Microsoft PowerPoint – Chapter2 – Parallel Programming Platforms
Introduction to
Parallel Computing
George Karypis
Parallel Programming Platforms
Elements of a Parallel Computer
Hardware
Multiple Processors
Multiple Memories
Interconnection Network
System Software
Parallel Operating System
Programming Constructs to Express/Orchestrate Concurrency
Application Software
Parallel Algorithms
Goal:
Utilize the Hardware, System, & Application Software to either
Achieve Speedup: Tp = Ts/p
Solve problems requiring a large amount of memory.
Parallel Computing Platform
Logical Organization
The user’s view of the machine as it is being
presented via its system software
Physical Organization
The actual hardware architecture
Physical Architecture is to a large extent
independent of the Logical Architecture
Logical Organization Elements
Control Mechanism
SISD/SIMD/MIMD/MISD
Single/Multiple Instruction Stream
& Single/Multiple Data Stream
SPMD:
Single Program Multiple Data
Logical Organization Elements
Communication Model
Shared-Address Space
UMA/NUMA/ccNUMA
Message-Passing
Physical Organization
Ideal Parallel Computer Architecture
PRAM: Parallel Random Access Machine
PRAM Models
EREW/ERCW/CREW/CRCW
Exclusive/Concurrent Read and/or Write
Concurrent Writes are resolved via
Common/Arbitrary/Priority/Sum
Physical Organization
Interconnection Networks (ICNs)
Provide processor-to-processor and processor-to-memory
connections
Networks are classified as:
Dynamic
The network consists of
switching elements that the
various processors attach to
indirect network
Historically used to link
processors-to-memory
shared-memory systems
Static
Consist of a number of
point-to-point links
direct network
Historically used to link
processors-to-processors
distributed-memory
system
Static & Dynamic ICNs
Evaluation Metrics for ICNs
Diameter
The maximum distance between any two nodes
Smaller the better.
Connectivity
The minimum number of arcs that must be removed to break it into two
disconnected networks
Larger the better
Measures the multiplicity of paths
Bisection width
The minimum number of arcs that must be removed to partition the network into
two equal halves.
Larger the better
Bisection bandwidth
Applies to networks with weighted arcs—weights correspond to the link width
(how much data it can transfer)
The minimum volume of communication allowed between any two halves of a
network
Larger the better
Cost
The number of links in the network
Smaller the better
Metrics and Dynamic Networks
Network Topologies
Bus-Based
Networks
Shared medium
Information is being
broadcasted
Evaluation:
Diameter: O(1)
Connectivity: O(1)
Bisection width: O(1)
Cost: O(p)
Network Topologies
Crossbar Networks
Switch-based network
Supports simultaneous
connections
Evaluation:
Diameter: O(1)
Connectivity: O(1)?
Bisection width: O(p)?
Cost: O(p2)
Network Topologies
Multistage Interconnection Networks
Multistage Switch Architecture
Pass-through
Cross-over
Connecting the Various Stages
Blocking in a Multistage Switch
Routing is done by comparing the bit-level
representation of source and destination addresses.
-match goes via pass-through
-mismatch goes via cross-over
Network Topologies
Complete and star-connected networks.
Network Topologies
Cartesian Topologies
Network Topologies
Hypercubes
Network Topologies
Trees
Summary of Performance Metrics
Physical Organization
Cache Coherence in Shared Memory
Systems
A certain level of consistency must be
maintained for multiple copies of the same
data
Required to ensure proper semantics and
correct program execution
serializability
Two general protocols for dealing with it
invalidate & update
Invalidate/Update Protocols
Invalidate/Update Protocols
The preferred scheme depends on the
characteristics of the underlying application
frequency of reads/writes to shared variables
Classical trade-off between communication
overhead (updates) and idling (stalling in
invalidates)
Additional problems with false sharing
Existing schemes are based on the invalidate
protocol
A number of approaches have been developed for
maintaining the state/ownership of the shared data
Communication Costs in Parallel
Systems
Message-Passing Systems
The communication cost of a data-transfer
operation depends on:
start-up time: ts
add headers/trailer, error-correction, execute the routing
algorithm, establish the connection between source &
destination
per-hop time: th
time to travel between two directly connected nodes.
node latency
per-word transfer time: tw
1/channel-width
Store-and-Forward & Cut-Through
Routing
Cut-through Routing Deadlocks
Messages 0, 1, 2, and 3
need to go to nodes A, B,
C, and D, respectively
Communication Model Used for
this Class
We will assume that the cost of sending a
message of size m is:
In general true because ts is much larger
than th and for most of the algorithms that
we will study mtw is much larger than lth
Routing Mechanisms
Routing:
The algorithm used to determine the path that
a message will take to go from the source to
destination
Can be classified along different
dimensions
minimal vs non-minimal
deterministic vs adaptive
Dimension Ordered Routing
There is a predefined ordering of the dimensions
Messages are routed along the dimensions in that order
until they cannot move any further
X-Y routing for meshes
E-cube routine for hypercubes
Topology Embeddings
Mapping between networks
Useful in the early days of parallel computing
when topology specific algorithms were being
developed.
Embedding quality metrics
dilation
maximum number of lines an edge is mapped to
congestion
maximum number of edges mapped on a single
link
Mapping a Cartesian Topology
onto a Hypercube
Cool things ☺
Mapping a Cartesian Topology
onto a Hypercube