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

G-DayGent9 November Modelling Real World Virtual World

G-DayGent9 November Modelling Minimize data storage Fast answer Resemble real-life as much as possible

G-DayGent9 November 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

G-DayGent9 November Road Network Spatial problems : Graph theoretical problems A Shortest path Travelling Salesman problem (visit all nodes) Chinese Postman problem (visit all edges) Etc.

G-DayGent9 November Road Network Mapping of a road network onto a graph Nodes : intersections and endpoints Edges : connections between intersections and endpoints

G-DayGent9 November Road Network Adding Direction (Different Costs, OneWay) By means of a Directed Graph : D(N,E,c)

G-DayGent9 November Road Network Adding Turn Cost and Prohibitions Cadwell (1961), Kirby and Potts(1969) node expansion (Directed or not)

G-DayGent9 November 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))

G-DayGent9 November Road Network Adding Turn Cost and Prohibitions e.g. Jiang et al. By Using 'Turn Tables ’ For Shortest path same complexity O(nlogn)

G-DayGent9 November Road Network Adding Turn Cost and Prohibitions E.g. Winter (2002) Using a line graph

G-DayGent9 November Road Network Adding Turn Cost and Prohibitions Difference in Navigation Winter Turn Tables

G-DayGent9 November Road Network Adding Turn Cost and Prohibitions E.g. Winter (2002) Better data structure then ‘ node expansion ’ Complexity for SP worse then using turn tables O (n log n) vs. O (e log e)

G-DayGent9 November Road Network Adding Turn Cost and Prohibitions E.g. Winter (2002) Advantages vs. Normal representation Round toursCycles

G-DayGent9 November Road Network Adding Turn Cost and Prohibitions E.g. Winter (2002) Advantages vs. Normal representation U- turns

G-DayGent9 November 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

G-DayGent9 November 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

G-DayGent9 November Road Network Adding Turn Cost and Prohibitions Possible solution Using TurnTables in Combination with the line graph

G-DayGent9 November Road Network Adding Turn Cost and Prohibitions Possible solution Turn Table: Defines Line * Line graph

G-DayGent9 November Conclusions and Future Work Conclusion Possible solution Combining the advantages of Line Graph and Turn Tables Levels in Topologic relations with line graph Future Work Implementing 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?