Method for minimizing time overhead resource allocation based on directed acyclic graph and related apparatus

Abstract

A minimum time cost resource allocation method based on directed acyclic graph and related device, including: for the data transmission energy and transmission rate of user node, energy constraint and information transmission constraint are established respectively; according to the priority order and time delay requirement of task, a directed acyclic graph is established; based on the directed acyclic graph, the execution time constraint of task is established, and based on all constraint conditions, the system objective function is established; the task unloading decision is calculated, and the system minimum time cost is calculated given the unloading decision. The present application studies the problems of task unloading and minimum time delay cost in wireless energy supply communication network, jointly considers the dependence relationship of task, the processing rate of edge node to different tasks, the transmission rate from edge node to edge node, the acquisition energy of user node, etc., so as to make the optimal task unloading strategy and time allocation decision.

Description

Technical Field

[0001] This invention belongs to the field of optimization in wireless network task offloading, and specifically relates to a method and apparatus for minimizing time overhead resource allocation based on directed acyclic graphs. Background Technology

[0002] Wireless power communication networks (WPCs) are a novel type of network integrating both energy and information communication, primarily addressing application scenarios where user nodes have limited energy and require large uplink data transmission volumes. Unlike traditional networks, WPCs are designed to "drive data transmission with energy," achieving integrated management of energy harvesting and information transmission through flexible allocation, control, and scheduling of resources such as time, power, and links. Since user nodes have limited energy acquisition, their data needs to be offloaded to edge nodes or the cloud for processing. However, the choice of which edge nodes to offload tasks to directly impacts processing latency. A mismatch between task and edge node performance can lead to tasks that have already reached the edge nodes not being processed in a timely manner, or data generated by some tasks failing to be transmitted to the next edge node. Furthermore, if task offloading, energy acquisition, and information transmission are not considered in conjunction, it can result in increased system latency due to incomplete consideration of their coupling relationships. Summary of the Invention

[0003] The purpose of this invention is to provide a method and apparatus for minimizing time overhead resource allocation based on directed acyclic graphs, in order to solve the problem that the failure to consider task offloading, energy acquisition and information transmission together will lead to an increase in system latency due to the incomplete consideration of the coupling relationship between the three.

[0004] To achieve the above objectives, the present invention adopts the following technical solution:

[0005] In a first aspect, the present invention provides a method for minimizing time-cost resource allocation based on a directed acyclic graph, comprising:

[0006] Energy constraints and information transmission constraints are established for the data transmission energy and transmission rate of user nodes, respectively.

[0007] Based on the priority order and latency requirements of the tasks, construct a directed acyclic graph;

[0008] Based on the directed acyclic graph, the execution time constraints of the task are established, and based on all constraints, the system objective function is established.

[0009] Calculate the task unloading decision, and given the unloading decision, calculate the minimum system time cost.

[0010] Optionally, energy constraints can be constructed, specifically as follows:

[0011] The channel gain between user node j and power supply point h is g.j，h Let μ be the energy conversion efficiency of the power supply node, then the energy constraints are as follows:

[0012]

[0013] The left-hand side of the inequality represents the energy consumed by user node j during uplink data transmission, and the right-hand side represents the effective energy acquired by user node j; P j E represents the transmission power of the j-th user node. j This represents the energy provided by the power supply node to the j-th user node during the power supply time, where t represents the length of each time slot during information transmission, and C represents the energy provided by the power supply node to the j-th user node during the power supply time. i This represents the set of user nodes active in the i-th time slot.

[0014] Optionally, establish information transmission constraints, specifically:

[0015] In a channel with a bandwidth of W Hz, the user node should satisfy the following data transmission model:

[0016]

[0017] Where η represents the noise power, P j E represents the transmission power of the j-th user node. j This represents the energy provided by the power supply node to the j-th user node during the power supply time, where t represents the length of each time slot during information transmission, and C represents the energy provided by the power supply node to the j-th user node during the power supply time. i This represents the set of user nodes active in the i-th time slot, where the source data contains the amount of data from the j-th user node. User node j and corresponding information access point H j The channel gain between them, where W represents the bandwidth (Hertz); This indicates that during the information transmission task phase, sensor node j needs to send data to the corresponding information access point H. j The amount of data transmitted (in bits).

[0018] Optional, in directed acyclic graphs:

[0019] Phase 0 is the phase where user nodes transmit information; Phases 1-K are the phases where tasks are executed and task results are transmitted to the next dependent task; there are a total of K+1 phases; for task u to begin, it must collect the processing results of all tasks from the set Pr(u) of dependent tasks in the previous phase; tasks with the same or overlapping Pr(u) are placed in the same phase, with tasks with higher latency priority placed in earlier phases, and each edge node in the same phase is independently occupied by one task.

[0020] Optionally, based on the directed acyclic graph, establish the task's execution time constraints as follows:

[0021]

[0022]

[0023] Wherein, the first term on the left of the constraint is the time for the z-th task in the k-th stage to complete; the second term on the left represents the time required for the output of the z-th task in the k-th stage to be transmitted to the dependent tasks in the next stage; if two dependent tasks are executed on the same edge node, then Y k+1，u，m =1, meaning the information transmission time is 0; the third term on the left represents the time required to execute the z-th task in the k-th stage; t kzm Let represent the completion time of task z in stage k of the formed directed acyclic graph at edge node m; Pr(u) represents the set of dependent tasks of task u in the previous stage. This represents the result data generated by the z-th task in the k-th stage of the formed directed acyclic graph; Y represents the data transmission rate from edge node m to edge node m; k+1，u，c This indicates whether the u-th task in the (k+1)-th stage of the formed directed acyclic graph is unloaded to the edge node m for execution; This represents the amount of data for the u-th task in the (k+1)-th stage of the formed directed acyclic graph; t represents the rate at which the u-th task in the (k+1)-th stage of the formed directed acyclic graph is executed on the edge node c; k+1，u，c This represents the completion time of task u in stage k+1 of the formed directed acyclic graph at edge node c; n k+1 This represents the workload in the (k+1)th stage.

[0024] Optionally, by using a relaxation optimization method, x ij Relaxation is handled as a continuous linear variable; the problem is transformed into a convex optimization problem using a continuous convex optimization algorithm, and a feasible solution is obtained; a greedy algorithm is used to combine the characteristics of the obtained solution to obtain the sensor node scheduling decision x. ij ;

[0025] Based on the constraints, the established system objective function is:

[0026] mint K,1

[0027] Where K is the total number of stages in the directed acyclic graph.

[0028] Optionally, the Gale-Shapley algorithm is used to match tasks and edge nodes at each stage to obtain a matching decision. Given the matching decision, the subproblem of time allocation and selection of the set of activated user nodes is considered. Through the column generation method, a feasible solution to the original problem is obtained, and the minimum completion time cost of the dependent tasks is obtained.

[0029] A second aspect of the present invention provides a resource allocation system for minimizing time overhead based on a directed acyclic graph, comprising:

[0030] The constraint establishment module is used to establish energy constraints and information transmission constraints for the data transmission energy and transmission rate of user nodes, respectively.

[0031] The Directed Acyclic Graph (DAG) module is used to build a DAG based on the priority order and latency requirements of tasks.

[0032] The objective function creation module is used to establish the execution time constraints of the task based on the directed acyclic graph, and to establish the system objective function based on all constraints.

[0033] The output module is used to calculate the task unloading decision, and given the unloading decision, calculate the minimum system time cost.

[0034] In a third aspect, the present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the steps of a method for minimizing time-cost resource allocation based on a directed acyclic graph.

[0035] In a fourth aspect, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of a method for minimizing time-cost resource allocation based on a directed acyclic graph.

[0036] Compared with the prior art, the present invention has the following technical effects:

[0037] This invention studies the problem of task offloading and minimizing latency costs in wireless power supply communication networks. It takes into account the dependencies between tasks, the processing rate of edge nodes for different tasks, the transmission rate between edge nodes, and the energy acquisition of user nodes, in order to make optimal task offloading strategies and time allocation decisions.

[0038] This invention addresses the problem of task offloading failure or excessive task completion time caused by the lack of joint optimization of task offloading, energy acquisition, and information transmission in wireless power supply communication networks. It proposes to jointly optimize resource allocation by combining task offloading and time allocation, and proposes an optimization based on the Galshapley algorithm and column generation algorithm. This optimization not only ensures efficient use of resources and orderly task offloading, but also effectively reduces the time cost of task completion. Attached Figure Description

[0039] Figure 1 The overall architecture of the wireless power supply communication network;

[0040] Figure 2 It is a directed acyclic graph built based on task dependencies and priorities;

[0041] Figure 3 The structure diagram of the column generation algorithm is shown. Detailed Implementation

[0042] The specific embodiments of the present invention will now be described in more detail with reference to the accompanying drawings. The advantages and features of the present invention will become clearer from the following description and claims. It should be noted that the drawings are all in a very simplified form and use non-precise proportions, and are only used to facilitate and clarify the illustration of the embodiments of the present invention.

[0043] like Figure 1 As shown, the overall architecture of the wireless power supply communication network in this patent consists of user nodes, power supply nodes (which transmit energy and aggregate user node information), and edge nodes. User nodes first harvest energy through power supply nodes and then use the acquired energy to transmit data back to the power supply nodes. Next, edge nodes are matched with tasks to determine which task each edge node will perform at which stage. Then, using a column generation algorithm, a feasible set of active users for each time slot is determined, and the problem is solved to obtain a feasible solution. Finally, to improve the quality of the solution, through continuous iteration of the main problem and subproblems in the column generation algorithm, an approximate optimal solution to minimizing system time overhead is obtained.

[0044] The resource allocation optimization method for minimizing time overhead implemented in this invention includes the following steps:

[0045] Step 1: Power supply node H(1, 2, ..., h), user node J(1, 2, ..., j), edge node M(1, 2, ..., m), source data contains the data volume of the j-th user node. P j E represents the transmission power of the j-th user node. j This represents the energy provided by the power supply node to the j-th user node during the power supply time, where t represents the length of each time slot during information transmission, and r represents the energy provided by the power supply node to the j-th user node during the power supply time. tj C represents the transmission rate of the j-th sensing node in the i-th time slot; i This represents the set of user nodes active in the i-th time slot; after information is transmitted to the power supply node, the edge nodes begin to obtain data from the power supply node, t kzm Let represent the completion time of task z in stage k of the formed directed acyclic graph at edge node m; Pr(u) represents the set of dependent tasks of task u in the previous stage. This represents the result data generated by the z-th task in the k-th stage of the formed directed acyclic graph, which needs to be transmitted to the dependent tasks in the next stage and used as input for the dependent tasks in the next stage. This represents the amount of data for the z-th task in the k-th stage of the formed directed acyclic graph. This represents the data transmission rate from edge node m to edge node m. This represents the rate at which the z-th task in the k-th stage of the formed directed acyclic graph is executed on the edge node m.

[0046] The second step involves energy constraints in user node communication, where μ is the energy conversion efficiency of the power supply node. The energy constraints are as follows:

[0047]

[0048] The third step, to meet the data transmission requirements of user nodes, is to establish information transmission constraints. In a channel with a bandwidth of W Hz, the data transmission of user nodes should satisfy the following data transmission model:

[0049]

[0050] Where η represents the noise power. The constraints ensure that each user node can transmit all the data it needs to transmit after the information transmission time has ended.

[0051] The fourth step is to construct a directed acyclic graph (DAG) based on task priority and latency requirements, as shown below. Figure 2 As shown. Phase 0 is the phase where user nodes transmit information. Phases 1-K are the phases where tasks are executed and their results are transmitted to the next dependent task. Therefore, there are a total of K+1 phases. For task u to begin, it must collect the processing results of all tasks in the set Pr(u) of its dependent tasks from the previous phase. The processing time for different tasks in the same phase can be different.

[0052] Fifth step: Construct an optimization problem model that minimizes time overhead:

[0053]

[0054]

[0055]

[0056] t kzm ≥0

[0057] Y k+1,u,m ∈{0,1}

[0058] The algorithm is a complex mixed-integer optimization problem, and the constraints contain a large number of continuous variables, making the problem more difficult to solve.

[0059] Step 6: Obtain the matching strategy using the Gael-Shapley algorithm to eliminate the influence of integer variables on the problem. The Gael-Shapley algorithm is a stable matching algorithm. Its core idea is to treat tasks and edge nodes as two sets at each stage and perform a one-to-one matching between the two sets. Since the Gael-Shapley algorithm requires setting the preference of each set element for the other set element, in this patent, the preference is determined based on the transmission latency plus the processing latency. As edge nodes, the transmission time required for each task and the execution time of the task are calculated and arranged in ascending order. The task with the shortest time has the highest preference in the edge node ranking. Similarly, tasks are ranked in the same way. The Gael-Shapley algorithm is shown below.

[0060]

[0061] Step 7: Given a matching decision, the problem is transformed into an optimization problem related only to time variables. However, choosing which combination of active nodes to use for information transmission in each time slot leads to a large scale of time variables to consider. Therefore, a column generation algorithm is used to solve the minimum time cost problem given the matching decision.

[0062]

[0063] In another embodiment of the present invention, a resource allocation system based on a directed acyclic graph with minimized time overhead is provided, which can be used to implement the above-mentioned resource allocation method based on a directed acyclic graph with minimized time overhead. Specifically, the system includes:

[0064] The constraint establishment module is used to establish energy constraints and information transmission constraints for the data transmission energy and transmission rate of user nodes, respectively.

[0065] The Directed Acyclic Graph (DAG) module is used to build a DAG based on the priority order and latency requirements of tasks.

[0066] The objective function creation module is used to establish the execution time constraints of the task based on the directed acyclic graph, and to establish the system objective function based on all constraints.

[0067] The output module is used to calculate the task unloading decision, and given the unloading decision, calculate the minimum system time cost.

[0068] The module division in this embodiment of the invention is illustrative and represents only one logical functional division. In actual implementation, other division methods may be used. Furthermore, the functional modules in the various embodiments of the invention can be integrated into a single processor, exist as separate physical entities, or be integrated into a single module. The integrated modules described above can be implemented in hardware or as software functional modules.

[0069] In another embodiment of the present invention, a computer device is provided, the computer device including a processing

[0070] The processor and memory are used to store computer programs, including program instructions. The processor is used to execute the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, and is suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions in the computer storage medium to realize the corresponding method flow or corresponding function. The processor described in this embodiment of the invention can be used for operation based on a directed acyclic graph-based method for minimizing time overhead resource allocation.

[0071] In another embodiment of the present invention, a storage medium is provided, specifically a computer-readable storage medium (Memory), which is a memory device in a computer device used to store programs and data. It is understood that the computer-readable storage medium here can include both the built-in storage medium in the computer device and extended storage media supported by the computer device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, the storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more computer programs (including program code). It should be noted that the computer-readable storage medium here can be high-speed RAM or non-volatile memory, such as at least one disk storage device. The processor can load and execute one or more instructions stored in the computer-readable storage medium to implement the corresponding steps of the time-cost-minimizing resource allocation method based on a directed acyclic graph in the above embodiments.

[0072] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0073] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0074] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0075] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0076] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for minimizing time overhead resource allocation based on a directed acyclic graph, characterized in that, Comprise: Data transmission energy and transmission rate of user nodes are used to establish energy constraints and information transmission constraints respectively; According to the priority order and the time delay requirement of the task, a directed acyclic graph is established; Based on the directed acyclic graph, the execution time constraint of the task is established, and the system objective function is established based on all constraint conditions; The task offloading decision is calculated, and the minimum time cost of the system is calculated given the offloading decision; The energy constraint is constructed, specifically: The energy constraint is shown as follows for the energy conversion efficiency of the energy supply node: where the left item of the inequality represents the user node the right item represents the user node the effective energy obtained; the transmission power of the th user node, the energy provided by the energy supply node for the th user node in the energy supply time, the length of each time slot in the information transmission process, the set of user nodes activated in the th time slot; The information transmission constraint is established, specifically: In a channel with a bandwidth of W hertz, the user node should meet the following data transmission model when transmitting information: in This represents the noise power, and the source data contains the first... Data volume per user node , For user nodes and corresponding information access points Channel gain between This indicates bandwidth, measured in Hertz (Hz). This indicates the sensor nodes in the information transmission task phase. It is necessary to contact the corresponding information access point. The amount of data transmitted; In the directed acyclic graph: The task of the 0th stage is the stage of transmitting information of the user node; the 1st-Kth stage is the stage of executing the task and transmitting the task result to the next dependent task; there are K+1 stages in total; u All the dependent tasks from the previous stage must be completed before the task can start The processing results of all the tasks; tasks with the same or intersecting placement are placed in the same stage, tasks with high time delay priority are placed in the earlier stage, and one edge node is independently occupied by one task in the same stage; Based on the directed acyclic graph, the execution time constraint of the task is established as follows: Among them, the first term on the left side of the constraint is the first term. Phase 1 The time when the task was completed; the second item on the left indicates the completion time. Phase 1 The time required to transmit the output of a task to the next stage of dependent tasks; if two dependent tasks are executed on the same edge node, then That is, the information transmission time is 0; the third item on the left indicates the first... Phase 1 The time required to execute the task; In the directed acyclic graph formed, the first... Phase 1 Task at edge node Completion time; Indicates task The set of dependent tasks from the previous stage; In the directed acyclic graph formed, the first... Phase 1 The results data generated by the task; This indicates that the data originates from the edge node. The data transmission rate to edge node c; In the directed acyclic graph formed, the first... Phase 1 Should the task be unloaded to the edge node? Execute above; In the directed acyclic graph formed, the first... Phase 1 The amount of data in the task; In the directed acyclic graph formed, the first... Phase 1 Task at edge node The execution rate; In the directed acyclic graph formed, the first... Phase 1 Task at edge node Completion time; Indicates the first Task volume for each stage; By using relaxation optimization methods, Relaxation is performed using continuous linear variables; the problem is transformed into a convex optimization problem using a continuous convex optimization algorithm, and a feasible solution is obtained; a greedy algorithm is then used to combine the characteristics of the obtained solution to obtain the sensor node scheduling decision. ; Based on the constraint conditions, the system objective function established is: Where K is the total number of stages of the directed acyclic graph; Through the Gale-Shapley algorithm, the matching decision is obtained by matching the task and the edge node of each stage, and the minimum completion time cost of the dependent task is obtained by considering the time allocation and the selection of the activated user node set through the column generation method.

2. A minimum time overhead resource allocation system based on a directed acyclic graph, characterized in that, Comprise: The constraint establishment module is used to establish energy constraints and information transmission constraints for data transmission energy and transmission rate of user nodes respectively; The directed acyclic graph establishment module is used to establish a directed acyclic graph according to the priority order and the time delay requirement of the task; The objective function establishment module is used to establish the execution time constraint of the task based on the directed acyclic graph, and to establish the system objective function based on all constraint conditions; The output module is used to calculate the task offloading decision, and to calculate the minimum time cost of the system given the offloading decision; The energy constraint is constructed, specifically: The energy constraint is shown as follows for the energy conversion efficiency of the energy supply node: where the left item of the inequality represents the user node the right item represents the user node the effective energy obtained; the transmission power of the th user node, the energy provided by the energy supply node for the th user node in the energy supply time, the length of each time slot in the information transmission process, the set of user nodes activated in the th time slot; The information transmission constraint is established, specifically: In a channel with a bandwidth of W hertz, the user node should meet the following data transmission model when transmitting information: in This represents the noise power, and the source data contains the first... Data volume per user node , For user nodes and corresponding information access points Channel gain between This indicates bandwidth, measured in Hertz (Hz). This indicates the sensor nodes in the information transmission task phase. It is necessary to contact the corresponding information access point. The amount of data transmitted; In the directed acyclic graph: The task of the 0th stage is the stage of transmitting information of the user node; the 1st-Kth stage is the stage of executing the task and transmitting the task result to the next dependent task; there are K+1 stages in total; u All the dependent tasks from the previous stage must be completed before the task can start The processing results of all the tasks; tasks with the same or intersecting placement are placed in the same stage, tasks with high time delay priority are placed in the earlier stage, and one edge node is independently occupied by one task in the same stage; Based on the directed acyclic graph, the execution time constraint of the task is established as follows: Among them, the first term on the left side of the constraint is the first term. Phase 1 The time when the task was completed; the second item on the left indicates the completion time. Phase 1 The time required to transmit the output of a task to the next stage of dependent tasks; if two dependent tasks are executed on the same edge node, then That is, the information transmission time is 0; the third item on the left indicates the first... Phase 1 The time required to execute the task; In the directed acyclic graph formed, the first... Phase 1 Task at edge node Completion time; Indicates task The set of dependent tasks from the previous stage; In the directed acyclic graph formed, the first... Phase 1 The results data generated by the task; This indicates that the data originates from the edge node. The data transmission rate to edge node c; In the directed acyclic graph formed, the first... Phase 1 Should the task be unloaded to the edge node? Execute above; In the directed acyclic graph formed, the first... Phase 1 The amount of data in the task; In the directed acyclic graph formed, the first... Phase 1 Task at edge node The execution rate; In the directed acyclic graph formed, the first... Phase 1 Task at edge node Completion time; Indicates the first Task volume for each stage; By using relaxation optimization methods, Relaxation is performed using continuous linear variables; the problem is transformed into a convex optimization problem using a continuous convex optimization algorithm, and a feasible solution is obtained; a greedy algorithm is then used to combine the characteristics of the obtained solution to obtain the sensor node scheduling decision. ; Based on the constraint conditions, the system objective function established is: Where K is the total number of stages of the directed acyclic graph; Through the Gale-Shapley algorithm, the matching decision is obtained by matching the task and the edge node of each stage, and the minimum completion time cost of the dependent task is obtained by considering the time allocation and the selection of the activated user node set through the column generation method.

3. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, The processor executes the computer program to realize the steps of the minimum time cost resource allocation method based on the directed acyclic graph of claim 1.

4. A computer-readable storage medium storing a computer program, the computer program comprising instructions that, when executed by a computer, cause the computer to perform the method of any one of claims 1 to 3. The computer program is executed by the processor to realize the steps of the minimum time cost resource allocation method based on the directed acyclic graph of claim 1.

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