Understanding Computer Science: Algorithms, Distributed Systems, and Clock Synchronization, Study notes of Computer Science

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Distributed Computing

Presentation to CPSC 181 October 2008 Prof. Jennifer L. Welch Parasol Lab & Department of Computer Science Texas A&M University

Outline

 Centrality of notion of algorithm  What is an algorithm?  Designing and analyzing algorithms  Understanding lower bounds and impossibility results  Distributed systems  Some sample distributed algorithms

• clock synchronization
• routing based on link reversal

What is Computer Science?

 Brookshear: "Computer Science is the

discipline that seeks to build a scientific

foundation for such topics as computer

design, computer programming, information

processing, algorithmic solutions of problems,

and the algorithmic process itself."

• Most fundamental concept of CS is an algorithm: a set of steps that defines how a task is performed
• An algorithm is instantiated in a program and then executed on a machine

Brookshear's Diagram

Algorithm Limitations of Execution of Communication of Analysis of Discovery of Representation of theory of computation,… architecture, operating systems, networks,… software engineering,… algorithmics,… artificial intelligence,… data structures, programming language design,…

Schneider & Gersting's Diagram Algorithmic Foundations of CS The Hardware World The Virtual Machine The Software World Applications Social Issues design & analysis of algorithms,… computer organization,… assemblers, operating systems… programming langs, compilers,… artificial intelligence,…

What is Computer Science?

 C.A.R. Hoare: the central core of computer science is "the art of designing efficient and elegant methods of getting a computer to solve problems"  D. Reed: Identifies 3 main themes:

• hardware: circuit design, chip manufacturing, systems architects, parallel processing
• software: systems software (e.g., operating systems), development software (e.g., compilers), applications software (e.g., web browsers)
• theory: understand inherent capabilities and limitations of different models of computation (for instance, proving that certain problems CANNOT be solved algorithmically)

Sorting Example

 Solves a general, well-specified problem

• given a sequence of n keys, a 1 ,…,a n , as input, produce as output a reordering b 1 ,…,b n of the keys so that b 1 ≤ b 2 ≤ … ≤ b n

 Problem has specific instances

• [Dopey, Happy, Grumpy] or [3,5,7,1,2,3]

 Algorithm takes every possible instance and

produces output with desired properties

• insertion sort, quicksort, heapsort, …

Challenge

 Hard to design algorithms that are

• correct
• efficient
• implementable

 Need to know about

• design and modeling techniques
• resources - don't reinvent the wheel

Tour Finding Problem

 Given a set of n points in the plane,

what is the shortest tour that visits each

point and returns to the beginning?

• application: robot arm that solders contact

points on a circuit board; want to minimize

movements of the robot arm

 How can you find it?

Finding a Tour: Nearest Neighbor

 start by visiting any

point

 while not all points

are visited

• choose unvisited point closest to last visited point and visit it

 return to first point

How to Prove Correctness?

 There exist formal methods

• even automated tools  Even informal reasoning is better than none  Seeking counter-examples to proposed algorithms is important part of design process

Efficiency

 Software is always outstripping

hardware

• need faster CPU, more memory for latest

version of popular programs

 Given a problem:

• what is an efficient algorithm?
• what is the most efficient algorithm?
• does there even exist an algorithm?

Faster Algorithm vs. Faster CPU

 A faster algorithm running on a slower

machine will always win for large enough

instances

problem size running time faster alg, slower machine slower alg, faster machine

Modeling the Real World

 Cast your application in terms of well-studied

abstract data structures

text, characters, patterns strings shapes, regions, boundaries polygons sites, positions, locations points network, circuit, web, relationship graph hierarchy, ancestor/descendants, taxonomy trees cluster, collection, committee, group, packaging, selection subsets arrangement, tour, ordering, sequence permutation Concrete Abstract