Università degli Studi dell'Aquila
Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica
Via Vetoio, Località Coppito, 67010 L'AQUILA


COURSE PROGRAM
Distributed Systems
A.Y. 2022/23 Prof. Guido Proietti

 


Introduction

September 27, 2022: Message Passing System (MPS). Synchronicity, symmetry, uniformity, anonymity. Example: distributed Depth First Search tree computation.

Slides: Introductory elements

 

PART I: Algorithms for COOPERATIVE Distributed Systems (DS)

1. Leader Election

September 29, 2022: Leader election in rings. Sense of direction. Impossibility for the anonymous case. The Chang & Roberts algorithm.

October 4, 2022: The Hirschberg & Sinclair algorithm. Leader election in synchronous non-uniform rings with synchronized start.

October 6, 2022: Leader election in synchronous uniform rings: the Frederickson & Lynch algorithm. Leader election in general topologies (summary of results).

October 11, 2022: Again on the Frederickson & Lynch algorithm: counting the number of slow messages when the leader is sleeping. Exercise: execution of the slow-fast algorithm and pseudo-code generation.

Slides: Leader election

 

2. Minimum Spanning Tree

October 13, 2022: The Minimum Spanning Tree (MST) problem for non-anonymous arbitrary topologies. Preliminary lemmas. Asynchronous and synchronous distributed version of the Prim sequential algorithm.

October 18, 2022: High-level description of the Borůvka sequential algorithm. Synchronous version of the Gallager, Humblet e Spira (GHS) algorithm. Correctness and time/message complexity analysis.

October 20, 2022: Asynchronous version of the GHS algorithm. Correctness and time and message complexity analysis.

Slides: MST

October 25, 2022: Exercise: execution of the GHS algorithm in a pseudo-synchronous system.

Slides: GHS execution

 

3. Some classic NP-hard problems: Maximal Independent Set, Minimum Dominating Set, and Vertex Coloring

October 27, 2022: The Maximal Independent Set (MIS) problem. A sequential and a generalized greedy algorithm for finding a MIS. A randomized distributed algorithm for finding a MIS with O(D log n) rounds w.h.p.

Slides: MIS

November 3, 2022 (Dott. Stefano Leucci): The Luby’s algorithm for finding a MIS with O(logD log n) rounds w.h.p.

Slides: Luby

November 8, 2022: Network monitoring: the 1-node-failure problem. Hardness of the Minimum Dominating Set (MDS) problem. The O(log n)-approximation ratio greedy centralized algorithm for MDS, and its distributed version. Notable cases: unit-disk graphs and planar graphs.

Slides: Network monitoring

November 10, 2022: The Vertex Coloring problem. A (D+1)-coloring algorithm based on the Luby’s algorithm. A 2D-coloring algorithm running w.h.p. in O(log n) rounds.

Slides: Vertex coloring

 

Mid-term exam: November 17, 2022 at 14.30 in Room A1.3.

 

PART II: Algorithms for CONCURRENT DS: Mutual exclusion

November 22, 2022 (Dott. Mattia D’Emidio): Shared-memory model. The mutual exclusion (mutex) problem. The mutex problem with Read/Write registers. The bakery algorithm. Waiting boundedness, unboundedness of the register values.

November 24, 2022 (Dott. Mattia D’Emidio): Mutex algorithm for 2 processors with bounded register values. Extension to the case of n processors: the tournament tree algorithm.

Slides: Mutex.

 

PART III: Algorithms for UNRELIABLE DS: The consensus problem

November 29, 2022: Fault-tolerance in MPSs: the consensus problem.  Link failures: the 2-general problem. Node crash failures: (f+1)-rounds algorithm for f crash failures. Lower bound for f crash failures.

December 1, 2022: Byzantine failures: the King algorithm. Exercise: failing execution of the King algorithm with n=4 and f=1.

Slides: Consensus (Part I) .

December 6, 2022: Byzantine failures: impossibility with 3 processors out of which one is Byzantine. General impossibility result. Exponential-Gathering Information (EGI) algorithm: the auxiliary tree data structure.

December 13, 2022: Exercise: failing execution of the EGI algorithm with n=3 and f=1. Correctness and analysis of the EGI algorithm.

December 15, 2022: Randomized Byzantine consensus. Exercise: Non-termination of the randomized protocol with n=9 and f=1.

January 10, 2023: Consensus in the shared-memory model: impossibility result for the Read-Write type variable.

Slides: Consensus (Part II) .

 

PART IV: Distributed methods of payment

December 16, 2022: The distributed ledger problem. Cryptographic elements of Bitcoin: Hash functions, One-way functions, Cryptographic hash functions and attacks, Digital Signatures.  Drawbacks of a centralized implementation. Architecture of Bitcoin: Addresses, Wallets, Transactions, Blocks and the Blockchain. Mining and the Proof-of-Work idea. Lightweight (SPV) nodes and proof of inclusion using Merkle trees.

Slides: Bitcoins (Part I)

December 21, 2022: Advanced issues on the Bitcoin protocol. Blockchain forks and their resolution. Miners and incentives. The Double-Spend attack, the 51% attack. Consistency and eventual consistency in the distributed ledger problem. Bitcoin as a repeated consensus problem. Fault-tolerance aspects: crash failures, and byzantine failures. The sybil attack. The Fair Consensus problem and a solution through randomized leader election. Strategic aspects: rational selfish failures, the Rational Fair Consensus problem, equilibria concepts, selfish mining.

Slides: Bitcoins (Part II)