single source shorest path
- 2. Approach Dijksra’s Algorithm Use Application Improvements Advantages Disadvantages In Future
- 3. Dijkstra’s algorithm: -- Solving only problem with non-negatives cost. Floyd- Warshall and Bellman-Ford algorithm solve the problem on graphs that do not have a cycle with negative cast.
- 4. TIME COMPLEXITY O(E + V Log V) O(E) AUTHOR Dijksra’s 1959 Tharp (required constant-time Multipulication)
- 6. X YS Shortest distance from S to all nodes initially ”unsettled”. Shortest distance to S is zero. Tentative distance to other is ∞. Put all nodes in Queue ordered by tentative distance from S.
- 7. Take out nearest unsettled node, X settle its distance Y of x. If going from S to Y through X is shortest than shortest path through settled nodes, updates tentative distance to Y. Repeat from step-4 until distance to Y to destination is settled. EXAMPLE: Google map, Road Routing
- 8. Head sort requires only space of one record, quick sort o(log n) and merge sort requires o(n) node J&T(v) represent the label of node o to end n. The cost from node o to D is the sum of cost WOA and cost W. Reuse Dijkstra’s Algorithm to get optional path SPAD from A to D node.
- 9. Find Shortest path in o(E + V log(V)) if you use a minpriority Queue. This is true only if you implement priority queue with Fibonacci heap, then o(1). Otherwise, if you use any other implementation of priority-queue. If should take , E log(E)+V.
- 10. Fails in cases where you have a negative edges. It has a blind searching method for this it take a huge amount of time.
- 11. For a dance graph it is: O{E + (V*V)} For a Sparse graph it is: O{E + (V log V)}
- 12. Using in mapping. Using in city distance measurement. Traffic criteria management. Will use in networking station distance. Will use in space distance measurement.
- 13. The compute time complexity for each of the Dijkstra’s Algorithm are acceptable in items of their overall performance in solving the shortest path problem. All of algorithm produce only one solution.
- 14. THANK YOU!!!