Coverage and Mobile Sensor Placement for Vehicles on Predetermined

Routes: A Greedy Heuristic Approach

Junade Ali and Vladimir Dyo

Department of Computer Science and Technology, University of Bedfordshire, Luton, U.K.

Keywords:

Mobile Sensors, Intelligent Transportation Systems, Smart Cities, Optimal Route Selection, Set Cover

Problem.

Abstract:

Road potholes are not only nuisance but can also damage vehicles and pose serious safety risks for drivers.

Recently, a number of approaches have been developed for automatic pothole detection using equipment such

as accelerometers, image sensors or LIDARs. Mounted on vehicles, such as taxis or buses, the sensors can

automatically detect potholes as the vehicles carry out their normal operation. While prior work focused on

improving the performance of a standalone device, it simply assumed that the sensors would be installed on the

entire ﬂeet of vehicles. When the number of sensors is limited it is important to select an optimal set of vehicles

to make sure that they do not cover similar routes in order to maximize the total coverage of roads inspected

by sensors. The paper investigates this problem for vehicles that follow pre-determined routes, formulates it as

a linear optimization problem and proposes a solution based on a greedy heuristic. The proposed approach has

been tested on an ofﬁcial London bus route dataset containing 713 routes and showed up to 78% improvement

compared to a random sensor placement selected as a baseline algorithm.

1 INTRODUCTION

Road surface condition monitoring is essential for

maintaining a safe and efﬁcient public transportation.

Road defects such as potholes cause accidents, dam-

age vehicles and slow down trafﬁc, and for this rea-

son, municipalities invest millions to maintain and re-

pair the roads. However, timely detection of potholes

remains problematic due to very high cost of inspec-

tion vehicles and the massive total length of the roads.

Recently, a number of approaches have been devel-

oped, where mobile wireless sensors deployed on

taxis, buses or utility vehicles, automatically inspect

the road as the vehicles carry their normal operation,

opening a way for a large scale and autonomous road

monitoring. While prior work focused on improv-

ing the sensor detection performance, data collection

and energy efﬁciency, it was largely assumed that the

set of vehicles on which sensors would be deployed

is either random (in case of taxis), pre-determined

(known) or that the sensors would be deployed on the

entire ﬂeet. The problem arises when a limited num-

ber of sensors needs to be optimally deployed on vehi-

cles that typically follow pre-determined routes, such

as buses or utility vehicles, because placing sensors

on the vehicles that follow similar routes would result

in sub-optimal road coverage.

The problem of coverage for mobile sensors has

been explored in the context of path planning for pa-

trolling applications (Murray, 2016), persistent moni-

toring tasks for autonomous vehicles (Kuhlman et al.,

2014) and data collection (Di Francesco et al., 2011).

In particular, (Kuhlman et al., 2014) investigates the

optimal mobile coverage problem in the context of

unmanned vehicles, and proposes an automated path

planner that minimizes vehicle’s path length whilst

maximizing the information gathered along that path.

The method however was designed for a single un-

manned vehicle and does not scale to multiple vehi-

cles. (Contreras et al., 2016) tackles an optimal sen-

sor placement problem for sensor networks deployed

on highway segments to maximize information col-

lected while minimizing monetary cost. This work is

similar in spirit to the proposed approach but targets

ﬁxed rather than mobile sensors. To the best of our

knowledge, no previous work considers an optimal

placement of mobile sensors on vehicles that follow

pre-determined routes.

In this paper we present a novel approach for an

optimal mobile sensor placement that maximises the

total length of the road inspected by sensors. The ap-

proach starts by representing each vehicle route as a

Ali, J. and Dyo, V.

Coverage and Mobile Sensor Placement for Vehicles on Predetermined Routes: A Greedy Heuristic Approach.

DOI: 10.5220/0006469800830088

In Proceedings of the 14th International Joint Conference on e-Business and Telecommunications (ICETE 2017) - Volume 6: WINSYS, pages 83-88

ISBN: 978-989-758-261-5

set of road segments, and using set cover theory to

formulate the problem as a linear optimisation prob-

lem that maximises the total number of segments for a

given number of vehicle routes. A greedy heuristic al-

gorithm is then proposed, which solves the problem in

a computationally efﬁcient way. The implementation

of the algorithm is not trivial as it requires an efﬁcient

method for subtracting geographical routes, for which

a simple solution is proposed. The approach has been

implemented in Go programming language, and eval-

uated on the ofﬁcial Transport for London (TfL) bus

dataset. The simulations have been conducted to eval-

uate the algorithm performance for different number

of selected routes. Based on the simulation results,

we found that the proposed approach provides a sig-

niﬁcant improvement over a random route selection

selected as a baseline algorithm.

2 RELATED WORK

The traditional pothole detection relies on manual

road surface inspection or automated inspection using

specialised vehicles. Because of high cost and labour-

intensive process, a typical survey is only done once

in 4 years (Zhang et al., 2014) whereas potholes can

develop quickly, with little or no advance warning.

Recently, the rapid advances in low cost wireless

sensors, open source hardware platforms and sens-

ing technologies has led to a surge of projects on low

cost pothole detection systems in both academia and

industry. A number of such systems have been de-

signed, deployed and evaluated by researchers around

the world (Mohan et al., 2008) (Eriksson et al., 2008).

The majority of low cost systems are vibration-based,

and use an accelerometer to detect a jolt, which hap-

pens when a vehicle drives over a pothole. The de-

tection accuracy depends on multiple factors includ-

ing vehicle type, pothole location, road conditions

and driver behaviour. The approach proposed by

(Eriksson et al., 2008) was able to correctly detect

88.9%-92.4% of potholes in an experiment with hand-

labelled training data and loosely labelled data respec-

tively. It should be noted that the system mounted on

utility vehicles can repetitively check the same road

segment over and over again, so may not require very

high detection rate. This is in contrast to dedicated

pothole monitoring systems, which are designed to re-

liably detect potholes through a single passing of the

road and therefore optimised for high detection accu-

racy. (Hull et al., 2006) introduces a mobile sensor

computing system known as CarTel, this system al-

lows data consumers to issue SQL queries to assess

data from CarTel devices.

Most deployments relied on random deployment

on either taxi cars or on specially selected cars. To

the best of our knowledge, none of the works consid-

ers the problem of mobile sensor placement under the

scenario, where sensors need to be deployed on ve-

hicles that run along speciﬁc routes, such as garbage

trucks, buses or other utility vehicles.

At the same, there have been a number of works

on route planning in the public transportation net-

works, such as optimal journey planning depending

on passenger and service preferences (Botea et al.,

2013), trust-oriented trip planning, app-based taxi

pooling (Chen, 2014) and public vehicles tracking

(Zhu et al., 2016). None of these works consid-

ers a problem of optimal route selection for vehi-

cles equipped with mobile sensors. (Contreras et al.,

2016) tackles an optimal sensor placement problem

for sensor networks deployed on highway segments

to maximize information collected while minimizing

the monetary cost. Our work is similar in spirit, but

targets mobile rather than ﬁxed sensors.

Finally, some related work exists in the area

of mobile sensor networks but focuses mostly

on data collection algorithms, energy management

(Di Francesco et al., 2011) and path planning for

patrolling applications (Murray, 2016). The recent

works on mobile video surveillance and ubiquitous

video acquisition are also relevant, but they focus

mostly on improving image quality under constrained

resources, image processing and analysis issues, with-

out considering a problem of optimal sensor place-

ment to maximize the coverage.

3 OPTIMAL ROUTE SELECTION

Figure 1: Road segment representation.

We represent each bus route as a set of road segments,

= {m

, m

...m

}, where each segment m

rep-

resents part of the road between two adjacent inter-

sections and which can belong to more than one bus

route. The segments are directed, so a two-way street

would be represented by two segments as shown on

Fig. 1. The problem is formulated as follows: given a

WINSYS 2017 - 14th International Conference on Wireless Networks and Mobile Systems

collection of sets S = {R

, R

, ...R

} and an integer k,

ﬁnd a subset S

of S such that the number of covered

elements is maximized, and |S

| <= k, i.e. select a

set of k vehicle routes that maximizes the total num-

ber of selected segments. The vehicle route selection

problem can be expressed as an integer program:

maximize

∑

s.t.

routes

∑

i=1

= k

= {0, 1}, i = 1, 2, 3...N

routes

Where u

is a decision variable showing whether a

route R

has been selected, k is the number of routes

to select, N

routes

is the total number of routes.

3.1 Greedy Approximation

The formulated problem is an instance of a known

problem in combinatorics called a maximum cov-

erage problem, which is known to be NP-complete

(Hochbaum, 1997), meaning that an optimal solu-

tion requires analyzing every possible combination

of routes. This can be computationally very hard

for large number of routes. However, a number of

approximations exist, with the best known being in

θ(log n). The greedy algorithm is known as the best-

possible polynomial time algorithm for maximum

coverage problem and works by iteratively selecting

a set R

that contains the largest number of elements

(road segments), and then removing selected elements

from all the remaining sets in the collection. The pro-

cess repeats until K sets are selected. The proof of

correctness is not described here, but can be found in

(Hochbaum, 1997).

However, the greedy algorithm’s limitation is that

it assumes that all road segments are of equal length,

resulting in a route with 2 short road segments be-

ing preferred over a route with 1 long road segment.

Overcoming this limitation requires redeﬁning a road

segment as a segment with a unit length, so that the

number of segments is proportional to route distance.

This way, a single long road segment can be repre-

sented as multiple unit length elements, and will be

preferred over shorter road segments without modiﬁ-

cations to an algorithm. The pseudocode based on a

direct translation of a classic greedy algorithm for a

route selection problem is shown in Algorithm 1. The

proposed algorithm is computationally lightweight

and requires O(N

) operations.

Data: {R

, R

, ...R

routes

} - a set of bus routes

= {m

, m

, ...m

} - each vehicle route as a

set of road segments

routes

- total number of vehicle routes

k - number of routes to select

Result: MaximumRouteSet - a set of route IDs

that maximizes coverage

initialization;

MaximumRouteSet :=

repeat

// Route retrieval: select the route that has

the largest number of uncovered elements

i := argmax(U ncoveredLength(R

))

MaximumRouteSet := MaximumRouteSet +

// Route Exclusion: Subtract the covered road

segments from the remaining routes. Note that

an efficient implementation can simply ’mark’

the covered road segments without actual

’subtraction’

for j ∈ RemainingRoutesIDs do

:= R

- R

end

until length(MaximumRouteSet) = k;

Algorithm 1: Maximum route coverage.

4 EVALUATION

4.1 Data Set

The algorithm is evaluated on Transport for Lon-

don dataset (TFL, 2016) containing 713 bus routes

in Greater London, released for application devel-

opers to create apps such as locating nearest bus

stops or perform journey planning. The data is

available as a CSV ﬁle, where each record speci-

ﬁes the coordinates of a bus stop (Location Easting

and Location Northing), a bus route (Route), the

sequence number along the route (Sequence), the

name and the code for the bus stop (Stop Name and

Bus Stop Code), and the direction of travel (Run).

The dataset contains routes for a total of 19801 dif-

ferent bus stops. The summary of data format is de-

scribed in Table 1. The actual street by street path for

each bus route has been extrapolated from bus stop

coordinates by using Google’s turn-by-turn naviga-

tion API (Wallace et al., 2014). Here, an assump-

tion has been made that a bus moves along the short-

est path between consecutive bus stops, which works

well in most cases.

The processed data set contains GPS coordinates

of the turn-by-turn road segments for each bus route.

The need to run the bus routes through a turn-by-turn

Coverage and Mobile Sensor Placement for Vehicles on Predetermined Routes: A Greedy Heuristic Approach

Figure 2: The original dataset contains bus stop locations

only, which is not sufﬁcient for running a route selection

algorithm.

Figure 3: The processed dataset contains a more detailed

route information obtained through turn-by-turn direction

API.

direction API is visualized on Fig. 2 and Fig. 3:

The implementation was done in the Go pro-

gramming language known for its support for con-

current operations (Donovan and Kernighan, 2015).

The script iterates through all bus stops for each bus

route, extracts the coordinates of all road intersections

and saves the data in a KML ﬁle as well as MySQL

database. KML was used for visualizing the routes in

Google Earth, while MySQL was used for further pro-

cessing as described in the next subsection. Visualiz-

ing KML data in Google Earth proved to be beneﬁcial

for discovering defects in the data supplied. For ex-

ample, the Ordinance Survey Easting co-ordinate for

a stop on Summit Close contained an error which af-

fected three bus routes. This was reported to TfL, who

corrected the co-ordinate and updated their dataset ac-

cordingly. Whenever an individual bus route was pro-

cessed, it was processed concurrently with other bus

routes. This was advantageous in the fact that larger

bus routes with substantial API calls did not block the

processing of other routes. The script processed 10

routes concurrently on a laptop with a dual-core 2.7

GHz Intel i5 with 8GB RAM, and converted the en-

tire data set in 20 minutes.

4.2 Geographical Route Exclusion

Recall that the optimization algorithm works by itera-

tively repeating longest remaining route retrieval and

route exclusion procedures. Both procedures can be

implemented trivially, if all road segments were repre-

sented as abstract set elements with unique numerical

IDs. The actual data for each bus route comprises a set

of road segments deﬁned by their GPS coordinates as

illustrated on Fig. 4 where white lines indicate several

bus routes going around the same roundabout. Note

that each bus route uses its own set of road segments

(white lines) to describe the same road around the

roundabout, which complicates route exclusion. For

route exclusion to work correctly, removing any bus

route going through the roundabout should automati-

cally remove all nearby road segments that belong to

other bus routes in the same area.

We propose the following simple implementa-

tion for geographical route retrieval and route ex-

clusion. Let A = (longtitude1, latitude1) and B

= (longtitude2, latitude2) be the co-ordinates of

the start and end points of the selected road seg-

ment. The proposed route exclusion algorithm

works by placing a rectangle with AA

on a

map, where A

= (longtitude1, latitude2) and B

(longtitude2, latitude1), and then removing all road

segments that start and end within the rectangle, as

shown in Fig 5. In the diagram below the white lines

indicate a bus route, with the grey rectangles indicat-

ing the rectangles AA

, any other route segments

which touch or overlap the red squares will be re-

moved. This allows us to ensure that segments that

run parallel (but would not ordinary overlap), can still

be identiﬁed and removed alongside the target seg-

ment.

The distances between each co-ordinate are un-

equal, however in practice as each small turn on the

route creates a new segment, the route segments are

therefore small enough not to cause a problem (no

segment was greater than 100 meters apart). If there

is a particularly long segment running alongside a

road which has another road running parallel along-

side side it at limited proximity, it is possible that a

segment on the other road may be removed. There-

fore, it is vital that segment lengths are kept to a mini-

mum in order to avoid this behaviour. Our implemen-

tation is able to identify long segments in the dataset

and split them into smaller segments by modifying the

end point of a segment, and inserting a new segment.

An alternative method of removing nearby road seg-

ments would have been by identifying points which

are within a given radius of a set of midpoints of the

given segment. However, this approach would require

WINSYS 2017 - 14th International Conference on Wireless Networks and Mobile Systems

Figure 4: Charlie Chaplin Walk roundabout.

Figure 5: Route Exclusion problem.

the knowledge of which road a given segment is on to

validate the fact that two segments are indeed on the

same road.

The implementation process starts off by populat-

ing a MySQL database with an entry for each road

segment. The length of each route is calculated dy-

namically as a total length of road segments on that

route. By using a function that calculates the dis-

tance between co-ordinates we can calculate the to-

tal length of the routes and mark all segments of the

largest route as deleted. As we iterate through each

part of the route to mark it as a deleted, we accord-

ingly mark any other route segments on the remain-

ing routes as deleted if the segments’ co-ordinates

are within the start and end points of the route seg-

ment being deleted as described below. As the next

route that is removed depends on the previous route

removed, it was not possible to concurrently process

multiple routes together. We did not however feel that

this was a limiting factor as this step took a matter of

seconds.

5 RESULTS

The goal of the evaluation is to compare the perfor-

mance of the proposed greedy algorithm with a base-

line method, where the routes are selected randomly.

The baseline algorithm was run three times and the

average result was taken, whereas the Greedy algo-

rithm only needs to be run once, as it is deterministic

and always selects the same set of routes regardless of

how many times the simulation is run.

Fig. 6 shows the total route coverage in meters de-

pending on the number of selected routes for both pro-

posed greedy approximation and baseline algorithms.

The total route coverage increases linearly with the

number of selected routes for a baseline approach. It

can be seen that for each number of selected routes,

the proposed algorithm provides higher route cov-

erage. At just 100 selected routes (around 14% of

routes), greedy algorithm covers 25% of the total road

length compared to 14% achieved by a baseline algo-

rithm, which corresponds to 78% improvement. The

greedy algorithm provides a higher coverage because

it attempts to select the longest route each time, and

then excludes the relevant segments from the remain-

ing routes. This improvement in coverage decreases

to 54%, 38% and 12% for 200, 300 and 600 routes re-

spectively. Whilst the improvement reduces with the

number of selected routes, the result clearly demon-

strates that at any point, greedy approximation per-

forms better than a baseline. The results can be par-

ticularly useful to demonstrate an effectiveness of an

approach when not all the vehicles can be equipped

with pothole sensors. This can be the case for de-

ployments in large geographical areas that consist of

thousands of routes.

0 100 200 300 400 500 600 700

0 20 40 60 80 100

Routes removed

Total road length coverage, %

greedy

random

Figure 6: Total route coverage against the number of se-

lected routes.

6 CONCLUSIONS

Low cost mobile sensors provide a promising solution

for a large scale and timely pothole detection. While

a number of solutions have been proposed recently,

most focus on sensor design, signal processing and

Coverage and Mobile Sensor Placement for Vehicles on Predetermined Routes: A Greedy Heuristic Approach

data collection ignoring an important question of sen-

sor placements. We have proposed a novel approach

for selecting an optimal set of vehicles that maximizes

the geographical road coverage. We have formalised

the problem as a maximum coverage problem and

proposed a greedy heuristic, which was evaluated on

TfL London bus route data set. The evaluation has

shown up to 78% improvement over a random route

selection selected as a baseline algorithm. Some ap-

plications may ﬁnd it useful to assign priorities to cer-

tain roads depending on the road trafﬁc or road size.

For a pothole detection application, it may be useful

to have a higher scanning frequency for strategic and

secondary distributor roads and lower frequency for

local access and link roads. This can be modelled as a

weighted maximum coverage problem, the evaluation

of which we leave for future work.

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WINSYS 2017 - 14th International Conference on Wireless Networks and Mobile Systems