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IS 2610: Data Structures

IS 2610: Data Structures

IS 2610: Data Structures. Graph April 5, 2004. Graph Terminology. Graph : vertices + edges Induced subgraph of a subset of vertices Connected graph: a path between every pair Maximal connected: there is no path from this subgraph to an outside vertex. Representation.

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The Shortest Path problem in graphs with selfish edges

The Shortest Path problem in graphs with selfish edges

The Shortest Path problem in graphs with selfish edges. Recap. VCG- mechanism : pair M=< g,p > where g( r ) = arg max y ? X ? i v i ( r i ,y ) p i (g( r )) = - ? j ? i v j ( r j ,g ( r - i )) + ? j ? i v j ( r j ,g ( r ))

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287 views • 27 slides
The Shortest-Path problem in graphs with selfish-edges

The Shortest-Path problem in graphs with selfish-edges

The Shortest-Path problem in graphs with selfish-edges. f(t,x) : The length of a path w.r.t. the true edge costs. Buying a path in a network. F : set of all paths between s and z. Mechanism. decides the path and the payments. t 1. t 2. t e : cost of edge e. t 6. t 4. z. t 5.

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284 views • 27 slides
The Shortest-Path problem in graphs with selfish-edges

The Shortest-Path problem in graphs with selfish-edges

The Shortest-Path problem in graphs with selfish-edges. The selfish-edges SP problem.

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342 views • 26 slides
Minimum Spanning Trees

Minimum Spanning Trees

Minimum Spanning Trees. Minimum Spanning Trees. Create a Tree that connect all vertices If is weight between u and v , then: Our job: minimize w ( T ) We can use a greedy approach. General Proof for MSTs. General idea for loop invariant:

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460 views • 25 slides
The selfish-edges Shortest-Path problem

The selfish-edges Shortest-Path problem

The selfish-edges Shortest-Path problem. The selfish-edges SP problem.

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355 views • 25 slides

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