1. COMP308 Efficient Parallel Algorithms
Revision

2. COMP 308 Exam Time allowed : 2.5 hours
Answer 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

3. Topics: Metrics Sorting Networks PRAM model Communication algorithms
PRAM algorithms
Tree algorithms
Graph algorithms
Mesh connected networks & Sorting
Sorting Networks
Communication algorithms
Parallel Virtual Machine
Unconventional models and paradigms

4. 1. Metrics and basic notions
Parallel time
Cost
Efficiency,
Speed-up,
Bounds (Amdahl Law)
Complexity Classes: NC, P
Tractable and intractable problems for parallel computers (P-complete problems) Sp p
Efficiency = T1 Tp
S( p) =
Cost = p  Tp
Upper bound on speedup

5. Basics of parallel computing
Coarse and fine grained computations
Models
PRAM model
EREW, CRCW, CREW, ERCW
MIMD, SISD, SIMD, MISD
Network topologies:
Ring, Mesh, Tree, Hypercube

6. 2. PRAM algorithms Activation of n processors
Finding minimum of n numbers
Sum of elements in an array
Computing of the first 1 in the sequence of 0’s and 1’s
Simulation of CRCW algorithm by EREW model

7. 3. Basic parallel techniques
Balanced binary tree technique
Doubling technique
Parallel divide and conquer
The Euler-tour technique

8. 4. Tree and Graph algorithms
List ranking problem
Parallel prefix sum computation
Parallel 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.

9. 5. Sorting algorithms Mesh connected networks. Comparison 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

10. 6. Parallel Virtual Machine (PVM)
Basics of Message-Passing Programming
Broadcast
Scatter
Gather
Reduce

11. 7. Communication operations
Store and forward routing
Cut-through routing
Broadcasting problem
Broadcast on ring
Broadcast on mesh
Broadcast on tree
Broadcast on hypercube
Gossiping problem

12. Unconventional models and 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.