1. Lecture #18Distributed Algorithms (VI) CS492 Special Topics in Computer Science: Distributed Algorithms and Systems

2. Admin Stuff

3. Chapter 4 Algorithms in General Synchronous Networks

4. Minimum Spanning Tree (MST) Distributed algorithm for constructing an MST in an arbitrary weighted undirected graph

6. At level 0 • components with individual nodes and no edges • At level k • each process knows the UID of the leader • this UID is the identifier of the component • each process also knows which of its incident edges are in the component’s tree

7. At level k+1 • each level k component conducts a search along its spanning tree edges for MWOE (minimum-weight outgoing edge) • among its incident edges, each process finds the one with minimum weight that is outgoing from the component; by sending test messages along all non-tree edges, asking whether or not the other end is in the same component • then processes “convergecast” this local minimum-weight edge toward the leader

8. Leader election at merger • the new leader is the endpoint of the newly added edge having the larger UID • this new UID is broadcast to the entire component

9. Complexity Analysis Number of levels? Time complexity? Communication complexity?

10. Non-unique edge weights?

11. Maximal Independent Set • Definition: • A set of nodes is called an independent set if it contains no pair of neighboring nodes • An independent set is maximal if it cannot be increased to form a larger independent set by the addition of any other nodes

12. Motivation for MIS?

13. Basic Idea

14. Formal Statement of the Problem

19. Randomized algorithms Benefits