Spatial Research Group Presentation

Professor Ramnath-Bhavtosh Rath

1- What is the problem?To find the shortest path in a directed graph.Implementing Dijkstra's algorithm on a time-dependent network, where every node has a different travel time depending on when the traveller enters the edge.

2 – Why is it important?

• Application in the transportation sector

- Which path to choose from a given set of paths?- When to choose a specific path?

Concept could be applied to any network that suffers from time-dependent congestion problem .

3 – Why is it hard ?

• We have a large search space and need to navigate through this efficiently.

4- What are limitations of related work?

• Continuous approach does not prove bounds on the size of the structures created during search.

• Discrete approach does not act simultaneously on space and time.

5- What is the proposed approach?

Input :1. A graph G with a set of nodes ‘V’

and a set of edges ‘E’.2. Travel_time_series associated with

each edge.

Output:Quickest path to reach from start node to destination, for every time_slot.

Algorithm approach:

Step1 : Generate labels for all the nodes connected to the Start node. (i.e. s)

To do this, check the Travel_time_series associated with all edges beginning from the start node.

Add the Time_slot value with corresponding Travel_time_series values.

Step 2: Iteratively generate labels from the labels with least time_series generated so far.

Algorithm.

6 – Why is it novel and better ?

• Brings us closer to the idea of not exploring unnecessary paths.

7 – Validation Design ?

• Implement algorithm and compare wth Dijkstra for all start times.

• Parameters to be considered : Length of time series Desired accuracy Frequency with which travel time changes.

(The two algorithms will be tested for different values of these parameters).

Questions / Comments ?