Fault tolerance and related issues in distributed computing Shmuel Zaks GSSI - Feb 20161

2 Haifa

GSSI - Feb CS, Technion

Part 0: Part 0: Distributed computing – an overview: basic notions; seminar focus: from lower bounds, via impossibility, to fault tolerance and self-stabilization. Part 1: Part 1: Lower bounds Part 2: Part 2: Computing in spite of faults - impossibility of consensus Part 3: Part 3: Detecting faults - the snapshot algorithm Part 4: Self-stabilization - Self recovery from faults GSSI - Feb 20164

Part 0: Part 0: An overview Part 1: Part 1: Lower bounds Part 2: Part 2: Computing in spite of faults Part 3: Part 3: Detecting faults Part 4: Part 4: Self-stabilization GSSI - Feb 20165

processors communication problem Communication network GSSI - Feb A. The model

Anonymous GSSI - Feb 20167

12 a e 6 c Unique identities GSSI - Feb 20168

d a e b c message passing communication lines, channels topology communication GSSI - Feb 20169

ab c d e directed, undirected (message passing) GSSI - Feb

 message delivery mechanism  fifo  reliable, no faults  finite, arbitrary delay  queues of messages (message passing) GSSI - Feb

Distributed algorithm, protocol  Send a message  receive a message  do local computation GSSI - Feb (message passing) Execution

R4R4 GSSI - Feb R1R1 R2R2 R3R3 R5R5 e a b d c shared memory

A B read/write (shared memory) GSSI - Feb

synchronization Synchronous, Asynchronous d a e b c GSSI - Feb

Asynchronous Model GSSI - Feb ij time t+???time t Clock Network (synchronization)

Synchronous Model GSSI - Feb ij time t+dtime t Clock Network (synchronization)

Asynchronous Model - many executions GSSI - Feb Synchronous Model - unique execution rounds (synchronization)

Asynchronou s GSSI - Feb Synchronous Shared memory Message passing (synchronization)

GSSI - Feb Asynchronous model: for correctness, for upper bound analysis Synchronous model: for lower bound analysis

Topology GSSI - Feb Ring d a e b c

Clique d a e b c (Topology) GSSI - Feb

General (Topology) GSSI - Feb

Why simple networks? They enable the understanding of many design issues In existing general networks – assume a virtual simple network implemented (e.g. a ring) (Topology) GSSI - Feb

Complexity measures GSSI - Feb  Synchronous system  time  Asynchronous system  communication  communication (messages, bits)  time (synchronous time, longest chain, bounded delay)

Parallel vs. Distributed computing Parallel computing – given a problem … (ex: sorting) Distributed computing – Given a network … (ex: broadcast) GSSI - Feb

(Parallel vs. Distributed computing( Parallel computing : time vs. number of processors Distributed computing: number of messages Complexity goals: Parallel computing: efficiency Distributed computing: correctness GSSI - Feb

problem, task P1P1 P2P2 P3P3 input output Leader election yes no consensus GSSI - Feb b. Problems

issues GSSI - Feb  design and analysis of algorithms  impossibility, lower bounds  fault tolerance

problems GSSI - Feb  broadcast  snapshot  consensus  shortest path, maximal flow  leader election, breaking symmetry, maximum finding, spanning tree, center  termination  deadlock

Example: broadcast GSSI - Feb d a e b c f

Broadcast: bfs (breadth-first-search) GSSI - Feb d a e b c f

Broadcast: dfs (depth-first-search) GSSI - Feb d a e b c f

message complexity  each edge carries exactly one message at each direction  message complexity is 2|E| GSSI - Feb

time complexity GSSI - Feb synchronous time 2|E| longest chain 2|E| bounded delay 2|E|

pi (propogation of information), shout-echo GSSI - Feb d a e b c f

Algorithm pi ( p ropogation of i nformation) send m to each neighbour stop GSSI - Feb if receive m along edge e: send m on all edges except e stop

pi Theorem: The following holds for every execution of the pi algorithm: A processor receives the message m at most once. The execution terminates. each processor receives the message m. The edges on which processors receive m form a spanning tree. The message complexity is 2|E|-|V|+1. The time complexity … GSSI - Feb

pif (propogation of information with feedback) shout-echo GSSI - Feb d a e b c f

Distributed algorithms “Positive” results: design, analysis, upper bounds “Negative” results: lower bounds, impossibility GSSI - Feb c. In this seminar

P1P1 P2P2 P3P3 input output Leader election yes no GSSI - Feb Part 1: Part 1: Lower bounds

GSSI - Feb message passing asynchronous ? x x x x Leader election

GSSI - Feb We’ll see: a lower bound of Ω (n log n) messages

GSSI - Feb d a e b c f Lower bound and fault tolerance Usually all processors need to compute some function Lower bound of Ω(|E|) g

problem, task P1P1 P2P2 P3P3 input output consensus GSSI - Feb Part 2: Part 2: Computing in spite of faults

message passing asynchronous Consensus GSSI - Feb We’ll see: impossibility to reach consensus.

GSSI - Feb Snapshot Part 3: Part 3: Detecting faults

GSSI - Feb We’ll see: snapshot algorithm.

GSSI - Feb Example: clock synchronization Part 4: Self-stabilization

GSSI - Feb

4 Let’s try … GSSI - Feb

4 But … GSSI - Feb

GSSI - Feb We’ll see: self stabilizing algorithms, proofs and performance analysis.