initial optical signal through employing a link guide beacon sequence, and adjusting the position and direction of a first communication terminal according to the initial optical signal, so as to enable the first communication terminal to enter a communication coverage range of each other; establishing a half-duplex communication link for the two terminals according to a handshake protocol; transmitting data from a first communication data interface to a second communication terminal through the first communication terminal by using a first optical signal, and outputting the data to external equipment from a second communication data interface of the second communication terminal; transmitting the data from the second communication data interface to the first communication terminal through the second communication terminal by using a second optical signal, and outputting the data from the first communication data interface to the external equipment; the first communication terminal monitors and adjusts the relative poses of the two terminals according to the second optical signal, so that the two terminals are located in the communication coverage range of each other, the communication complexity is reduced, and the measurement precision is improved.

The invention discloses a multi-unmanned-aerial-vehicle power transmission line inspection method based on FedADMM batch optimization, and the method comprises the steps: firstly generating a target function for collected data, and carrying out the batch processing and weight distribution of multiple unmanned aerial vehicles; in the synchronous updating and aggregation process, each batch synchronously executes a FedADMM optimization algorithm to update local data, transmits the updated local data to a local node for aggregation and broadcasts the updated local data to the unmanned aerial vehicle of the batch; and in the aggregation process of the total end, the total end executes a BADM optimization algorithm, aggregates data sent by the local nodes of each batch, and broadcasts own information to the local nodes to achieve a final consistent value. According to the method, on the basis of ensuring efficient cooperative inspection of multiple unmanned aerial vehicles, the communication complexity is reduced and the communication time is shortened through batch processing, the consistency of communication information is realized by means of an optimization algorithm, and the intelligent level and the overall efficiency of transmission line inspection are powerfully improved.

This invention relates to the field of computer technology and discloses an in-band interrupt system, method, electronic device, and storage medium. By having the host end enter an interrupt waiting mode after completing a task in high-speed read / write mode, the slave end takes over the data read / write channel and sends an in-band interrupt command to the host end. Upon receiving an in-band interrupt command from any slave end, the host end does not need to exit the current high-speed read / write mode but directly responds to the in-band interrupt command. Based on the target slave end represented by the in-band interrupt command, the host end retrieves the data to be read from the target slave end in high-speed read / write mode. By inserting an interrupt waiting mode after the task is completed in high-speed read / write mode, the host end can directly respond to the in-band interrupt command sent by the slave end in high-speed read / write mode, avoiding the communication complexity caused by "exit-processing-re-entering" and improving communication efficiency.

The invention discloses a block consensus method and device, and relates to the technical field of block chains, and the method comprises the steps that a first node obtains an ith block broadcasted by a second node in sequence; the ith block is a new block generated by the second node in the round, and the ith block comprises position information of a plurality of historical blocks and aggregation pointers of the plurality of historical blocks; the plurality of historical blocks are a plurality of (i-1) th blocks in a local chain of the second node; the aggregation pointer is obtained by the second node based on the position certificates of the plurality of historical blocks; and the first node verifies the aggregation pointer, and adds the ith block to the local chain after the verification is passed and the fact that the position certificates of the plurality of historical blocks and the consistency certificates of the plurality of historical blocks are cached locally is confirmed. The communication complexity between global nodes and the global storage complexity are reduced under the condition that the security consensus of the block chain system is ensured.

The application discloses a consensus method and a terminal based on a blockchain sensor, a transaction request is initiated to a target general node connected with the blockchain sensor in a blockchain peer-to-peer network by using the blockchain, when the target general node is connected with multiple blockchain sensors, it is considered that the transaction between the blockchain sensors connected with the same general node is a local transaction, a consensus node can be directly and randomly selected to complete the consensus, otherwise, multiple master nodes are used to complete the consensus of non-local transactions, by dividing the local transactions and the non-local transactions, different consensus methods are used, the calculation resources can be effectively saved, the consensus is realized by using multiple master nodes for the non-local transactions, which is different from the single master node consensus in the prior art, the communication complexity can be effectively reduced, the consensus efficiency is greatly improved, and even the resource-limited blockchain sensor can participate in the blockchain consensus process.

This invention discloses an online anomaly detection method for time series data based on sensor grouping, comprising: sensor nodes collecting current time series data; uploading the current time series to a cloud server, so that the cloud server generates a correlation coefficient map of the wireless sensor network based on the correlation coefficients between the sensor nodes, and groups multiple sensor nodes based on the correlation coefficient map, and sends the grouping results to the wireless sensor network; using a pre-trained Bayesian network model to perform anomaly screening on its own current time series to obtain a primary detection result; for each grouped node set, performing anomaly screening on its own current time series according to a first preset threshold corresponding to its own node set to obtain a secondary detection result; and determining the detection result of the current time series of each sensor node. This invention can reduce the communication complexity in wireless sensor networks, reduce energy consumption, and improve the accuracy of anomaly detection.

The invention relates to the technical field of electric power system operation control, in particular to a point-to-point energy market clearing method and device for motivating a producer and a consumer to form a federated power plant, and the method comprises the steps: obtaining market participant demand data, real-time electricity price and the like, and inputting the data, the real-time electricity price and the like as parameters into an optimization model; based on the model, establishing a coordination mechanism of a power distribution system operator, a federated power plant manager and an energy producer, and proposing a dynamic price incentive mechanism; establishing a three-layer model, and converting the three-layer model into a mathematical programming problem with equilibrium constraint; applying an incentive mechanism in mathematical planning, encouraging production and disagger to form a federated power plant and relax complementary constraints, introducing a distributed bipartite graph matching algorithm to calculate an optimal transaction result, and solving the problem to obtain a market clearing result under the condition of satisfying power network physical constraints; a pruning distributed Hungary algorithm is utilized, a decentralized market settlement method is designed, bilateral negotiation of production and disagger is simulated, the transaction cost is clearly reflected, the communication complexity is reduced, and meanwhile privacy is protected.

A secure multi-party computing SPDZ protocol implementation method based on a six-tuple comprises the steps that the six-tuple based on a global key is installed in advance by all parties before online interaction computing, and local direct addition computing fragmentation is carried out according to a computing rule or multiplication computing fragmentation is carried out by obtaining the six-tuple during online interaction. According to the method, for most dishonest secure multi-party computation (MPC) protocols of a matrix ring, matrix multiplication and addition are supported, and addition sharing of a secret MAC value can be safely calculated under sub-linear communication complexity through improved vector linear oblivious evaluation (subfield VOLE).

Exemplary embodiments relate to location-based communications. In one method, a terminal device obtains identification information, the identification information being specific to a geographic area of a plurality of geographic areas covered by a non-terrestrial network (NTN). The terminal device then receives a reference signal in the geographic area according to the identification information. Therefore, the communication complexity in the NTN can be reduced.

The application discloses a Byzantine fault-tolerant method and device based on a tree topology network and a storage medium. The Byzantine fault-tolerant method based on the tree topology network comprises the following steps: (1) dividing consensus nodes into independent groups based on a tree topology network structure; (2) introducing a feedback mechanism to supervise and feedback the behavior of the nodes; (3) performing probability analysis on a feedback domain failure probability in the feedback mechanism; and (4) calculating communication complexity. The Byzantine fault-tolerant method based on the tree topology network, the device and the storage medium can improve node scalability and fault-tolerant performance, and reduce network communication complexity.

The invention belongs to the field of intelligent traffic systems and privacy computing, and particularly relates to a privacy protection k-means clustering method and system used in a vehicle scenario, and the method comprises the steps: a system configuration stage: generating and distributing encryption parameters under a shared Paillier public key when the system is initialized; in the report submitting stage, each vehicle encrypts and uploads the semantic feature vector of the report when submitting the report; in the privacy protection clustering stage, the server uses a self-defined distance function and an aggregation strategy to execute k-means clustering on the ciphertext; in the data center disclosure stage, only the decrypted clustering center is displayed during clustering center disclosure, so that further analysis is facilitated, and data of a single vehicle cannot be leaked. According to the method, non-interactive clustering is adopted, the vehicles only upload encryption features at one time, the vehicles do not need to participate in subsequent iteration, and the overall communication complexity is O (n).