1 / 11

Overview of Shortest Path Algorithms: Bellman-Ford and Dijkstra Methods in Routing

This resource provides a comprehensive outline of shortest path algorithms used in routing, including the Bellman-Ford and Dijkstra methods. It discusses the objectives of finding the shortest path between nodes in a graph, introduces dynamic programming concepts, and explains adaptive and QoS routing techniques. Examples and illustrations clarify how dynamic routing techniques can optimize paths based on congestion and quality of service parameters such as delay and bandwidth. Understanding these algorithms is crucial for efficient network routing design.

lani-cardenas
Télécharger la présentation

Overview of Shortest Path Algorithms: Bellman-Ford and Dijkstra Methods in Routing

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Routing Jean Walrand U.C. Berkeley www.eecs.berkeley.edu/~wlr

  2. Outline • Shortest Path • Objective • Bellman-Ford • Dijkstra • Adaptive Routing • QoS Routing

  3. 3 4 1 4 3 D S 3 2 4 1 Shortest Path • Objective: Find shortest path between two nodes (e.g., S and D) in a graph • Example: • Note: Myopic shortest path is not optimal!

  4. Shortest Path - Continued • “Dynamic Programming” or Bellman-Ford: 3 3 4 4 7 4 1 1 4 4 3 3 D D S S 3 3 3 2 2 7 4 4 1 1 5 5 = min{3 + 3, 4 + 1} 1 7 = min{1 + 7, 2 + 5}

  5. Shortest Path - continued • Dijkstra: 3 4 4 1 8 7 1 5 4 3 D S 3 5 2 4 1 2 6

  6. Dynamic Routing • Base route on “congestion” • Example: 0.4ms 0.2ms 0.5ms 0.25ms 0.3ms 0.1ms 0.1ms

  7. 0.8ms 0.1ms 0.1ms 0.8ms Dynamic Routing - continued • Difficulty: Oscillations

  8. Shortest length = A a b Shortest length = B Quality of Service Routing • Shortest Path: Single Additive “Cost” length(path) = sum of length(link) Shortest length = min{a + A, b + B}

  9. Max. bw = A a b Max. bw = B Quality of Service Routing (cd) • Maximum Bandwidth bandwidth(path) = minimum of bandwidth(link) Max bw = max{min{a, A}, min{b, B}}

  10. Quality of Service Routing (cd) • Multi-objective: e.g., (delay, bw) (min. d = 3, max. bw = 10) (min. d = 3, max. bw = 10) or (min. d = 6, max. bw = 15) (min. d = 6, max. bw = 15)

  11. Better bw A D B C Better d Quality of Service Routing (cd) [Min d, Max bw] • Example [12, 20] [7, 10] (d, bw) (8, 30) A [16, 18] B [11, 10] C [10, 10] D [13, 14] (4, 20) (4, 18) (4, 12) (3, 10) D (5, 15) (2, 14) (7, 30) [8, 10] [11, 20] (4, 20)

More Related