Homepage of the class in Distributed Algorithms

Class on Distributed Algorithms

Class number

202-2-5811

Schedule

Sun. 12:00-14:00, Zoom, Tue. 14:00-16:00, Zoom.

Office hours

Mine: Tue. 10:00-12:00 (Zoom)

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 exam (a one-day long examination, open-material) (80%), 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 or 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.
A 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, (not ready yet) Due to ??
Assignment 2, (not ready yet) Due to ??
Assignment 3, (not ready yet) Due to ??
Assignment 4, (not ready yet) Due to ??

Solutions to Assignments

Solution 1
Solution 2
Solution 3
Solution 4

Exercises

Exercises from David Peleg's book

Exam, Moed Aleph

Moed Aleph (not ready yet)

Moed Bet

Solution to Moed Aleph

(not ready yet) Solution to Moed Aleph

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

Class on Distributed Algorithms

Class number

Schedule

Office hours

Outline

General information

Syllabus

Topics for Presentation

Bibliography

Lecture Notes of Ariel Sapir

Assignments, Home Exam

Solutions to Assignments

Exercises

Exam, Moed Aleph

Moed Bet

Solution to Moed Aleph

Solution to Moed Bet

Latex

Exam (Feb. 2014) - Moed Aleph

Exam (Feb. 2014) - Moed Bet

Exam (Feb. 2013) - Moed Aleph

Exam (March 2013) - Moed Bet

Exam (Jan. 2012) - Moed Aleph

Exam (Feb. 2012) - Moed Bet

Exam (Jan. 2011) - Moed Aleph

Exam (Jan. 2011) - Moed Bet

Exam (Feb. 2010) - Moed Aleph

Exam (Feb. 2010) - Moed Bet

Exam (March 09) - Moed Aleph

Exam (May 09) - Moed Bet

Exam (Feb. 07) - Moed Aleph

Exam (Feb. 07) - Moed Bet

Exam (Feb. 06) - Moed Aleph

Exam (Feb. 05) - Moed Aleph

Exam (Feb. 05) - Moed Bet

Links to web-sites of previous years