With the wide application of automated guided vehicles(AGVs) in large scale outdoor scenarios with complex terrain,the collaborative work of a large number of AGVs becomes the main trend.The effective multi-agent path...With the wide application of automated guided vehicles(AGVs) in large scale outdoor scenarios with complex terrain,the collaborative work of a large number of AGVs becomes the main trend.The effective multi-agent path finding(MAPF) algorithm is urgently needed to ensure the efficiency and realizability of the whole system. The complex terrain of outdoor scenarios is fully considered by using different values of passage cost to quantify different terrain types. The objective of the MAPF problem is to minimize the cost of passage while the Manhattan distance of paths and the time of passage are also evaluated for a comprehensive comparison. The pre-path-planning and real-time-conflict based greedy(PRG) algorithm is proposed as the solution. Simulation is conducted and the proposed PRG algorithm is compared with waiting-stop A^(*) and conflict based search(CBS) algorithms. Results show that the PRG algorithm outperforms the waiting-stop A^(*) algorithm in all three performance indicators,and it is more applicable than the CBS algorithm when a large number of AGVs are working collaboratively with frequent collisions.展开更多
The authors propose an informed search greedy approach that efficiently identifies the influencer nodes in the social Internet of Things with the ability to provide legitimate information.Primarily,the proposed approa...The authors propose an informed search greedy approach that efficiently identifies the influencer nodes in the social Internet of Things with the ability to provide legitimate information.Primarily,the proposed approach minimizes the network size and eliminates undesirable connections.For that,the proposed approach ranks each of the nodes and prioritizes them to identify an authentic influencer.Therefore,the proposed approach discards the nodes having a rank(α)lesser than 0.5 to reduce the network complexity.αis the variable value represents the rank of each node that varies between 0 to 1.Node with the higher value ofαgets the higher priority and vice versa.The threshold valueα=0.5 defined by the authors with respect to their network pruning requirements that can be vary with respect to other research problems.Finally,the algorithm in the proposed approach traverses the trimmed network to identify the authentic node to obtain the desired information.The performance of the proposed method is evaluated in terms of time complexity and accuracy by executing the algorithm on both the original and pruned networks.Experimental results show that the approach identifies authentic influencers on a resultant network in significantly less time than in the original network.Moreover,the accuracy of the proposed approach in identifying the influencer node is significantly higher than that of the original network.Furthermore,the comparison of the proposed approach with the existing approaches demonstrates its efficiency in terms of time consumption and network traversal through the minimum number of hops.展开更多
The dynamic behavior,rapid mobility,abrupt changes in network topology,and numerous other flying constraints in unmanned aerial vehicle(UAV)networks make the design of a routing protocol a challenging task.The data ro...The dynamic behavior,rapid mobility,abrupt changes in network topology,and numerous other flying constraints in unmanned aerial vehicle(UAV)networks make the design of a routing protocol a challenging task.The data routing for communication between UAVs faces numerous challenges,such as low link quality,data loss,and routing path failure.This work proposes greedy perimeter stateless routing(GPSR)based design and implementation of a new adaptive communication routing protocol technique for UAVs,allowing multiple UAVs to communicate more effectively with each other in a group.Close imitation of the real environment is accomplished by considering UAVs’three-dimensional(3D)mobility in the simulations.The performance of the proposed intelligent greedy perimeter stateless routing(IGPSR)scheme has been evaluated based on end-to-end(E2E)delay,network throughput,and data loss ratio.The adapted scheme displayed on average 40%better results.The scenario has been implemented holistically on the network simulator software NS-3.展开更多
The flexible job shop scheduling problem(FJSP) is considered as an important problem in the modern manufacturing system. It is known to be an NP-hard problem. Most of the algorithms used in solving FJSP problem are ca...The flexible job shop scheduling problem(FJSP) is considered as an important problem in the modern manufacturing system. It is known to be an NP-hard problem. Most of the algorithms used in solving FJSP problem are categorized as metaheuristic methods. Some of these methods normally consume more CPU time and some other methods are more complicated which make them di cult to code and not easy to reproduce. This paper proposes a modified iterated greedy(IG) algorithm to deal with FJSP problem in order to provide a simpler metaheuristic, which is easier to code and to reproduce than some other much more complex methods. This is done by separating the classical IG into two phases. Each phase is used to solve a sub-problem of the FJSP: sequencing and routing sub-problems. A set of dispatching rules are employed in the proposed algorithm for the sequencing and machine selection in the construction phase of the solution. To evaluate the performance of proposed algorithm, some experiments including some famous FJSP benchmarks have been conducted. By compared with other algorithms, the experimental results show that the presented algorithm is competitive and able to find global optimum for most instances. The simplicity of the proposed IG provides an e ective method that is also easy to apply and consumes less CPU time in solving the FJSP problem.展开更多
Flow shop scheduling problem with time lags is a practical scheduling problem and attracts many studies. Permutation problem(PFSP with time lags) is concentrated but non-permutation problem(non-PFSP with time lags...Flow shop scheduling problem with time lags is a practical scheduling problem and attracts many studies. Permutation problem(PFSP with time lags) is concentrated but non-permutation problem(non-PFSP with time lags) seems to be neglected. With the aim to minimize the makespan and satisfy time lag constraints, efficient algo- rithms corresponding to PFSP and non-PFSP problems are proposed, which consist of iterated greedy algorithm for permutation(IGTLP) and iterated greedy algorithm for non-permutation (IGTLNP). The proposed algorithms are verified using well-known simple and complex instances of permutation and non-permutation problems with various time lag ranges. The permutation results indicate that the proposed IGTLP can reach near optimal solution within nearly 11% computational time of traditional GA approach. The non-permutation results indicate that the proposed IG can reach nearly same solution within less than 1% com- putational time compared with traditional GA approach. The proposed research combines PFSP and non-PFSP together with minimal and maximal time lag consideration, which provides an interesting viewpoint for industrial implementation.展开更多
Vehicle routing problem in distribution (VRPD) is a widely used type of vehicle routing problem (VRP), which has been proved as NP-Hard, and it is usually modeled as single objective optimization problem when mode...Vehicle routing problem in distribution (VRPD) is a widely used type of vehicle routing problem (VRP), which has been proved as NP-Hard, and it is usually modeled as single objective optimization problem when modeling. For multi-objective optimization model, most researches consider two objectives. A multi-objective mathematical model for VRP is proposed, which considers the number of vehicles used, the length of route and the time arrived at each client. Genetic algorithm is one of the most widely used algorithms to solve VRP. As a type of genetic algorithm (GA), non-dominated sorting in genetic algorithm-Ⅱ (NSGA-Ⅱ) also suffers from premature convergence and enclosure competition. In order to avoid these kinds of shortage, a greedy NSGA-Ⅱ (GNSGA-Ⅱ) is proposed for VRP problem. Greedy algorithm is implemented in generating the initial population, cross-over and mutation. All these procedures ensure that NSGA-Ⅱ is prevented from premature convergence and refine the performance of NSGA-Ⅱ at each step. In the distribution problem of a distribution center in Michigan, US, the GNSGA-Ⅱ is compared with NSGA-Ⅱ. As a result, the GNSGA-Ⅱ is the most efficient one and can get the most optimized solution to VRP problem. Also, in GNSGA-Ⅱ, premature convergence is better avoided and search efficiency has been improved sharply.展开更多
By considering the eigenratio of the Laplacian matrix as the synchronizability measure, this paper presents an efficient method to enhance the synchronizability of undirected and unweighted networks via rewiring. The ...By considering the eigenratio of the Laplacian matrix as the synchronizability measure, this paper presents an efficient method to enhance the synchronizability of undirected and unweighted networks via rewiring. The rewiring method combines the use of tabu search and a local greedy algorithm so that an effective search of solutions can be achieved. As demonstrated in the simulation results, the performance of the proposed approach outperforms the existing methods for a large variety of initial networks, both in terms of speed and quality of solutions.展开更多
Greedy propagation policy for unstructured P2P worms employs the neighboring node list of each node in peer-to-peer (P2P) network to speed up the propagation of P2P worms. After describing the technique background o...Greedy propagation policy for unstructured P2P worms employs the neighboring node list of each node in peer-to-peer (P2P) network to speed up the propagation of P2P worms. After describing the technique background of P2P worms, the algorithm of greedy propagation is addressed. Simulating design for this novel propagation policy is also described. Then, the effects of the greedy propagation policy on spreading speed, convergence speed, and attacking traffic in static P2P worms are simulated and discussed. The primary experimental results show that the greedy propagation is harmful and can bring severe damages to P2P network.展开更多
Currently,the top-rank-k has been widely applied to mine frequent patterns with a rank not exceeding k.In the existing algorithms,although a level-wise-search could fully mine the target patterns,it usually leads to t...Currently,the top-rank-k has been widely applied to mine frequent patterns with a rank not exceeding k.In the existing algorithms,although a level-wise-search could fully mine the target patterns,it usually leads to the delay of high rank patterns generation,resulting in the slow growth of the support threshold and the mining efficiency.Aiming at this problem,a greedy-strategy-based top-rank-k frequent patterns hybrid mining algorithm(GTK)is proposed in this paper.In this algorithm,top-rank-k patterns are stored in a static doubly linked list called RSL,and the patterns are divided into short patterns and long patterns.The short patterns generated by a rank-first-search always joins the two patterns of the highest rank in RSL that have not yet been joined.On the basis of the short patterns satisfying specific conditions,the long patterns are extracted through level-wise-search.To reduce redundancy,GTK improves the generation method of subsume index and designs the new pruning strategies of candidates.This algorithm also takes the use of reasonable pruning strategies to reduce the amount of computation to improve the computational speed.Real datasets and synthetic datasets are adopted in experiments to evaluate the proposed algorithm.The experimental results show the obvious advantages in both time efficiency and space efficiency of GTK.展开更多
Many problems in science and engineering require solving large consistent linear systems. This paper presents a relaxed greedy block Kaczmarz method (RGBK) and an accelerated greedy block Kaczmarz method (AGBK) for so...Many problems in science and engineering require solving large consistent linear systems. This paper presents a relaxed greedy block Kaczmarz method (RGBK) and an accelerated greedy block Kaczmarz method (AGBK) for solving large-size consistent linear systems. The RGBK algorithm extends the greedy block Kaczmarz algorithm (GBK) presented by Niu and Zheng in <a href="#ref1">[1]</a> by introducing a relaxation parameter to the iteration formulation of GBK, and the AGBK algorithm uses different iterative update rules to minimize the running time. The convergence of the RGBK is proved and a method to determine an optimal parameter is provided. Several examples are presented to show the effectiveness of the proposed methods for overdetermined and underdetermined consistent linear systems with dense and sparse coefficient matrix.展开更多
In this paper, an enhanced greedy bit and power allocation algorithms for orthogonal frequency division multiplexing (OFDM) communication systems are introduced. These algorithms combine low complexity greedy power al...In this paper, an enhanced greedy bit and power allocation algorithms for orthogonal frequency division multiplexing (OFDM) communication systems are introduced. These algorithms combine low complexity greedy power allocation algorithms with a simplified maximum ratio combining (MRC) precoding technique at the transmitter for maximizing the average data throughput of OFDM communication systems. Results of computer simulations show that precoding is an effective technique for improving the throughput performance of the proposed bit and power allocation algorithms.展开更多
In the big data era,data unavailability,either temporary or permanent,becomes a normal occurrence on a daily basis.Unlike the permanent data failure,which is fixed through a background job,temporarily unavailable data...In the big data era,data unavailability,either temporary or permanent,becomes a normal occurrence on a daily basis.Unlike the permanent data failure,which is fixed through a background job,temporarily unavailable data is recovered on-the-fly to serve the ongoing read request.However,those newly revived data is discarded after serving the request,due to the assumption that data experiencing temporary failures could come back alive later.Such disposal of failure data prevents the sharing of failure information among clients,and leads to many unnecessary data recovery processes,(e.g.caused by either recurring unavailability of a data or multiple data failures in one stripe),thereby straining system performance.To this end,this paper proposes GFCache to cache corrupted data for the dual purposes of failure information sharing and eliminating unnecessary data recovery processes.GFCache employs a greedy caching approach of opportunism to promote not only the failed data,but also sequential failure-likely data in the same stripe.Additionally,GFCache includes a FARC(Failure ARC)catch replacement algorithm,which features a balanced consideration of failure recency,frequency to accommodate data corruption with good hit ratio.The stored data in GFCache is able to support fast read of the normal data access.Furthermore,since GFCache is a generic failure cache,it can be used anywhere erasure coding is deployed with any specific coding schemes and parameters.Evaluations show that GFCache achieves good hit ratio with our sophisticated caching algorithm and manages to significantly boost system performance by reducing unnecessary data recoveries with vulnerable data in the cache.展开更多
基金Supported by the National Key Research and Development Program of China(No.2020YFC1807904).
文摘With the wide application of automated guided vehicles(AGVs) in large scale outdoor scenarios with complex terrain,the collaborative work of a large number of AGVs becomes the main trend.The effective multi-agent path finding(MAPF) algorithm is urgently needed to ensure the efficiency and realizability of the whole system. The complex terrain of outdoor scenarios is fully considered by using different values of passage cost to quantify different terrain types. The objective of the MAPF problem is to minimize the cost of passage while the Manhattan distance of paths and the time of passage are also evaluated for a comprehensive comparison. The pre-path-planning and real-time-conflict based greedy(PRG) algorithm is proposed as the solution. Simulation is conducted and the proposed PRG algorithm is compared with waiting-stop A^(*) and conflict based search(CBS) algorithms. Results show that the PRG algorithm outperforms the waiting-stop A^(*) algorithm in all three performance indicators,and it is more applicable than the CBS algorithm when a large number of AGVs are working collaboratively with frequent collisions.
基金This work was supported by the National Research Foundation of Korea(NRF)grant funded by the Korea government(MSIT)(No.2021R1A5A1021944 and 2021R1I1A3048013)Additionally,the research was supported by Kyungpook National University Research Fund,2020.
文摘The authors propose an informed search greedy approach that efficiently identifies the influencer nodes in the social Internet of Things with the ability to provide legitimate information.Primarily,the proposed approach minimizes the network size and eliminates undesirable connections.For that,the proposed approach ranks each of the nodes and prioritizes them to identify an authentic influencer.Therefore,the proposed approach discards the nodes having a rank(α)lesser than 0.5 to reduce the network complexity.αis the variable value represents the rank of each node that varies between 0 to 1.Node with the higher value ofαgets the higher priority and vice versa.The threshold valueα=0.5 defined by the authors with respect to their network pruning requirements that can be vary with respect to other research problems.Finally,the algorithm in the proposed approach traverses the trimmed network to identify the authentic node to obtain the desired information.The performance of the proposed method is evaluated in terms of time complexity and accuracy by executing the algorithm on both the original and pruned networks.Experimental results show that the approach identifies authentic influencers on a resultant network in significantly less time than in the original network.Moreover,the accuracy of the proposed approach in identifying the influencer node is significantly higher than that of the original network.Furthermore,the comparison of the proposed approach with the existing approaches demonstrates its efficiency in terms of time consumption and network traversal through the minimum number of hops.
基金Shanghai Summit Discipline in Design,ChinaSpecial Project Funding for the Shanghai Municipal Commission of Economy and Information Civil-Military Inosculation Project,China(No.JMRH-2018-1042)。
文摘The dynamic behavior,rapid mobility,abrupt changes in network topology,and numerous other flying constraints in unmanned aerial vehicle(UAV)networks make the design of a routing protocol a challenging task.The data routing for communication between UAVs faces numerous challenges,such as low link quality,data loss,and routing path failure.This work proposes greedy perimeter stateless routing(GPSR)based design and implementation of a new adaptive communication routing protocol technique for UAVs,allowing multiple UAVs to communicate more effectively with each other in a group.Close imitation of the real environment is accomplished by considering UAVs’three-dimensional(3D)mobility in the simulations.The performance of the proposed intelligent greedy perimeter stateless routing(IGPSR)scheme has been evaluated based on end-to-end(E2E)delay,network throughput,and data loss ratio.The adapted scheme displayed on average 40%better results.The scenario has been implemented holistically on the network simulator software NS-3.
基金Supported by National Natural Science Foundation of China(Grant Nos.51825502,51775216)Hubei Provincial Natural Science Foundation of China(Grant No.2018CFA078)Program for HUST Academic Frontier Youth Team
文摘The flexible job shop scheduling problem(FJSP) is considered as an important problem in the modern manufacturing system. It is known to be an NP-hard problem. Most of the algorithms used in solving FJSP problem are categorized as metaheuristic methods. Some of these methods normally consume more CPU time and some other methods are more complicated which make them di cult to code and not easy to reproduce. This paper proposes a modified iterated greedy(IG) algorithm to deal with FJSP problem in order to provide a simpler metaheuristic, which is easier to code and to reproduce than some other much more complex methods. This is done by separating the classical IG into two phases. Each phase is used to solve a sub-problem of the FJSP: sequencing and routing sub-problems. A set of dispatching rules are employed in the proposed algorithm for the sequencing and machine selection in the construction phase of the solution. To evaluate the performance of proposed algorithm, some experiments including some famous FJSP benchmarks have been conducted. By compared with other algorithms, the experimental results show that the presented algorithm is competitive and able to find global optimum for most instances. The simplicity of the proposed IG provides an e ective method that is also easy to apply and consumes less CPU time in solving the FJSP problem.
基金Supported by National Natural Science Foundation of China(Grant No.71301008)Beijing Municipal Natural Science Foundation of China(Grant No.9144030)
文摘Flow shop scheduling problem with time lags is a practical scheduling problem and attracts many studies. Permutation problem(PFSP with time lags) is concentrated but non-permutation problem(non-PFSP with time lags) seems to be neglected. With the aim to minimize the makespan and satisfy time lag constraints, efficient algo- rithms corresponding to PFSP and non-PFSP problems are proposed, which consist of iterated greedy algorithm for permutation(IGTLP) and iterated greedy algorithm for non-permutation (IGTLNP). The proposed algorithms are verified using well-known simple and complex instances of permutation and non-permutation problems with various time lag ranges. The permutation results indicate that the proposed IGTLP can reach near optimal solution within nearly 11% computational time of traditional GA approach. The non-permutation results indicate that the proposed IG can reach nearly same solution within less than 1% com- putational time compared with traditional GA approach. The proposed research combines PFSP and non-PFSP together with minimal and maximal time lag consideration, which provides an interesting viewpoint for industrial implementation.
基金supported by National Natural Science Foundation of China (No.60474059)Hi-tech Research and Development Program of China (863 Program,No.2006AA04Z160).
文摘Vehicle routing problem in distribution (VRPD) is a widely used type of vehicle routing problem (VRP), which has been proved as NP-Hard, and it is usually modeled as single objective optimization problem when modeling. For multi-objective optimization model, most researches consider two objectives. A multi-objective mathematical model for VRP is proposed, which considers the number of vehicles used, the length of route and the time arrived at each client. Genetic algorithm is one of the most widely used algorithms to solve VRP. As a type of genetic algorithm (GA), non-dominated sorting in genetic algorithm-Ⅱ (NSGA-Ⅱ) also suffers from premature convergence and enclosure competition. In order to avoid these kinds of shortage, a greedy NSGA-Ⅱ (GNSGA-Ⅱ) is proposed for VRP problem. Greedy algorithm is implemented in generating the initial population, cross-over and mutation. All these procedures ensure that NSGA-Ⅱ is prevented from premature convergence and refine the performance of NSGA-Ⅱ at each step. In the distribution problem of a distribution center in Michigan, US, the GNSGA-Ⅱ is compared with NSGA-Ⅱ. As a result, the GNSGA-Ⅱ is the most efficient one and can get the most optimized solution to VRP problem. Also, in GNSGA-Ⅱ, premature convergence is better avoided and search efficiency has been improved sharply.
基金Project supported by the grant from City University of Hong Kong (Grant No. 7008105)
文摘By considering the eigenratio of the Laplacian matrix as the synchronizability measure, this paper presents an efficient method to enhance the synchronizability of undirected and unweighted networks via rewiring. The rewiring method combines the use of tabu search and a local greedy algorithm so that an effective search of solutions can be achieved. As demonstrated in the simulation results, the performance of the proposed approach outperforms the existing methods for a large variety of initial networks, both in terms of speed and quality of solutions.
基金supported by the National Natural Science Foundation of China under Grant No. 60873075
文摘Greedy propagation policy for unstructured P2P worms employs the neighboring node list of each node in peer-to-peer (P2P) network to speed up the propagation of P2P worms. After describing the technique background of P2P worms, the algorithm of greedy propagation is addressed. Simulating design for this novel propagation policy is also described. Then, the effects of the greedy propagation policy on spreading speed, convergence speed, and attacking traffic in static P2P worms are simulated and discussed. The primary experimental results show that the greedy propagation is harmful and can bring severe damages to P2P network.
基金This research was supported in part by the Hunan Province’s Strategic and Emerging Industrial Projects under Grant 2018GK4035in part by the Hunan Province’s Changsha Zhuzhou Xiangtan National Independent Innovation Demonstration Zone projects under Grant 2017XK2058+1 种基金in part by the National Natural Science Foundation of China under Grant 61602171in part by the Scientific Research Fund of Hunan Provincial Education Department under Grant 17C0960 and 18B037.
文摘Currently,the top-rank-k has been widely applied to mine frequent patterns with a rank not exceeding k.In the existing algorithms,although a level-wise-search could fully mine the target patterns,it usually leads to the delay of high rank patterns generation,resulting in the slow growth of the support threshold and the mining efficiency.Aiming at this problem,a greedy-strategy-based top-rank-k frequent patterns hybrid mining algorithm(GTK)is proposed in this paper.In this algorithm,top-rank-k patterns are stored in a static doubly linked list called RSL,and the patterns are divided into short patterns and long patterns.The short patterns generated by a rank-first-search always joins the two patterns of the highest rank in RSL that have not yet been joined.On the basis of the short patterns satisfying specific conditions,the long patterns are extracted through level-wise-search.To reduce redundancy,GTK improves the generation method of subsume index and designs the new pruning strategies of candidates.This algorithm also takes the use of reasonable pruning strategies to reduce the amount of computation to improve the computational speed.Real datasets and synthetic datasets are adopted in experiments to evaluate the proposed algorithm.The experimental results show the obvious advantages in both time efficiency and space efficiency of GTK.
文摘Many problems in science and engineering require solving large consistent linear systems. This paper presents a relaxed greedy block Kaczmarz method (RGBK) and an accelerated greedy block Kaczmarz method (AGBK) for solving large-size consistent linear systems. The RGBK algorithm extends the greedy block Kaczmarz algorithm (GBK) presented by Niu and Zheng in <a href="#ref1">[1]</a> by introducing a relaxation parameter to the iteration formulation of GBK, and the AGBK algorithm uses different iterative update rules to minimize the running time. The convergence of the RGBK is proved and a method to determine an optimal parameter is provided. Several examples are presented to show the effectiveness of the proposed methods for overdetermined and underdetermined consistent linear systems with dense and sparse coefficient matrix.
文摘In this paper, an enhanced greedy bit and power allocation algorithms for orthogonal frequency division multiplexing (OFDM) communication systems are introduced. These algorithms combine low complexity greedy power allocation algorithms with a simplified maximum ratio combining (MRC) precoding technique at the transmitter for maximizing the average data throughput of OFDM communication systems. Results of computer simulations show that precoding is an effective technique for improving the throughput performance of the proposed bit and power allocation algorithms.
基金We would like to greatly appreciate the anonymous reviewers for their insightful comments.This work is supported by The National Key Research and Development Program of China(2016YFB1000302)The National Natural Science Foundation of China(61433019,U1435217).
文摘In the big data era,data unavailability,either temporary or permanent,becomes a normal occurrence on a daily basis.Unlike the permanent data failure,which is fixed through a background job,temporarily unavailable data is recovered on-the-fly to serve the ongoing read request.However,those newly revived data is discarded after serving the request,due to the assumption that data experiencing temporary failures could come back alive later.Such disposal of failure data prevents the sharing of failure information among clients,and leads to many unnecessary data recovery processes,(e.g.caused by either recurring unavailability of a data or multiple data failures in one stripe),thereby straining system performance.To this end,this paper proposes GFCache to cache corrupted data for the dual purposes of failure information sharing and eliminating unnecessary data recovery processes.GFCache employs a greedy caching approach of opportunism to promote not only the failed data,but also sequential failure-likely data in the same stripe.Additionally,GFCache includes a FARC(Failure ARC)catch replacement algorithm,which features a balanced consideration of failure recency,frequency to accommodate data corruption with good hit ratio.The stored data in GFCache is able to support fast read of the normal data access.Furthermore,since GFCache is a generic failure cache,it can be used anywhere erasure coding is deployed with any specific coding schemes and parameters.Evaluations show that GFCache achieves good hit ratio with our sophisticated caching algorithm and manages to significantly boost system performance by reducing unnecessary data recoveries with vulnerable data in the cache.