1 Introduction

1.1 Background

The term mobile crowd sensing (MCS) has been coined by Ganti et al. [1] in 2011, which introduced a new data collection method by leveraging mobile terminals such as smart phones. Compared with traditional data collection technologies, MSC has some unique characteristics. First, the mobile devices have more computing, communication, and storage capability than mote-class sensors. Second, by leveraging the mobility of the mobile terminal users, the deployment cost of specialized sensing infrastructure for large-scale data collection applications would be largely reduced. Currently, MSC has been widely used in many applications, including environmental monitoring [2], transportation [3], social behavior analysis [4], healthcare [5], and others [6,7,8,9], which demonstrates that MCS is a useful solution for large-scale data collection applications. In general, the MCS process always consists of four steps: assigning sensing tasks to mobile terminals, executing the task on the mobile terminals, collecting, and processing sensed results from the crowd [10,11,12,13,14]. Obviously, assigning sensing tasks to mobile terminals is the primary issue to deal with the following steps, which is also the main issue in this paper.

1.2 Related work

Recently, a lot of efforts have been focused on task allocation [15,16,17] and generally can be divided into two categories: rule-based task allocation method [18,19,20] and map-based task allocation method [21,22,23,24]. The rule-based task allocation mainly allocates task according to each node’s sensing capability, such as position and power of perception. By dividing node characteristics into different task groups, the system assigns the corresponding task to each task group. In Ref [18], a task assignment algorithm dual task assigner (DTA) has been designed. The DTA has leveraged learn weights to evaluate the sensing capability of participations for each task, and the server allocates tasks according to the sensing capability level to maximize the benefit. Angelopoulos et al. [19] have selected appropriate users by selecting the optimal characteristics of nodes (quotation and quality) to allocate tasks, achieving the equalization between cost and task completion ratio. Shibo et al. [20] have considered the number of mobile nodes, the number of tasks and the task completion time, and proposed the optimal scheduling algorithm for each user in the dispatching area to reduce the sensing cost. Secondly, map-based task allocation method has been used to combine the geographical locations to task types to build a task map, and participations can obtain the content and location of a task by downloading the task map. When participations arrive in a specific task location, they can form a task group by self-organizing, and coordinate with each other to accomplish the sensing task. Dang et al. [21] have proposed the map-based mobile sensing task allocation framework named Zoom for the first time. Based on Zoom, Huy et al. [22] have studied the assignment of pixel values in the task map, and proposed a scalable reuse method for task map pixel values. In Ref [23], a raster-vector mixed task distribution method for mobile crowd sensing system has been proposed, which raster the sensing area first, and encodes the task information to improve the information utilization and reduce the data redundancy. A vector task map has also been proposed in Ref [24], which can substantially reduce the amount of data in the task map by gradually distributing the sensing tasks.

In summary, the above methods for task allocation always believe that the mobile terminals can handle all types of required data. They seldom take into consideration the fact that a sensing node needs to carry out a data sensing task that beyond to its sensing capability. For example, to construct a radio environment map to monitor the wireless resource, the application requires more than twenty types of data: data collection time, GPS information, and the device identification, and some 2G/3G/4G/Wi-Fi network data. Usually, few nodes can collect all types of the data because of their limited sensing capability, and most of the nodes can perform a fraction of types of the sensing data. The problem is that the sensing node with lower sensing capability compared with high-dimensional data is difficult, and we defined it as high-dimension data sensing problem. In this situation, the first efficient step is to divide the high-dimension data sensing task into multiple lower dimensional tasks. The second step is to assign different sub-tasks to nodes with different sensing capability, and the optimal goal is to minimize the total cost, as well as improving the task completion ratio.

1.3 Methods and contributions

This paper proposes an efficient data collection mechanism based on two-stage task allocation named low-cost and balance-participating algorithm (LCBPA), and the contributions are as follows:

  • We design a two-stage task allocation algorithm LCBPA for high-dimensional data collection in MCS network. In the first stage, in order to divide a high m-dimension data collection task into k-multiple sub-tasks with lower dimensional data, we leverage the K-means method to make partition based on the similarity of sub-tasks. In the second stage, we allocate multiple nodes with different sensing capability with one or more sub-tasks based on certain optimal conditions.

  • To minimize the total sensing cost and avoid some nodes to be allocated with too many sub-tasks while some nodes have only few sub-tasks, we introduce the equality parameter λi to adjust the node participation probability to prevent the inequality problem stated above. We also make our node selection policy by trading-off between minimizing the total cost and maximizing the equality λi through the weight parameter α.

  • We also analyze the influence of the variation of sub-task number k and trade-off weight parameter α to the task completion ratio, total sensing cost, and node sub-task degree distribution in different scale of networks. Simulation results show that, compared with non-task-division methods, our LCBPA can reduce the total cost, and it can also make a more even sub-task degree distribution among sensing nodes.

The rest of this paper is organized as follows: System model and task allocation problem are discussed in Section 2. The detailed design of our proposed LCBPA algorithms is discussed in Section 3. The performance of our algorithm is evaluated in Section 4. Section 5 illustrates the conclusions and our future work.

2 Problem description and challenges

2.1 Problem description

As shown in Fig. 1, there is a sensing task which refers to m-dimension data collection, and there are N sensing nodes in a minimum sensing unit. It would be difficult for a node with limited sensing capability to finish m-dimension data collection in a particular place, for the node can only handle partial types of data sensing. In order to deal with the high-dimensional data collection, it needs to divide the high-dimensional data collection task into k sub-task with lower data dimension to reduce the load of a sensing node. For each sub-task, it corresponds to a sensing group with number C sensing nodes. The problem of task allocation is transformed into dividing the m-dimension data sensing task into k sub-tasks, and then for each sub-task, choosing enough sensing nodes to form a sensing group to finish the data collection.

Fig. 1
figure 1

Groups cooperatively complete the dimensions data sensing

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For simplicity, we make assumptions as follows: first, the data types contained in each sub-task will not overlap and the sum of all sub-tasks’ dimension is m; second, each sub-task requires the same minimum number of sensing nodes as C; third, in each group, the node number C can cover the whole sensing unit, and we will not consider the location of a node. As is shown in Fig. 1, we assume that all the sensing nodes in each group will cover the minimum sensing area.

2.2 Challenges in task allocation

We propose a task partition model to solve the problem of the high-dimensional data when we collecting data from a single node. Through this method, the data dimension is reduced, and multiple sensing nodes that work together can accomplish high-dimensional data collection tasks. Challenges for this high-dimensional data collection are as follows:

  1. (1)

    How to improve the task completion ratio. In conventional methods, one node has to sense all types of required data, and this may beyond its sensing capability, which will reduce the task completion ratio. In the MCS, by dividing a high-dimensional data into lower dimensions, a node only needs to collect partial types in all of the data types.

  2. (2)

    How to minimize the total sensing cost as much as possible. For a large-scale complex sensing task, it requires a significant number of nodes to collect data, and the cost of data collection is enormous for large-scale tasks. It needs to select nodes for a suitable sub-task to minimize the cost of data collection under the premise of guaranteeing the task completion.

  3. (3)

    How to equalize the participation probability of each node, that is to say, avoiding that some nodes join in a significant number of sub-tasks while others only join in very few sub-tasks. The current task allocation methods are always aiming to select the node that can minimize the total cost, which may result in the fact that some nodes may be overloaded to deal with a great number of sub-tasks, while some nodes only perform small number of sub-tasks. It is difficult to minimize the whole cost of the system while making sub-tasks distributed among participants evenly.

3 The proposed algorithm of LCBPA

3.1 Model definition

Assuming that a system requires mobile nodes (mobile terminals) to finish an m-dimension data collection task, and for simplicity, one dimension corresponds to one data type. The required data type set is A, which is a matrix with m rows and N columns. Let A = {G1, G2, ⋯, Gm} A = {G1, G2, …, Gm}, and each Gi denotes a data type in the m-dimension data task collection. For each vector Gi, the element gij represents that the data type Gi can be collected by node j, and j is the node number, (j ∈ (1, N)). If gij = 1, it means that the ith dimensional data can be collected by the node j, else gij = 0.

$$ A=\left[\begin{array}{ccccc}{g}_{11}& & \cdots & & {g}_{1N}\\ {}& \ddots & & & \\ {}\vdots & & {g}_{ji}& & \vdots \\ {}& & & \ddots & \\ {}{g}_{m1}& & \cdots & & {g}_{mN}\end{array}\right] $$
(1)

The divided sub-task set is S, and S = {s1, s2, …, sk},where k is the number of sub-task. For ∀si, (  1 ≤ i ≤ k  ), we assume that the data types contained in each sub-task are not overlapped and the sum of all sub-tasks’ dimension is m.

Each node corresponds to a triple ψi = {i, Ti, Vi}, where i is the node number, and i ∈ (1, N). Ti is the task which can be sensed by user i, which is a k-dimension vector. For each element tij in Ti, if tij = 0, it means that the node i does not have the capability to sense the data type required in the sub-task sj, while, if tij = 1, it means that node i can perform the sub-task sj. Vi is the cost of the sensing task, which is also a k dimensional vector. For each element vij, the value is the cost of node i for sensing sub-task sj.

The total cost for a mobile crowd sensing system to finish the data collection task is

$$ W=\sum \limits_{i=1}^N\sum \limits_{j=1}^k{t}_{ij}{v}_{ij} $$
(2)

The goal of our system is to find a matrix T∗, which will minimize W, that is

$$ {T}^{\ast }=\left[\begin{array}{ccccc}{t}_{11}^{\ast }& & \cdots & & {t}_{1k}^{\ast}\\ {}& \ddots & & & \\ {}\vdots & & {t}_{ij}^{\ast }& & \vdots \\ {}& & & \ddots & \\ {}{t}_{N1}^{\ast }& & \cdots & & {t}_{Nk}^{\ast}\end{array}\right] $$
(3)
$$ \min W=\sum \limits_{i=1}^k\sum \limits_{j=1}^N{t}_{ij}^{\ast }{v}_{ij} $$
(4)

The trade-off between minimizing the total cost and λi is performed as follows:

$$ {p}_{ij}={t}_{ij}\cdot \Big\{{\displaystyle \begin{array}{l}\frac{w_j-{v}_{ij}}{w_j\cdot \left({r}_j-1\right)}+\alpha \cdot \frac{1}{r_j},\kern1.6em \mathrm{if}\;j=1.\\ {}\frac{w_J-{v}_{ij}}{w_j\cdot \left({r}_j-1\right)}+\alpha \cdot \frac{1}{r_j}\cdot {\lambda}_i,\kern0.9000001em \mathrm{if}\kern0.4em j\ge 2.\;\end{array}} $$
(5)

Here, α denotes weight factor (0 ≤ α ≤ 1), which can be used to make the trade-off between cost constraints and node participation on the probability of node selection [25]. Let wj denote the total quoted price that all the nodes can sense Gj, then \( {w}_j={\sum}_{i=1}^N{v}_{ij} \). Let rj denote the number of nodes that can perform sub-task, and \( {r}_j={\sum}_{i=1}^N{t}_{ij} \).

As stated above, in order to avoid some nodes joining in too many sub-tasks while others only join in few sub-tasks, we introduce the adjustment coefficient λi [26]. When a node has already been selected in the previous sub-task allocation rounds, this parameter may reduce the probability that a node being selected. When we select a node to participate in a sub-task, the system will make a trade-off between the total cost and the adjustment coefficient λi. We compute λi by Eq. (6):

$$ {\lambda}_i=\Big\{{\displaystyle \begin{array}{l}1,\kern4.839998em \mathrm{if}\;j=1.\\ {}\prod \limits_{h=1}^{j-1}\left(1-\frac{\sum_{h=1}^{j-1}{t}_{ih}\cdot {r}_h}{\sum_{i=1}^N{\sum}_{j=1}^N{t}_{ij}}\right),\kern0.56em \mathrm{if}\;j\ge 2.\end{array}} $$
(6)

where tih represents whether the node i was assigned with the sub-task sh, and tih = 1 means that the node i is assigned to sub-task h, else tih = 0. rh denotes the node number that can perform the sub-task sh, which can be computed by Eq. (7):

$$ {r}_h={\sum}_{i=1}^N{t}_{ih} $$
(7)

3.2 The two-stage task allocation algorithm of LCBPA

The detail steps for the system to select sensing nodes are divided into two stages:

Stage one: Dividing an m-dimensional data collection task into k sub-tasks by K-means method. According to the sensing capability attributes (the data type a node can sense) of each node, we need to divided the whole sensing task into k sub-tasks. Here, we choose the K-means algorithm, which is a classical algorithm to solve the clustering problem, and it is simple and fast. When processing large data sets, the k-means algorithm maintains scalability and efficiency. The general processes are as follows: First, chose k data types from data type set A as the initial clusters center randomly. Second, for the remaining data types in A, assign them to the nearest k initial clusters according to the distance D. When calculating the cluster center of each new cluster, keep repeating the process until the standard measure function D is converged.

The standard measure function D for converging clusters is

$$ D=\min \sum \limits_{i=1}^k\sum \limits_{X\in {s}_i} dist\left({G}_i,{G}_j\right) $$
(8)

where the distance D is computed by the Euclidean distance dij from Gi and Gj. The shorter the distance between them, the higher similarity between those two data types, and the higher probability those two data types will be divided into the same sub-task.

$$ dist\left({G}_i,{G}_j\right)=\sqrt{\sum_{i=1}^N{\left({G}_i-{G}_j\right)}^2} $$
(9)

The correspondent algorithm for the first stage is as follows:

figure a

However, dividing the whole sensing task into k sub-tasks is only a basic step in our proposal, we need further to adjust the mapping between participating nodes and sub-tasks by other considerations, such as minimizing the total cost and avoiding a node being assigned too many sub-tasks in the following step.

Stage two: Assigning different nodes with different sensing capability to a suitable sub-task by the trade-off between minimizing the total cost and node participation equality. After the first data type clustering stage, the system will allocate node to each sub-task. For each sub-task sj ∈ S, it will judge whether a node can perform the sub-task and calculate the adjustment factor λi according to formula 6. It will also calculate the probability pij to decide whether a node can be selected in a sub-task by Eq. 5. The system will sort the probabilities pij of all the nodes from high to low, and select the top-C nodes for sub-task sj. The correspondent algorithm for the second stage is stated in algorithm 2:

figure b

4 Results and discussion

4.1 Simulation setting

In this section, we will evaluate the performance of our proposed LCBPA scheme by simulation. Our simulation environment is Ubuntu 14.04. We compare the performance of our LCBPA with non-task-division (NTD) method, which is the method that nodes participate high-dimension data collection directly. The simulation parameters are set as follows: the sensing area is 600 × 600 m2, and the sensing radius of each node is 25 m. The network size (sensing node number) varies from 50 to 500, the data dimension is 50, and the sub-task number ranges from 10 to 50, and the trade-off weight parameter α varies from 0.1 to 0.9, the minimum node number required in a minimum sensing unit is 50.

We analyze the performance of the LCBPA algorithm in the following parameters: (1) Task completion ratio η; (2) The total cost of data collection W; (3) The equality of node participation ui. The parameters η and ui are defined as follows:

  1. (1)

    The task completion ratio η is defined as the number of the whole m-dimension tasks that can be completed, that is

$$ \eta =\frac{B}{C} $$
(10)

where

$$ B=\Big\{{\displaystyle \begin{array}{l}\underset{1\le j\le k}{\min}\sum \limits_{i=1}^N{t}_{ij},\kern1em \mathrm{if}\underset{1\le j\le k}{\min}\sum \limits_{i=1}^n{t}_{ij}<C;\\ {}C,\kern4.699998em \mathrm{if}\underset{1\le j\le k}{\min}\sum \limits_{i=1}^N{t}_{ij}\ge C;\kern2.999999em \end{array}}\kern1.6em $$
(11)
  1. (2)

    μi denotes the participation equality of node i, which is the percentage of the total number of sub-tasks assigned to each node:

$$ {\mu}_i=\frac{1}{k}\cdot {\sum}_{j=1}^k{t}_{ij} $$
(12)

4.2 Simulation results

4.2.1 Comparison of task completion ratio

Figure 2 shows the comparison of the task completion ratio of our LCBPA with NTD method under different network scale. In this scenario, the number of sub-task is 20, and α = 0.5. The simulation shows our LCBPA has a higher task completion ratio, and the ratio increases as the network node number increases, which is because the node number for participating each sub-task is increased.

Fig. 2
figure 2

Task completion ratio comparison of LCBPA and NTD under different network scale when k = 20, α = 0.5

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Figure 3 shows the comparison of the task completion ratio of our LCBPA with various sub-task number k varies from 10 to 50 under different network scale. The result in Fig. 3 shows that the task completion rate is increasing as a high-dimensional task is divided into more sub-tasks. Under the same network scale condition, the task completion ratio is increased when k is increased, which may be because the more detailed the division of the high-dimension task, the higher probability a node is assigned to the right sub-task, improving task completion ratio.

Fig. 3
figure 3

Task completion ratio comparison of LCBPA with different sub-task number k, when α = 0.5 under different network scale

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Figure 4 shows the comparison of the task completion ratio of our LCBPA with the weight parameter α varying from 0.1 to 0.9 under a different network scale. The result in Fig. 4 shows that the five lines are overlapped, which means that the task completion rate remains unchanged with different value of α. It may because that the total number of nodes that need to perform a sub-task is more than C, which makes no difference on the task completion ratio.

Fig. 4
figure 4

Task completion ratio comparison of LCBPA with different α varying from 0.1 to 0.9 when k = 20 under different network scale

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4.2.2 Comparison of the total cost

Figure 5 shows the comparison of the total cost of data sensing in our LCBPA with NTD method under different network scale. In this scenario, the number of sub-task is 20, and α = 0.5. The simulation result shows that our LCBPA has a lower total cost, and the total cost increases as the network scale is extended, which may be because the participating node number for each sub-task is increased.

Fig. 5
figure 5

Total cost comparison of LCBPA and NTD when k = 20, α = 0.5 under different network scale

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Figure 6 shows the comparison of the total cost of our LCBPA with different sub-task number k varying from 10 to 50 under different network scale. The result in Fig. 6 shows that as the size of the network increases, the total cost also increases. Under the same network scale, the larger the number of the sub-task k, the lower the total cost of the system, which may be because more sub-task k makes different nodes being assigned to more different suitable sub-tasks, saving some unnecessary cost.

Fig. 6
figure 6

Total cost comparison of LCBPA with different sub-task number k, when α = 0.5under different network scale

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Figure 7 demonstrations the comparison of the total cost of our LCBPA at different network with trade-off weight parameter α varying from 0.1 to 0.9 and at k = 20. The result in Fig. 7 shows that the total cost is increased as the network scale is higher. Under the same network scale, the larger the number of the sub-task, the higher the total cost of the system because a large α value may take less consideration of minimizing the total cost, improving the total cost.

Fig. 7
figure 7

Total cost of LCBPA with different trade-off parameter α when k = 20 under different network scale

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4.2.3 Comparison of the node participation equality under a different network scale

Figure 8 shows the comparison of the node participation equality of our LCBPA with NTD method under the same network scale. In this scenario, the sub-task number is 20, and α = 0.5. The simulation shows that in our LCBPA, a larger proportion of nodes are allocated with a smaller proportion of sub-tasks, and the proportion of nodes to perform more sub-tasks are significantly reduced.

Fig. 8
figure 8

Comparison of node participation equality of LCBPA and NTD when k = 20, the nodes number α = 0.5, N = 300

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Figure 9 shows the comparison of the node participation equality of LCBPA with the sub-task number k varying from 10 to 50 under same network scale. The result in Fig. 9 shows that the node participation becomes more concentrated when a high-dimensional task is divided into more sub-tasks. It means that the proportion of nodes performing too many tasks will be reduced, and most of the nodes are assigned to an average amount of sub-tasks.

Fig. 9
figure 9

Comparison of node participation equality of LCBPA with different sub-task number k when α = 0.5, N =300

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Figure 10 shows the comparison of the node participation equality of our LCBPA with different trade-off weight parameter α which varies from 0.1 to 0.9. Figure 10 shows that the participation of nodes become more concentrated as α increased, which means that the proportion of nodes performing too many tasks will be reduced as α is increased, and most of the nodes are assigned to an average amount of sub-tasks.

Fig. 10
figure 10

Comparison of node participation equality of LCBPA with different trade-off parameter α when k = 20, N = 500

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5 Conclusion

This paper proposes a high-dimension data collection algorithm LCBPA for mobile crowd sensing network. In particular, we introduce the two-stage operation scheme to deal with the problem that a node with lower sensing capability confronted with the higher dimensional collection data. To evaluate our proposed scheme, we formulate the evaluation parameters, and we also calculate the task completion ratio, the total cost of the data, and the node participation equality. As a result, our scheme can effectively work when the network scale varies from 50 to 500, and the sub-task number k varies from 10 to 50, with trade-off weight parameter α varying from 0.1 to 0.9. However, there are also some limitations of our proposed schemes: (1) we only simulated our proposed method by simulations, not in the real sensing activities; (2) Our method can reduce the sensing cost and difficulty, while it is only works based on the assumption that each dimension of the data can be collected independently, which means that there is no correlation between different dimensions of the data, which may be not always the case. (3) When assigning each sensing task to different nodes, we do not consider the location and mobility of a node. (4) In practical, the value of the data will be elapsed as the time passed, which is also not considered in our proposed method. In the future work, we will evaluate hardware-based experiments, and take the node mobility and location into consideration, and we will also consider the data value as one of the factors in task allocation.