1

A New Data Structure to Represent Road Networks

Bogaert, P., Van de Weghe, N., Maddens, R., De Temmerman, L., De Maeyer, P.

Ghent University

2

G-Day Gent 9 November 2005 2

Modelling

Modelling

Real World Virtual World

3

G-Day Gent 9 November 2005 3

Modelling

Modelling

Minimize data storage

Fast answer

Resemble real-lifeas much as possible

4

G-Day Gent 9 November 2005 4

Road Network

Modelling

Specific case of a road network for navigation purposes on the network itself

A Graph G(N, E, c)

N {a,b,c,d,e,f, …} : a set of nodes

E {(a,b) ; (a,c) ; (b,d) ; …} : a set of connections between nodes

c : a cost that can be mapped onto each edge

5

G-Day Gent 9 November 2005 5

Road Network

Spatial problems : Graph theoretical problems

A Shortest path

Travelling Salesman problem (visit all nodes)

Chinese Postman problem (visit all edges)

Etc.

6

G-Day Gent 9 November 2005 6

Road Network

Mapping of a road network onto a graph

Nodes : intersections and endpoints

Edges : connections between intersections and endpoints

5

26

7

7

G-Day Gent 9 November 2005 7

Road Network

Adding Direction (Different Costs, OneWay)

By means of a Directed Graph : D(N,E,c)

5

26

7

2

6

6

8

G-Day Gent 9 November 2005 8

Road Network

Adding Turn Cost and Prohibitions

Cadwell (1961), Kirby and Potts(1969)

node expansion (Directed or not)

9

G-Day Gent 9 November 2005 9

Road Network

Adding Turn Cost and Prohibitions

Cadwell (1961), Kirby and Potts(1969)

Disadvantage:

Data storage

Calculation time (e.g. Dijkstra with heaps O(n log n))

10

G-Day Gent 9 November 2005 10

Road Network

Adding Turn Cost and Prohibitions

e.g. Jiang et al.

By Using 'Turn Tables’

For Shortest path same complexity O(nlogn)

11

G-Day Gent 9 November 2005 11

Road Network

Adding Turn Cost and Prohibitions

E.g. Winter (2002)

Using a line graph

12

G-Day Gent 9 November 2005 12

Road Network

Adding Turn Cost and Prohibitions

Difference in Navigation

WinterTurn Tables

13

G-Day Gent 9 November 2005 13

Road Network

Adding Turn Cost and Prohibitions

E.g. Winter (2002)

Better data structure then ‘node expansion’

Complexity for SP worse then using turn tablesO (n log n) vs. O (e log e)

14

G-Day Gent 9 November 2005 14

Road Network

Adding Turn Cost and Prohibitions

E.g. Winter (2002)

Advantages vs. Normal representation

Round tours Cycles

15

G-Day Gent 9 November 2005 15

Road Network

Adding Turn Cost and Prohibitions

E.g. Winter (2002)

Advantages vs. Normal representation

U- turns

16

G-Day Gent 9 November 2005 16

Road Network

Adding Turn Cost and Prohibitions

E.g. Winter (2002)

Problem concerning specific turns (U-turns)

Winter : Splits Nodes (one lane = one node)

Doubles number of nodes

17

G-Day Gent 9 November 2005 17

Road Network

Adding Turn Cost and Prohibitions

E.g. Winter (2002)

Problem concerning specific turns (U-turn)

Winter : Splits Nodes (one lane = one node)

Doubles number of nodes

18

G-Day Gent 9 November 2005 18

Road Network

Adding Turn Cost and Prohibitions

Possible solution

• Using TurnTables in Combination with the line graph

19

G-Day Gent 9 November 2005 19

Road Network

Adding Turn Cost and Prohibitions

Possible solution

Turn Table: Defines Line * Line graph

20

G-Day Gent 9 November 2005 20

Conclusions and Future Work

ConclusionPossible solution

Combining the advantages of Line Graph and Turn Tables

Levels in Topologic relations with line graph

Future WorkImplementing the different structures and comparing the different ‘real life’ calculation times

21

A New Data Structure to Represent Road Networks

Bogaert, P., Van de Weghe, N., Maddens, R., De Temmerman, L., De Maeyer, P.

Ghent University

Thanks

Q/A?