COMP308COMP308Efficient Parallel Efficient Parallel Algorithms Algorithms Revision

COMP 308 ExamCOMP 308 ExamTime allowed : 2.5 hoursAnswer four questions (out of

five). If you attempt to answer more questions

than the required number of questions, the marks awarded for the excess questions will be discarded (starting with your lowest mark).

In each question you will see 3 problems which usually marked as 10,10 and 5

Topics:Topics:

MetricsPRAM modelPRAM

algorithmsTree algorithmsGraph

algorithmsMesh connected

networks & Sorting

Sorting NetworksCommunication

algorithmsParallel Virtual

MachineUnconventional

models and paradigms

1. Metrics and basic 1. Metrics and basic notionsnotions

Parallel timeCostEfficiency,Speed-up, Bounds (Amdahl Law)------------------------------------------------------Complexity Classes: NC, PTractable and intractable problems

for parallel computers (P-complete problems)

S( p) =T1

Tp

Efficiency =Sp

p

Cost = p Tp

fS

1

Upper bound on speedup

Basics of parallel Basics of parallel computingcomputingCoarse and fine grained computationsModels

◦ PRAM model EREW, CRCW, CREW, ERCW

◦ MIMD, SISD, SIMD, MISD Network topologies:

◦ Ring, Mesh, Tree, Hypercube

2. PRAM algorithms2. PRAM algorithmsActivation of n processorsFinding minimum of n numbersSum of elements in an arrayComputing of the first 1 in the

sequence of 0’s and 1’sSimulation of CRCW algorithm by

EREW model

3. Basic parallel 3. Basic parallel techniquestechniquesBalanced binary tree techniqueDoubling technique Parallel divide and conquerThe Euler-tour technique

4. Tree and Graph 4. Tree and Graph algorithmsalgorithmsList ranking problemParallel prefix sum computationParallel algorithms for expression

evaluation ◦ Simultaneous Substitutions Method◦ A parallel pebble game

Parallel Computation of Transitive Closure Problem (Warshall algorithm)◦ Coarse grained vs. Fine grained

Parallel construction of Euler cycles.

5. Sorting algorithms5. Sorting algorithmsMesh connected networks.

◦Sorting on 1-dim mesh ◦Sorting on 2-dim mesh

Comparison networks◦The zero-one principle◦Bitonic and Merging sorting networks◦Batcher’s merging network

You need to be able to construct sorting networks

6. Parallel Virtual Machine 6. Parallel Virtual Machine (PVM)(PVM)Basics of Message-Passing ProgrammingBroadcastScatterGatherReduce

7. Communication 7. Communication operationsoperations

Store and forward routing Cut-through routingBroadcasting problem

◦ Broadcast on ring◦ Broadcast on mesh◦ Broadcast on tree◦ Broadcast on hypercube

Gossiping problem

Unconventional models Unconventional models and paradigmsand paradigms Cellular automaton

◦ Majority problem – Rule 184◦ Simulation with 2D environment

Swarm algorithms◦ Swarming – Characteristics◦ Culture model and Adaptive Culture model

Membrane computing: P-systems◦ Basic definition, ◦ Maximal parallelism in membrane computation model ◦ Square function and divisibility

DNA computing◦ Adleman Experiment: Hamiltonian Path Problem

Quantum computations◦ Deutsch's problem. Main ideas of quantum

computations, quantum information.