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TD2 ALGORES MIS-DS-Matching-BFS

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Exercise 1 : Centralized MIS-DS-Matching

1. Recall the definition of a MIS, a DS and a (Maximal) Matching.

1. Recall the centralized implementations of MIS, DS and Maximal Matching and discuss their complexity.

Exercise 2 : Distributed MIS-DS-Matching

1. Recall the distrbuted implementation of MIS seen in class. Compute its complexity (time + messages). Is this algorithm working for ring topologies ?

2. Propose a distributed MIS algorithm for trees (different from the one seen in class). Evaluate the complexity of your algorithm.

3. Propose a solution for constructing connected dominating sets given a MIS.

4. Propose a solution for Maximal Matching different from the one seen in class and compute its complexity.

Exercise 3 : BFS

1. Write the pseudo-code of the protocole «Dijkstra-like».

2. Write the pseudo-code of the protocole «Bellman-Ford».

3. Execute both protocols on the topology proposed on figure below.

Exercise 4 : Edge coloring

1. Propose a distributed algorithm for solving the edge coloring problem (no two adjacent edges in a graph have the same color). Compute its complexity !

2. Discuss practical applications of this problem !

TD2 ALGORES

MIS-DS-Matching-BFS

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