The Improved Algorithm Based on DFS and BFS for Indoor Trajectory Reconstruction

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1 The Improved Algorithm Based on DFS and BFS for Indoor Trajectory Reconstruction Min Li 1, Jingjing Fu 1,2, Yanfang Zhang 1(&), Zhujun Zhang 1, and Siye Wang 1,3 1 Institute of Information Engineering, CAS, Beijing, China {limin,fujingjing,zhangyanfang, zhangzhujun,wangsiye}@iie.ac.cn 2 University of Chinese Academy of Sciences, Beijing, China 3 Beijing Jiaotong University, Beijing, China Abstract. The trajectory of moving objects in large spaces is important, as it enables a range of applications related to security, guidance and so on. Trajectory reconstruction is the process which uses searching algorithms to find a reasonable trajectory. Due to the complexity of indoor environment and the larger area which multi-floor causes, it exits the problem of low searching efficient. To solve the problem, this paper proposes the improved algorithm which combines the Branch and Bound method based on Depth-First-Search (DFS) and Breadth-First-Search(BFS). It helps construct the trajectory quickly on topological map. Experimental results validate the improved algorithm is effective by comparing other algorithms. 1 Introduction With the development of indoor position technology, people often use trajectory data to find the behavior information of target. Moreover, combining the trajectory data and geography information can help people know the habits of moving targets [1]. The real trajectory is the basement of getting effective message. There are many ways to reconstruct the trajectory of targets. Using RFID technology to reconstruct [2], it can speculate the room of target at a certain time by history trajectory data. But the trajectory may cross the indoor barrier by connecting the rooms where the target passed. But the trajectory is not reasonable. Using grid map and A* algorithm can get the reasonable trajectory [3]. However, its more storage information [4] make it not be applied for many floors of architecture. The searching efficient is low because of much grids and complex algorithm. Using odometry data from smartphone sensors to find the real trajectory [6], it can identify the trajectory of human. It uses the topological map to construct the indoor environment and DFS algorithm to reconstruct the trajectory. The topological map stores less information than grid map. DFS is simple searching algorithm. But when applying for larger area, it may search many useless nodes and its efficiency is low. To solve the problem of low efficiency of trajectory reconstruction, this paper proposes the improved algorithm based on topological map [7]. The improved algorithm can apply to larger area or many floors of architecture. The paper improves the Springer International Publishing Switzerland 2016 Q. Yang et al. (Eds.): WASA 2016, LNCS 9798, pp , DOI: / _41

2 The Improved Algorithm Based on DFS and BFS 465 algorithm based on DFS and BFS [9]. DFS and BFS are normal searching algorithm. They are easy to accomplish and don t need a lot of auxiliary conditions. In addition to DFS, BFS, A* algorithm, A*algorithm [5] is complex and needs function to calculate the value. Dijkstra [8] algorithm is also normal algorithm, but Dijkstra algorithm is used for the problem of shortest path. The paper supposes that there are many monitoring points which are entrances, conference offices and where you want to monitor. When the target passes the monitoring point, we can get the position information of target at the moment. The position information is same with the monitoring point. These information informs the trajectory of the target. We discuss the topological map corresponding to indoor environment has no loop. This paper first introduces the system model of trajectory reconstruction. Secondly, this paper describes the overview of DFS, BFS and the improved algorithm. The pseudo code of algorithms is given. Thirdly the experiment study is presented. This part display the comparison of DFS, BFS and improved algorithm. The final part is conclusion which introduce the future work. 2 System Model Trajectory reconstruction contains three aspects. The first part is constructing the topological map of indoor environment. Topological map provides the feasible paths and monitor points corresponding to the real indoor environment. The second part designs the attributes of storage information. It is convenient for querying trajectory information we needed. The third part is using the searching algorithm to get trajectory. The Topological Map of Indoor Environment. The topological map is the basement of trajectory reconstruction, which combines the normal path and monitoring points. The normal path is area which the monitoring target can move. Monitoring points are Fig. 1. An example of indoor environment and topological map.

3 466 M. Li et al. corresponding to some sensitive area. When the target passes these places, they are detected and their information is recorded. Figure 1 presents the example of indoor environment [10] and it s topological map [11, 12]. It is one floor. M1, M2, M3, M4 are monitoring points. Other nodes are auxiliary nodes for trajectory reconstruction. When the building contains many floors, the topological map can be constructed. In reality, floors are connected by elevators or stairs. We can set these connections as the boundary nodes of topological map. Connect the boundary nodes of adjacent floors. Then, we can construct only one topological map of many floors. Figure 2 presents the connection of topological maps of adjacent floor. Fig. 2. The topological of Multi-floor The topology Graph G is defined by (V, E, M, NM), where: V is the set of nodes. E is the set of undirected edges:e ¼f\v i v j [ jv i v j 2 V ^ v i 6¼ v j, there is no weigh of edge, because the trajectory is not related to the length of edge. M is the set of monitor points: M V; M 6¼ fg. NM is the set of auxiliary nodes: NMV; NM ¼ V M. The information structure of the node is stored in Table 1. Table 1. The property of the node NodeID The id of node. X The horizontal ordinate of node Y The vertical ordinate of node AdjacentNodeNum The number of adjacent nodes of current node AdjacentNode The NodeID of adjacent nodes Mark If the node v i 2 M, Mark = 1. If the node v i 2 MN, Mark = 0.

4 The Improved Algorithm Based on DFS and BFS 467 Trajectory Data. Trajectory data is the input of trajectory reconstruction. When the moving target is detected, the information of target is recorded. The information contains the location of the target. The example of monitor data in Table 2 is presented following. There are six records. The information of record is < Target, Location, T >. Target is the object which is detected. Location is the position which the target is detected. T is the time is when the detection occurred. Table 2. The record of trajectory Record Target Location T 1 T1 M1 t 1 2 T2 M1 t 2 3 T1 M3 t 18 4 T1 M4 t 19 5 T2 M2 t 24 6 T3 M4 t 25 Trajectory Reconstruction. Reconstruct the trajectory using monitoring data and topological map. Take locations of the target corresponding to the nodes of topological map. Then, use the path searching algorithm to find a reasonable trajectory. For example, the target T1 passes M1, M3, M4 by order. The trajectory displays in Fig. 3. Fig. 3. The trajectory of T1

5 468 M. Li et al. 3 The Improved Algorithm Based on DFS and BFS As described in Sect. 2, we use the topological map for model indoor environment. The last step is finding the reasonable trajectory by searching algorithms. In this section, we describe the achievement of trajectory reconstruction by DFS and BFS. Then a detail method of improved algorithm is given. 3.1 DFS and BFS DFS is the classical searching algorithm. The core idea of Depth-First-Search is: Visit one node which has never been visited. Set the value of mark which is corresponding to searching node to 1. Search for adjacent nodes which have never been visited of current. If it exits, then visit the node by above steps until finding the target node. Algorithm 1 is DFS algorithm to achieve the searching over Topological map. BFS is the classical searching algorithm. The core idea of Breadth-First-Search (BFS): Visit node has never been visited. Set the value of Visited[] which is corresponding to searching node to 1. Visit all adjacent nodes have never been visited in order. From these adjacent nodes, visit their adjacent nodes have been not visited in turn. Make sure that first visited adjacent node has been visited before visited adjacent node later until searching the target node. Algorithm 2 is BFS algorithm to achieve the path searching over Topological map.

6 The Improved Algorithm Based on DFS and BFS The Indoor Trajectory Reconstruction Algorithm Based on DFS and BFS Indoor Trajectory Reconstruction based on DFS and BFS (ITRBDB) combines DFS and BFS for searching. In the process of searching, it also uses the Branch and Bound method for deleting the impossible paths. Comparing DFS and BFS, ITRBDB can narrow the scope of searching scope and improves efficiency using above method. ITRBDB is based on DFS because of the structure of topological map. One feature of indoor topological structure is longitudinal extension, such as museums, banks, national important apartment. Topological map is longitudinal extension and each node has no much branches. ITRBDB uses BFS for judging whether the target node is one of adjacent nodes. It doesn t cost a lot of time. Because the adjacent nodes of the current is not too much. The time complexity of ITRBDB remains constant even though in the condition of many branches.

7 470 M. Li et al. Firstly, we can delete the adjacent node whose degree is 1. In the process of searching, it can determine whether adjacent nodes of current node is target node. If it is, then end searching. If the degree of adjacent node is 1 and it is not the target node, then give up the search of adjacent node. Secondly, we can delete the adjacent node which is monitoring point but not the target node. The reason is following: All monitoring points which item passed are saved in p[]. The algorithm searches by segment. Assuming the adjacent node which is the monitoring point is a node of path from p[i] to p[i + 1], then the adjacent node is p [i + 1], If not, the adjacent node is not in the path. In this case, we should give up the path which contain this adjacent node in this segment. The coal idea of ITRBDB is following: visit the adjacent nodes of current node and judge whether the target node is. If it is, then end searching. Otherwise, if there are location nodes or nodes which their degree is 1, then mark these nodes and give up searching the branch. Select the node which is not marked for searching. If all adjacent nodes have been marked, then return the above node of current. The detail achievement is Algorithm 3.

8 The Improved Algorithm Based on DFS and BFS Experimental Result This paper only discusses the topological map which has no loop. We generate the undirected graph to simulate topological map of indoor environment. The time complexity of three algorithms is Oðn 2 Þ. To compare the searching efficiency of three algorithms, there are two parameters to vary in experiment. One is the number of important monitoring points, the other is the number of nodes of topological map. We calculate the average of searching nodes of algorithms in the same condition. Ave = P numberofsearchingnodesbetweenadjacentmonitoringpoints P adjacentmonitoringpoints Indoor environment is complex and various. So we can generate the topological map randomly. Figure 4 is a topological map generated by Matlab. This graph corresponds as the complex indoor environment. It contains 100 nodes. Firstly, we suppose the number of points is fixed and vary the number of monitoring points. The density and positions of monitoring points are determined by actual application and can affect the efficiency of algorithms. So we can change the number of monitoring points by the function randi() of Matlab. The serial number of each important monitoring point is also generated randomly. The array of monitoring points is [6, 13, 24, 33, 65, 40, 53, 79, 92, 94]. The comparing result of three algorithms is followed in Fig. 5. We can see that the ITRBDB algorithm is more efficient than DFS and BFS. The trend of algorithms is consistent. With the increase of monitoring points, the efficient of three algorithms is similar. The reason is when the density of monitoring points is big enough, the Branch and Bound method is invalid. But in actual application, we cannot make every point as the monitoring point because of cost. The number of average searching nodes is Fig. 4. Topological map of experiment

9 472 M. Li et al. Fig. 5. The result of varying monitoring points increasing when the number of monitoring points is 20 and 30. One possible reason is the positions of monitoring points generated maybe sparse. Secondly, we vary the number of nodes of topological map. The points array is [100, 200, 500, 800, 1000]. Set the number of monitoring points for each randomly. Result is displayed in Fig. 6, We can see that ITRBDB algorithm is more efficient than DFS and BFS. When the number of important points is fixed, the ITRBDB will be more efficient with the increase of number of points. Fig. 6. The result of varying the number of topological map

10 The Improved Algorithm Based on DFS and BFS 473 We have applied the ITRBDB algorithm for our project to monitor items. The trajectory of the item can be reconstructed. 5 Conclusion and Future Work In this paper, we apply the topological map for indoor trajectory reconstruction and propose improved algorithm to achieve the trajectory of the moving object. But there exits some problems to solve. Firstly, the improved algorithm is only applied in indoor environment whose topological map has no loop. When the indoor environment is complex, in other words, the topological map has loop, there may be many ways between monitoring points. We don t know whether the way is the real trajectory. We should find the real trajectory in some ways. Secondly, the topological map is constructed by labor. How to construct the topological map of indoor environment automatically is worth to research. Finally, we only construct the trajectory but not analysis the trajectory. For example, the motion state of the target. So we can describe the trajectory data in detail by some methods. Acknowledgement. This work was supported in part by the Innovation Program of Institute of Information Engineering Chinese Academy of Sciences (Grant No. Y5Z ). References 1. Huang, W.Q., Ding, C., Wang, S.Y., Jing, X., Luo, Y.J., Zhang, Y.F., Zhang, Z.J.: An efficient visualization method of RFID indoor positioning data. In: 2nd International Conference on Systems and Informatics (ICSAI), pp IEEE, Shang Hai (2014) 2. Kang, H.Y., Kim, J.S., Li, K.J.: STrack: tracking in indoor symbolic space with RFID sensors. In: Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems (GIS 2010), pp ACM, San Jose (2010) 3. Yang, M.: The Research and Achievement of Visualization of indoor location data. Shanghai Jiaotong University (2012) 4. Huang, Y., Du, J., Chen, H.: Construct three-dimensional route from blueprint. J. Beijing JiaoTong Univ. Image Build. 34(2), (2010) 5. Li, Z.: The optimization of Trajectory Reconstruction of Indoor Location System. G01C21/32GK SQ (2012) 6. Wang, R., Shroff, R., Zha, Y., Seshan, S., Veloso, M.: Indoor trajectory identification: snapping with uncertainty. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp (2015) 7. Zheng H, Peng C.: Collaboration and fairness in opportunistic spectrum access. In: IEEE ICC, pp (2005) 8. Randria, I., Khelifa, M.M.B., Bouchouicha, M., Abellard, P.: A comparative study of six basic approaches for path planning towards an autonomous navigation. In: 33rd Annual Conference of the IEEE Industrial Electronics Society, IECON 200, pp IEEE, Taipei (2007)

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