Università degli Studi dell’Aquila Academic Year 20 10 /20 11

1. Università degli Studi dell’Aquila Academic Year 2010/2011 Course: Algorithms for Distributed Systems Instructor: Prof. Guido Proietti Time: Monday: 11.45 – 13.15 – Room 2.5 Wednesday: 11.45 – 13.15 – Room 2.5 Questions?: Wednesday 16.00-17.00 Slides plus other infos: http://www.di.univaq.it/~proietti/didattica.html

2. Distributed System • Set of computational devices connected by a communication network. • Old platform : Usually a number of WSs over a LAN • Now, ranges from a LAN to a sensor network to a mobile network • Each node in a DS : • is autonomous • communicates by messages • needs to synchronize with others to achieve a common goal (load balancing, fault tolerance, an application…)

3. Modern Distributed Applications • Collaborative computing • Military command and control • Online strategy games • Massive computation • Distributed Real-time Systems • Process Control • Navigation systems, Airline Traffic Monitoring (ATM) Mobile Ad hoc Networks Rescue Operations, emergency operations, robotics Wireless Sensor Networks Habitat monitoring, intelligent farming Grid Stock market …

4. The Internet

5. Some Issues in Building Distributed Applications • Reliability (connectivity) • Security (cryptography) • Consistency (mutual exclusion) • Cooperativeness (game theory) • Fault-tolerance (failures, recoveries…) • Performance: What is the efficiencyof the designed algorithm? • Scalability: How is the performance affected as the number of processors increase ?

6. Course structure • FIRST PART: Algorithms for COOPERATIVE DS • Leader Election • Minimum spanning tree • Maximal independent set • SECOND PART: Algorithms for UNRELIABLE DS • Benign failures: consensus problem • Byzantin failures: consensus problem • THIRD PART: Algorithms for CONCURRENT DS • Mutual exclusion • Mid-term Written Examination:Last week of November • FOURTH PART: DS SECURITY • Elements of cryptography • FIFTH PART: Algorithms for NON COOPERATIVE (STRATEGIC) DS • Strategic equilbria theory • Algorithmic mechanism design (AMD) • AMD for Graph optimization problems • SIXTH PART (???): Algorithms for WIRELESS DS • Final Oral Examination: depending of the mid-term rate

7. Cooperative distributed algorithms: Message Passing System A Formal Model

8. The System • Topology: a network (connected undirected graph) • Processors (nodes) • Communication channels (edges) • Degree of synchrony: asynchronous versus synchronous (universal clock) • Degree of symmetry: anonymous (processors are indistinguishable) versus non-anonymous • Degree of Uniformity: uniform (number of processors is unknown) versus non-uniform Local algorithm: the algorithm associated to a single processor Distributed algorithm: the “composition” of local algorithms

9. Notation • n processors: p0, p1, … , pn-1. • Each processor knows nothing about the network topology, except for its neighbors, numbered from from 1 to r • Communication takes place only through message exchanges, using buffers associated with each neighbor, namely outbufi[k], inbufi[k], i=1,…,r. • qi: the state set for pi, containing a distinguished initial state; each state describes the internal status of the processor and the status of the buffers

10. Configuration and events • System configuration: A vector [q0,q1,…,qn-1] where qi is the state of pi • Events: Computation events (internal computations plus sending of messages), and message delivering events

11. Execution C01 C1 2 C2 3 … where • Ci : A configuration • i : An event • C0 : An initial configuration

12. Asynchronous Systems • No upper bound on delivering times • Admissible execution: each message sent is eventually delivered

13. Synchronous Systems • Each processor has a (common) clock, and computation takes place in rounds. • At each round each processor: • Reads the incoming messages buffer • Makes some internal computations • Sends messages which will be read in the next round.

14. Message Complexity • The total number of messages sent during any admissible execution of the algorithm (in other words, the number of delivery events). • However, the size of a message will count as well…

15. Time Complexity • Synchronous: The number of rounds until termination. • Asynchronous: not really meaningful

16. Example:Distributed Depth-First Search • General overview of a sequential algorithm: • Begin at some source vertex, r0 • when reaching any vertex v • if v has an unvisited neighbor, then visit it and proceed from it • otherwise, return to parent(v) • when we reach the parent of some vertex v such that parent(v) = NULL, then we terminate since v = r0 • DFS defines a tree, with r0 as the root, which reaches all vertices in the graph • “back edges” = graph edges not in tree • sequential time complexity = O(|edges|+|nodes|)

17. DFS: an example (1/2)

18. DFS: an example (2/2)

19. Distributed DFS (cont’d.) • Distributed version (token-based): the token traverses the graph in a depth-first manner using the algorithm described above • Start exploration (visit) at a waking-up node (root) r. • When v is visited for the first time: 2.1 Inform all neighbors of v that v has been visited. 2.2 Wait for acknowledgment from all neighbors. 2.3 Resume the DFS process. 2.4 If no undiscovered node exists, then pass token to the parent node • Message complexity is O(|E|) (optimal, because of the lower bound of (|edges|) to explore every edge) • note that edges are not examined from both endpoints; when edges (v,w) is examined by v, w then knows that v has been visited

20. Distributed DFS (cont’d.) • Time complexity analysis (sync. DS) We ensure that vertices visited for the first time know which of their neighbors have/have not been visited; thus we make no unnecessary vertex explorations: • algorithm: freeze the DFS process; inform all neighbors of v that v has been visited; get Ack messages from those neighbors; restart DFS process  constant number of rounds (i.e., 2) for each new discovered node • only O(n) nodes are discovered  time complexity = O(n)