Class on Distributed Algorithms

 

Class number

202-2-5811

Schedule

Sun. 12:00-14:00, 34/205, Thurs. 10:00-12:00, 34/103.

Office hours

Mine: Tue. 14:00-16:00 (Bldng 37, room 217),

Outline

The class is devoted to the theory of distributed algorithms in the message-passing model. The network is modeled by a graph, the processors of the network reside in the vertices of the graph, and the edges of the graph serve as an abstraction of communication links. The aim is to design distributed algorithms that solve graph problems on the infrastructure network.

General information

The grade of the course will be set as the weighted average of the grade for the presentation of one of the topics below in class, notes from somebody's else presentation (80% together), and homework assignments (20%). There will be 4-8 homework assignments during the course. Students are allowed not to submit one of those assignments. Assignments are for individual submission (submissions by groups of 2 and more students will not be accepted).

Syllabus

The design of distributed algorithms is an active area of research. It has multiple applications in the areas of Communication Networks (particularly, for Internet programming) and Distributed Systems. From theoretical standpoint, the area is a natural extension of the classical algorithmic theory, and its study has provided significant advances in our understanding of such basic concepts as Locality and Randomization. The course will concentrate on the theory of distributed algorithms. Particular focus will be given to the model in which the processors share no common memory. The specific topics that will be covered (with possible variations due to time limitations, and the desires of the audience) are:

1) The definition of the model, and of the complexity measures in this model.

2) Basic algorithms: broadcast, convergecast, downcast, upcast, breadth-first-search tree construction, upcast-based MST (minimum-weight spanning tree) construction.

3) The issue of synchronization, basic synchronizers (alpha and beta).

4) Upper and lower bounds on the complexity of vertex coloring and maximal-independent-set problems. This topic will be very central in the course.

5) Routing.

If time permits:

6) The theory of graph decomposition, and its application to distributed computing.

7) Spanners, distance-labeling, more advanced routing.

8) Gallager-Humblet-Spira MST construction.

9) More advanced synchronization (gamma, delta, and beyond).

The discussion will be conducted from mathematical perspective, trying to provide rigorous proofs wherever possible along with the intuition. The class will be self-contained, but will assume some basic knowledge of algorithmics and discrete mathematics.

Topics for Presentation

A paper by D. Peleg and V. Rubinovich
Lower Bounds for the Minimum Spanning Tree problem

My paper on constructing spanners in streaming and distibuted models
Streaming and Distributed Algorithm for Constructing Spanners


A paper of Thorup and Zwick about distributed routing
Compact Routing Schemes,

A paper by Barenboim, Pettie, Schneider and myself:
The Locality of Distributed Symmetry Breaking
A part of this paper would be enough for a presentation.

Bibliography

The book of David Peleg, Distributed Computing: a Locality-Sensitive Approach, SIAM, Philadelphia, PA, 2000.
SIAM web-page of the book

The monograph of Leonid Barenboim and myself:
Distributed Graph Coloring: Fundamentals and Recent Developments

Papers by L. Barenboim and myself that will be used in the second part of the course:

Sublogarithmic Distributed MIS Algorithm for Sparse Graphs Using Nash-Williams Decomposition,
Distributed Computing, special issue of PODC'08, vol. 22, pp. 363-379, 2010 ,

Distributed (Delta+1)-Coloring in Linear (in Delta) Time,
In Proc. Symp.
on Theory of Computing, STOC'09, pp.111-120, Bethesda, MD, 2009.

Deterministic Distributed Coloring in Polylogarithmic Time. In Proc. of International Symp. on Principles of Distributed Computing, PODC'10, pp. 410-419 Zurich, Switzerland, July 2010.

Lecture Notes of Ariel Sapir


Lectures 1-2
Lectures 3-4
Lectures 5-7
Lectures 8-9
Lectures 14-17
Lectures 18-21
Lectures 22-24

Assignments, Home Exam



Assignment 1, Due to 20/11/17

Solutions to Assignments


Solution 1
Solution 2
Solution 3
Solution 4

Exercises


Exercises from David Peleg's book

Exam, Moed Aleph


Moed Aleph

Moed Bet


Moed Bet

Solution to Moed Aleph


Solution to Moed Aleph

Solution to Moed Bet


Solution to Moed Bet

Latex

Latex is a program for scientific writing. Using special symbols one can write an ascii file, compile it with a latex-compiler (type "latex" from unix command-line), and get a nice postscript with all sorts of mathematical formulae. For more information see:
An online manual of latex
An example of a paper written in Latex

Exam (Feb. 2014) - Moed Aleph


The exam (pdf format)
A solution to moed aleph (pdf)

Exam (Feb. 2014) - Moed Bet


The exam (pdf format)
A soution to moed bet (pdf)

Exam (Feb. 2013) - Moed Aleph


The exam (pdf format)
A solution (pdf format)

Exam (March 2013) - Moed Bet


The exam (pdf format)
A solution (pdf format)

Exam (Jan. 2012) - Moed Aleph


The exam (pdf format)
A solution (pdf format)

Exam (Feb. 2012) - Moed Bet


The exam (pdf format)
A solution (pdf format)

Exam (Jan. 2011) - Moed Aleph


The exam (pdf format)
A solution (pdf format)

Exam (Jan. 2011) - Moed Bet


The exam (pdf format)
A solution (pdf format)

Exam (Feb. 2010) - Moed Aleph


The exam (pdf format)
A solution (pdf format)

Exam (Feb. 2010) - Moed Bet


The exam (pdf format)
A solution (pdf format)

Exam (March 09) - Moed Aleph


The exam (pdf format)
A solution (pdf format)

Exam (May 09) - Moed Bet


The exam (pdf format)
A solution (pdf format)

Exam (Feb. 07) - Moed Aleph


The exam (Word document)
A solution (pdf format)

Exam (Feb. 07) - Moed Bet


The exam (Word document)
A solution (pdf format)

Exam (Feb. 06) - Moed Aleph


The exam (pdf format)
A solution (pdf format)

Exam (Feb. 05) - Moed Aleph


The exam (pdf format)
A solution (pdf format)
A correction to the solution of question 3b (eml format - outlook message)

Exam (Feb. 05) - Moed Bet


The exam (pdf format)
A solution (pdf format)

Links to web-sites of previous years


The webpage of the class of Autumn 2016
The webpage of the class of Autumn 2014
The webpage of the class of Autumn 2013
The web-site of the class of Autumn 2012
The web-site of the class of Autumn 2011
The web-site of the class of Autumn 2010
The web-site of the class of Autumn 2009
The web-site of the class of Autumn 2008
The web-site of the class of Autumn 2006
The web-site of the class of Autumn 2005
The web-site of the class of Autumn 2004