Wireless Pers Commun (2014) 78:1995–2007 DOI 10.1007/s11277-014-2058-7
Safe Path Planning Strategy for Bike Net Wen Ouyang · Chang-Wu Yu · Kun-Ming Yu · Ko-Jui Lin · Huai-Tse Chang
Published online: 20 September 2014 © Springer Science+Business Media New York 2014
Abstract Biking has gained much popularity recently due to its unique characteristics. It is simultaneously a sport, a leisure activity, and a means of transportation. It has low negative environmental impact and it conserves energy. It can be a solo or a group activity and it applies to all ages. Path planning is essential for all tour activities, including biking. However, most path planning services focus on the shortest path finding when other qualities of service also deserve attention. Among them, safety is always the first priority for any type of activity. There are tools which help people plan for biking tour paths. However, safety is not a major concern in these. This work proposes an innovative and practical safe path planning strategy which addresses the issue with the concept of safety factors and a safety recurrence relation. A dynamic programming solution is provided accordingly. The idea is illustrated using real site data to demonstrate the result of the strategy. Keywords Biking · Safety · Safe path · Path planning · Bike net · Shortest path · Graph theory 1 Introduction In recent years, biking has attracted much public attention. Bike sales volume increases every year and more people ride bicycles for leisure, commuting, or just exercising. There W. Ouyang (B) · C.-W. Yu · K.-M. Yu · K.-J. Lin · H.-T. Chang Department of Computer Science and Information Engineering, Chung Hua University, Hsinchu, Taiwan e-mail:
[email protected] C.-W. Yu e-mail:
[email protected] K.-M. Yu e-mail:
[email protected] K.-J. Lin e-mail:
[email protected] H.-T. Chang e-mail:
[email protected]
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are many reasons for this phenomenon. Firstly, tourism has become one of the fastest growing sectors of the world economy [1,2]. People in modern societies are under more stress and are thus looking for more leisure activities. Travel and touring provide great opportunities that serve this purpose. Moreover, after the global economic and financial crisis starting in 2008, local and inexpensive tours have become more attractive to the public, making biking tours even more appealing. In addition, the twenty-first century is an era with a higher awareness of environmental and energy conservation. As the global environmental crisis we face has caused more serious changes in global weather and, due to several reasons, an energy shortage, we have been led to a lot of rethinking and adjustment to our lifestyles. Thus green issues serve to make biking more popular than ever. Biking is attractive also because it is so easy to learn and can be enjoyed by people of all ages. Public Bicycle Systems (PBS), also called Public Bike Sharing System, is an integrated, automated system for bike renting which provides secure and convenient bicycles management for short trips. People can rent bicycles for their journeys to and from certain shortdistance areas by paying a small fee. Furthermore, since bike stations are located at different places, the biker can rent the bicycle from one station and return it to another station near their destination, which makes it even more convenient to use a PBS. Many countries and cities have adopted the idea of a PBS and have built their own systems. These include Paris, France; Barcelona, Spain; Berlin, Germany; Washington, DC, USA; Montreal, Canada; and Hangzhou, China [3,4]. There are many issues that require consideration when designing a PBS. A successful PBS should exhibit good quality of service (QoS), such as high availability and high usage. Good services encourage high usage. Biking path planning is actually a commonly provided service in many systems [5] and most of them focus on finding the shortest path. A path can simply tie together all the desired destinations. When considering the quality of a planned biking path, many factors come into the picture. From a user’s, or biker’s, point of view, the type of path that is most attractive becomes a very complicated question to analyze. In this work, we focus on proposing innovative safe path strategies for bicycle networks. We formally define safety factors and formulate safety coefficient (SC) for edges and safety value (safety) for paths. Finally, a dynamic programming strategy to find an optimal path is designed and implemented on a real site to verify the result. The situation where intermediate stops is needed is also addressed. This work considers static situations where the environmental factors are stable. Circumstances with dynamic environments are not discussed in-depth here. However, wireless sensor systems incorporated into Internet of Things can be designed to monitor environmental factors in real time, especially in the areas with high safety risk. This way, in case of any changes, such as safety degradation during disasters like hurricanes or earthquakes, the system can notify or alarm the user and provide alternative routes or paths for safe travel. This paper is organized as follows: Related work is summarized in Sect. 2. The safe path planning problem and the proposed safe path algorithm are explained on Sect. 3. This is followed by simulation results in Sect. 4. Section 5 concludes this paper.
2 Related Work Path finding has drawn the attention of people long before the Seven Bridges of Königsberg had been resolved by Euler [6] (through converting the problem to the very first graph theory problem in eighteenth’s century). The problem transforms into finding a cycle that goes through each edge exactly once, and the solution is easy, with the result being the Euler
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Safe Path Planning Strategy for Bike Net Table 1 Some bicycle lanes in Taiwan
1997
City
Scenic spots
Taipei
Muzha Maokong
12
Taipei
Hot Springs of Beitou
20
Taoyuan
Green Aisle of Xinwu
Taoyuan
Roman Road
Taichung
Gaomei Wetland
1.7
Tainan
Bikeway of Anping
6.6
Hualien
Bikeway of Ruisui
Kinmen
Jinhu
Penghu
Bikeway of Jibei Island
Length of lane (km)
4 35.7
7.6 17 7
cycle. On the other hand, finding a Hamiltonian cycle, which needs to go through each vertex exactly once, becomes an NP-hard problem. While dwelling in graph theory, path finding can be done using either breadth-first or depthfirst methods. However, these two schemes only promise to find one path—if it exists—with no guarantee toward the quality of the path. To pursue the shortest path, the greedy Dijkstra’s algorithm is the choice when there is no negative edge. When negative edges exist without a negative cycle, Bellman-Ford or Floyd dynamic programming schemes can be applied. In real life, any travel needs to define a path between the origin and the destination. The shortest path stands out because of its practicality for many bikers, especially commuters [7,8]. However, for biking, which leans more towards leisure purposes, the shortest path may not be of the highest priority. When considering safety issue, many other factors show up. Broach, Gliebe, and Dill [7] studied cyclist preferences by mounting a GPS unit on bicycles that retrieved data for analysis of bicycle route choices model. The result shows that cyclists are sensitive to distance, turn frequency, slope, intersection control, and traffic volumes. Many of them are safety-related. The derived choice model has been integrated into a regional travel forecasting system in Portland, Oregon, USA. Similar research [8] was conducted in San Francisco, California, U.S.A and similar result was reached. One way to help with biking safety is by building bike lanes dedicated to cyclists only. In Taiwan, many bike lanes were built in national parks and around sceneries. Table 1 depicts some bike lanes around certain scenic spots in Taiwan [9]. These lanes were constructed according to strict standards to ensure riders’ safety. Most of these bike lanes were built before many people went there. Bike lanes are not in all scenic areas that bikers are interested in visiting, though. Hood, Sall, and Charlton [8] discovered that bike lanes are preferred while, on the other end, steep slopes are not favored for bikers. A slope, sometimes referred to as a gradient, is a measure of the steepness or inclination of the road relative to the horizontal. When biking on the road, bikers may experience sloping fields, which may be uphill or downhill, that pose challenges. Usually, safety concerns come with these slopes as well. Figure 1 and Eq. (1) [10] show the basic definition of slopes,where D is the horizontal distance derived from the longitude and latitude acquired by the GPS recorder, and H is the height above elevation, also acquired from the GPS. H (1) D The above formula works for a single climb in the road. However, for a long segment of road, there are other metrics for climb classification. A very commonly used measure Slope(%) = tan α =
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Fig. 1 Slope
Table 2 Bergwertung and climbs classification
Bergwertung values
Climbs classification
0–20
G1
20–50
G2
50–120
G3
120–200
G4
>200
HC
called Bergwertung [11], meaning “mountain classification,” was introduced. This measurement system originated from mountain biking and was used to classify the toughness of the path for biking. Mountain biking usually follow paths off-the-road, which are often very rough and challenging. Bergwertung has been utilized in the Tour de France and many other biking competitions to categorize, in levels, the mountains based on steepness and length. Equation (2) is used for finding Bergwertung data. Table 2 displays the climbsclassifications corresponding to Bergwertung ranges. 3 Bergwertung = Slope(%) 2 × Total Elevation(m) 100 (2) In this work, road types and the slope of the road are considered to formulate our safety measure.
3 Safe Path Planning Strategy Algorithm This study focuses on the determination of a safe path from the origin to the destination in a given geographical area. A path can be composed of a set of road segments, which, step-by-step, connects the source location to the destination. To find such a path, we have to define safety characteristics for each road segment and define the safety value for a path. This concerns collecting safety-related information for each road segment along the road of interest and using the safe path planning strategy to develop a path which satisfies the safety criteria. The safe path planning problem for a bike network considers several safety factors for each road segment. Besides the two factors mentioned in the previous segment, slope and road type, three other factors are also considered: road width, signs on the road, and road lighting. Each factor is granted different weight levels for different situations. All weights are set between 0 and 1 with 1 meaning the safest condition and 0 meaning the least safe condition. Weights for different road types are listed on Table 3. If the road has a bike lane, its weight is 1, since riding on dedicated lanes is the safest. Asphalt or cement road surfaces are the
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Safe Path Planning Strategy for Bike Net Table 3 Road type
Table 4 Road width
Table 5 Signs on the road
Table 6 Road lighting
Road type
1999 Weight
Bike Lane
1
Paved surface (asphalt or cement)
0.8
Rugged
0.6
Road width
Weight
With slow lane
1
Wider than two cars
0.8
Two cars
0.6
One car
0.1
Signs on the road
Weight
With signs
1
Without signs
0.8
Road lighting
Weight
Full lighting
1
Partial lighting
0.4
None
0.1
Day light riding
1
second safest for riding bikes, so the weight is 0.8. A rugged road means the road is rough or lacks any pavement. It receives the lowest weight of 0.6. Road width is another important factor. Normally, bikers share roads with many other types of vehicles. The wider the road, the more space bikers can use, and thus the more safety assurance there is. Four different categories are used here with the thought of the number of cars that go through the road at the same time (Table 4). When a road allows only one car to pass (narrow road), the weight is assigned 0.1. If two cars can pass the road, 0.6 is the weight. For cases when road width can accommodate more than two cars, the weight is 0.8. And if the road has a slow lane (which is the most luxurious), the bikers are in the safest road width since they are most distant from cars in the road. Signs on the road are also a safety indicator helping bikers to be more aware of the road conditions or direction so that bikers can concentrate on biking itself. The weights are 1 and 0.8 for roads with signs and roads without signs, respectively (Table 5). Some riders may want or need to ride at night; thus, road lighting is essential for safety. Although bicycles can be equipped with head and tail lights, too, for the purposes of our study, we will consider lights on the roads only. If, when riding at night,the road is not equipped with any lighting, the weight is 0.1. Partial lighting gets 0.5 and full lighting gets 1 as their weights respectively. If riding does not happen at night, the weight is 1 as in Table 6. We also consider the climb classification according to Bergwertung values. There are five levels of climbs classification as mentioned in previous section. Table 7 depicts the weights for different climbs classifications. G1 to G3 are the most common levels for an ordinary
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W. Ouyang et al. Climbs classification
Weight
G1
1
G2
0.7
G3
0.5
G4
0.3
HC
0.1
Fig. 2 Different road conditions: a a bike lane, b a bad road
rider. If the level is over G3, riders on this path need to be more focused and more experienced to avoid dangerous situations. Figure 2a shows a bike lane in Nashville, Tennessee, U.S.A. which protects bikers from other vehicles. Figure 2b displays bad road conditions in Baoshan, Taiwan for which signs on the road can help with the bikers’ safety. Now we need to define a single unified safety coefficient (SC) for each road segment so that we can compare road segments with each other. The idea is that any unsafe factor usually downgrades the safety of the whole road segment even if other factors are comparably safer. Thus, we set the highest SC value of a road segment to be 1, while multiplying the five safety factors to create the SC value for that road segment. Any low safety factor can lower the SC value dramatically. For a road segment to be considered safe, it has to maintain good (high) weights on all factors. The following example shows how the SC values are evaluated for two road segments A and B. Assume that road segment A is a paved surface (0.5 in road type, T). It allows two cars to pass through (0.6 in road width, W ), has no signs (0.8 in signs on Road, I ), and has lighting on the road (1 for road lighting, L, since it is daytime), and is G1 (1 in climbs classification, S). Road segment B has 0.1 in road type (T ), 0.6 in road width (W ), 1 in signs on road (I ), 1 in road lighting (L) since the biking happens at daytime, and 1 in climbs classification (S). Equation 3 derives the safety coefficient for these road segments. Table 8 shows the resulting SC values for road segments A and B. SC = T × W × I × L × S
(3)
After all the SC values for all road segments are evaluated, it is time to derive a safe path finding strategy. The goal is to find the safest path. Note that the path found in this way has a good possibility of being shorter than other paths. To find the safest path between the source and destination, we propose a safe path algorithm. The technique of the algorithm is based on dynamic programming. Here we define the safety value of a path to be the product of the SC values of the road segments which form
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Safe Path Planning Strategy for Bike Net Table 8 SC values for road segments A and B
2001
Road segment
T
W
I
L
S
SC
A
0.5
0.6
0.8
1
1
0.24
B
0.1
0.6
1
1
1
0.6
Fig. 3 Recurrence relation situations for sa f et y(i, k)
this path. The idea behind this evaluation is that the safely of a path should be a product of all the road segments, since one unsafe road segment leads to an unsafe path, but a safe segment does not guarantee a safe path. Only when all segments are safe is whole path safe. The path with the highest safety value is called the optimal path, which is what our method tries to find. For a graph G = (V, S) where V is a set of vertices, set S consists of undirected road segments (R S). That is, S = {R S1 , R S2 , R S3 . . . R S|S| } where each road segment R S j connects two vertices in V and has two values: a unique id and a pre-computed safety coefficient, SC. The algorithm requires two inputs, which are the source vertex (vs ) and the destination vertex (vd ). The algorithm starts from vs to find a path to vd . The following symbols are defined. k : the maximum number of edges allowed in the path. sa f et y(i, k): the safety value of the path with at most k edges and the highest safety value from source vs to vertex i. pr evious(i, k): the vertex immediately before i in the path of sa f et y(i, k). w: a vertex connected to i. The goal is to derive sa f et y(i, n − 1) where n is the number of vertices and construct the safe path from pr evious(i, n − 1). By applying dynamic programming technique, it can be surmised that the base condition is when k is 0, which means there is no edge between the source and any vertices. When k is greater than 0, there are two cases. Case one is an easy case when the optimal path with at most k edges is the same as the one with at most k − 1 edges; that is, sa f et y(i, k) = sa f et y(i, k − 1). In case two, the optimal path with at most k edges is not the one with at most k − 1 edges. Thus, we need to consider those paths from the source with at most k − 1 edges which lead to all possible vertices, w, connecting directly to vertex i. Figure 3 depicts the two cases. The first two paths (from the top) are for case two and the last is for case one. Equation (4) shows the recurrence relation for safety (i, k). The dynamic programming algorithm starts by calculating sa f et y(i, 0) for all i belongs to V . It then proceeds to find sa f et y(i, k) for k = 1, 2, . . . , and n − 1. The resulting path will be for safety (Vd , n − 1). The data structure pr evious(i, n − 1) is used to track the optimal path.
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⎧ 0, ⎪ ⎪ ⎨ 1, sa f et y(i, k) = max{sa f et y(i, k − 1), ⎪ ⎪ ⎩ max{sa f et y(w, k − 1) ∗ SCwi}}
k = 0 and Vs = i k = 0 and Vs = i
(4)
k≥1
Naturally, sometimes a biker needs to make several stops while traveling from source to destination. The algorithm can work with this need by arranging all the stop points, including source and destination, in order. Then, it finds a mini safe path between each pair of consecutive points. By connecting all these mini safe paths together, the result is a safe path from source to destination.
4 Simulation Results A system has been developed to find a safe path with the test data derived from a field investigation of Baoshan Township, Hsinchu County, Taiwan (R.O.C.). Information for each road segment was collected and analyzed. GPS data, including latitude, longitude and elevation, were also collected as shown in Fig. 4. Data are saved in KML format. Figure 4 shows totally 31 road segments with their corresponding safety data displayed in Table 9. The resulting SC values of all road segments are then shown in Table 10. After running the program with specified source and destination locations, Fig. 5 shows the result comparing the safe path derived from the program and the shortest path. Red
Fig. 4 GPS data of certain roads in Baoshan
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Safe Path Planning Strategy for Bike Net Table 9 Data for road segments in Fig. 4
Road Seg.
2003 Type
Width
Signs
Light
Slope
Len.
1
0.8
0.1
0.8
0.4
1
7.17
2
0.8
0.6
0.8
0.4
1
3
3
0.8
0.6
0.8
0.4
1
3.26
4
0.8
0.6
0.8
0.4
0.7
0.83
5
0.8
0.6
0.8
0.4
1
0.65
6
0.8
0.1
0.8
0.4
1
4.16
7
0.8
0.8
0.8
0.4
1
3.25
8
0.8
0.6
0.8
0.4
1
7
9
0.8
0.8
0.8
0.4
0.7
1.13
10
0.8
0.6
1
0.4
0.7
1.89
11
0.8
0.6
0.8
0.4
0.5
1.28
12
0.8
0.1
0.8
0.4
1
0.42
13
0.8
0.1
0.8
0.4
0.7
0.96
14
0.8
0.8
0.8
0.4
1
0.63
15
0.8
0.6
0.8
0.4
0.7
0.36
16
0.8
0.1
0.8
0.1
0.7
0.26
17
0.8
0.6
0.8
0.4
0.5
2.11
18
0.8
0.6
0.8
0.4
0.7
3.62
19
0.8
0.6
0.8
0.4
1
2.79
20
0.8
0.6
0.8
1
1
0.91
21
0.8
0.8
1
1
1
1.21
22
0.8
0.6
0.8
0.4
1
2.51
23
0.8
0.1
0.8
0.1
1
2.21
24
0.8
0.6
0.8
0.4
0.7
2.56
25
0.8
0.6
0.8
1
0.7
3.21
26
0.8
0.6
0.8
1
1
0.83
27
1
0.8
0.8
1
0.7
0.85
28
0.8
0.1
0.8
0.4
1
4.48
29
0.8
0.6
0.8
1
0.7
2.88
30
0.8
0.1
0.8
1
1
3.23
31
0.8
0.6
1
0.4
0.7
2
lines indicate road segments 31, 26, 25, 23, 13, 16, 15, 9, 7, and 8, which make up the optimal path found from the safety path finding algorithm. Green lines display the road segments of the shortest path, going through segments 31, 26, 25, 24, 5, 6, 7, and 8. The blue lines denote the rest of the road segments. The shortest path has a length of 21.21 and the safety value is 3.45616E−12, while the safe path has length 23.66 and a safety value of 1.84502E−07. To demonstrate the program’s adaptability to path finding with intermediate nodes, another run shows not only the source and destination but also an intermediate node as in Fig. 6. Two paths, namely safe path and shortest path, are demonstrated. This time, the shortest path goes through road segments 2, 3, 4, 24, 23, 13, 16, 15, and 9 with path length 14.57 and safety value 2.1601E12. The safe path passes road segments 2, 29, 27, 26, 25, 24, 5, and 6. The path length is 18.14 and the safety value is 8.07197E−07.
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2004 Table 10 SC values for road segments
W. Ouyang et al.
1
2
3
4
5
6
0.0256
0.1536
0.1536
0.10752
0.1536
0.0256
7
8
9
10
11
12
0.2048
0.1536
0.14336
0.1344
0.0768
0.0256
13
14
15
16
17
18
0.01792
0.2048
0.10752
0.00448
0.0768
0.10752
19
20
21
22
23
24
0.1536
0.384
0.64
0.1536
0.0064
0.10752
25
26
27
28
29
30
0.2688
0.384
0.448
0.0256
0.2688
0.064
31 0.1344
Fig. 5 Safe path planned for Baoshan. Red is the planned safe route. Green is the shortest path. it Blue depicts other road segments. Vertex S is the source and E is the destination. (Color figure online)
Fig. 6 Safe path with intermediate stops planned for Baoshan. Red denotes the planned route. Green denotes the shortest path. Blue depicts other road segments. Vertex S is the source, E is the destination, and R is the intermediate stop vertex. (Color figure online)
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5 Conclusion This work considers the problem of finding a safe path from the origin to destination with a practical perspective. The work moves from first defining a safety coefficient for each road segment, to evaluating the safety value for each path, and, finally, developing a dynamic programming algorithm to derive the shortest safe path. For the purpose of quantitative analysis, five major safety factors for each road segment are considered and quantified. Associated weights are assigned to each factor for different situations. Then, an equation is defined and evaluated for each road segment to derive its safety coefficient. After that, the safety value for each path as a whole is also derived from its individual road segments. Thus, the problem of finding the safest path is to find the path with the highest safety value. A dynamic programming algorithm is proposed to solve this problem while a real site in Baoshan Township is investigated, where information is gathered and used in a simulation conducted to retrieve the safest path. The safe path is calculated for this site and the result is demonstrated. The strategy used to apply the algorithm to an additional requirement of intermediate stops is also proposed and demonstrated in the simulation. This work marks an innovative step in practically formulating the search for optimal safe path for biking. Acknowledgments This work is sponsored by the Ministry of Science and Technology of Taiwan under Grant Number NSC 100-2632-E-216-001-MY3-2.
References 1. Tourism Economics Summary. http://www.sustainabletourismonline.com/tourism-economics. 2. Edition UNWTO Tourism Highlights. http://mkt.unwto.org/en/publication/unwto-tourism-highlights2012-edition. 3. Lin, J.-R., Yang, T.-H., & Chang, Y.-C. (2011). A hub location inventory model for bicycle sharing system design: Formulation and solution. In Computers & Industrial Engineering. doi:10.1016/j.cie.2011.12.006. 4. Public Bike Share System. http://carsharingus.blogspot.tw/2007/06/public-bicycle-systems.html. 5. https://bikemap.net/. 6. Bondy, J. A., & Murty, U. S. R. (1982). Graph theory with applications, 5th printing. New York: NorthHolland. 7. Broach, J., Gliebe, J. P. & Dill, J. (2011). Bicycle route choice model developed from revealed-preference GPS data. In: Transportation research board 90th annual meeting, paper #11-3901, January 23–27, 2011 (pp. 1–14). Washington, DC. 8. Hood, Jeffrey, Sall, Elizabeth, & Charlton, Billy. (2011). A GPS-based bicycle route choice model for San Francisco, California. Transportation Letters: The International Journal of Transportation Research, 3, 63–75. 9. http://www.cycling-update.info/k/mth/8_bicy_g_l.htm. 10. Grade (slope). http://en.wikipedia.org/wiki/Grade_(slope). 11. Mountain valuation. http://wikipedia.qwika.com/de2en/Bergwertung.
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W. Ouyang et al. Wen Ouyang received her Ph.D. degree in Computer Science from the University of Texas at Dallas in 1993. From then on, she worked as a Member of Scientific Staff and Senior Member of Scientific Staff in Bell North Research, later becoming Nortel Networks where she was involved in large-scale telecommunication systems research and development. Since 2003, she has been an Assistant Professor at the Department of Computer Science and Information Engineering, Chung Hua University in Taiwan. Her current research interests include fault tolerance, routing schemes and sensor localization and tracking for wireless sensor networks. She also works in topics involving software verification and validation techniques.
Chang-Wu Yu (James) received Ph.D. degree from National Taiwan University in 1993, all in computer sciences. Currently, he is a Professor at the Department of Computer Science & Information Engineering, Chung Hua University. Dr. Yu serves as an editor of Ad Hoc & Sensor Wireless Networks: His current research interests include graph techniques, routing protocols, modeling and evaluation for wireless Ad Hoc and Sensor Networks.
Kun-Ming Yu received the B.S. degree in Chemical Engineering from National Taiwan University in 1981, and the M.S. and Ph.D. degrees in Computer Science from the University of Texas at Dallas in 1988 and 1991, respectively. From August 1993 to July 1996, he was the head of and an associate professor in the Department of Information Management, Chung-Hua Polytechnic Institute. From 1996 to 2000, he was the chair of the Department of Computer Science and Information Engineering, Chung-Hua University. He is currently the Dean of the College of Computer Science and Informatics, Chung-Hua University. His research interests include load balancing, distributed and parallel computing, high performance computing, ad hoc networks, and computer algorithms.
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Ko-Jui Lin received his B.S. and M.S degrees from the Department of Computer Science and Information Engineering of Chung Hua University, Taiwan in 2011 and 2014, respectively. He is currently an app development engineer in Ding Yue Information Management CO Ltd.
Huai-Tse Chang received the B.S. degree in Computer Science and Information Engineering in 2011 from Chung-Hua University. Currently, he is a M.S. student. His current research interest is path planning for bike net.
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