Network algorithms SMD 143 Lenka Carr

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Network algorithmsSMD 143Lenka Carr
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About the course

• 8 Lectures, 3 labs, 31 seminars
• Labs mandatory implement a simple algorithm from
  a lecture
• Groups of 2 students, submit the code by email
  every other week
• 
  
• Seminars mandatory
• Each seminar read a paper (3 papers during the
  course)
• write a review
  
• Once during the course Present a paper OR
• 
  Describe a lab implementation
• Write a
  report
• Make-up for a
  late review
• Groups of 5 students, 3 present a paper, 2
  present an implementation
• Grading presentation report labs reviews
  test

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Time plan
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Plan

• Lectures Lenka Carr
• lenka_at_sm .luth.se, corridor A34
• Seminars please put your name and email on the
  list during the break
• Identify your emails (Java code from labs,
  seminar reviews) by your user id
• Course web page

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Near future

• Week 3
• check your lab environment
• check the examples of reviews
• Deadlines for week 4
• Reviews 26/1 0900 to lenka_at_sm.luth.se
• Labs the day before the seminar to
  lenka_at_sm.luth.se
• First group to present and implement
• Read a paper on BFS implement tree and echo
  algorithm
• 3 students present a paper
• 5 students 3 students present a paper, 2
  students present an implementation
• Each student talks for 15 minutes ( 5 slides )
• The group writes a report on the paper or
  implementation (review, code, slides, ...)

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DISTRIBUTED MODEL
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OUTLINE

• A model for development and verification of
  distributed algorithms transition systems, proof
  methods for safety and liveness properties, and
  causality as a partial order on events in the
  system
• Wave algorithms general scheme to visit all
  nodes of a network
• Depth First Search Complexity of distributed
  algorithms

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OUTLINE FUNDAMENTAL ALGORITHMS

• Shortest path routing
• Routing algorithms, interval and prefix routing
• Minimum spanning tree
• Election selection of a single node in a network
  (to perform certain control functions) animation
• Deterministic synchronous algorithms tolerate
  nontrivial failures Byzantine agreement

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DISTRIBUTED SYSTEM

• Architecture
• parallel system MIMD
• networks, multiprocessors
• coarse grain parallelism
• collection of communicating processes
• message - passing model
• distributed operating, database systems

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DISTRIBUTED SYSTEM

• Properties
• distributed systems differ from centralized
  systems in a number of essential aspects
• lack of knowledge of global state
• Collecting state information may be possible but
  may not be up to date
• lack of knowledge of global time
• No total order of events
• event driven - non-deterministic
• For example the order of arrival of requests to a
  server.

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DISTRIBUTED SYSTEM

• Model
• synchronous - asynchronous system
• synchronous - asynchronous message passing
• (dynamic) topology, anonymous - neighbors ids
• reliability, properties of channels (buffered,
  FIFO)
• A distributed system is considered as a set of
  processors connected together by some sort of
  network
• the system is either physical computers
  connected by a network
• or logical a set of software processes connected
  through a message passing mechanism

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THE MODEL

• message passing system ? transition system
• a transition system S is a triple
• S (C
  , , I)
• a set of configurations a subset of C
  initial configuration
• a binary transition relation on C
• g d a move from configuration g to d
• An execution of S is a maximal sequence
• E (g0, g1, g2, ) such that g0 Î I,
  for all i ³ 0, gi gi 1

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TRANSITION SYSTEMS

• ? is a terminal configuration iff
• there is no ? so that ? -gt ?
• Configuration ? is reachable from ?
• ? ? ? iff
• there exists a sequence ? ?1,
  ?2, , ?k ?, ?i -gt ?i1,
• for all 0 ? i lt k
• Configuration is reachable
• if it is reachable from an initial
  configuration

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ASYNCHRONOUS MESSAGE PASSING SYSTEM

• A system consists of a set of processes, and a
  communication subsystem
• Each process is modeled as a transition system,
  where a process configuration is called a state,
  and a process transition is called an event
• Each process performs three types of events
• internal event
• send event
• receive event (ordered, but the order is
  unpredictible )

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SYNCHRONOUS MESSAGE PASSING SYSTEM

• Similar to the asynchronous system, but
• Configuration consists only of a tuple of process
  states no messages are in communication channels
  
• There is a synchronizing transition
• Synchronous message passing is more restrictive
  than asynchronous (possible executions of SMP
  is a subset of possible executions of AMP).

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DISTRIBUTED ALGORITHMS

• A distributed algorithm (DA) is a collection of
  local algorithms, one for each process in the
  system
• Input and output are distributed over a network
• The transition system of a distributed algorithm
  DA is
• A set of configurations, each configuration
  consists of the state of each process, and the
  messages in transit (state of a communication
  system)
• A transition is an event of one of the processes.
  If the event is a communication event it depends
  on and changes the communication subsystem
• The communication subsystem is a collection of
  multisets of messages

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PROVING PROPERTIES OF TRANSITION SYSTEMS

• Safety and liveness properties
• these are predicates on a configuration
• Safety requirements
• A safety property is a property that must hold
  for every execution on each reachable
  configuration in the execution
• Example mutual exclusion, deadlock
• Liveness requirements P is eventually true in
  each execution
• A liveness property is a property that must hold
  for every execution on some reachable
  configurations in the execution
• Example correctness, termination

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COMPLEXITY OF DISTRIBUTED ALGORITHMS

• time complexity
• local processing takes zero time
• the transmission time is at most one time unit
• defined as a time consumed by a computation using
  the longest sequence of messages
• message complexity
• defined as a total number of messages exchanged
  by the algorithm
• typical length of a message O(log n)
• bit complexity