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What are Bernstein's conditions?
A set of conditions allowing two processes to execute in parallel.
The parallelism relation is commutative but not transitive.
True
The minimum number of links that must be cut to divide the network into two equal halves is called _____.
Bisection Bandwidth
What is the formula for the diameter of a linear array with P processors?
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In a 2D mesh topology with P processors, how is the bisection bandwidth calculated?
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What is the diameter of a balanced binary tree with P processors?
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How many links must be cut to bisect a d-dimensional hypercube?
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What does the diameter of a hypercube represent?
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Study Notes
Bernstein's Conditions
- Bernstein's conditions are a set of rules that determine whether two processes can execute concurrently.
- Two processes can execute concurrently if they are flow-independent, anti-independent, and output-independent.
- Flow Independence: A process does not read any output variables written by another process.
- Anti-Independence: A process does not write to any variable that another process reads.
- Output Independence: Two processes do not write to the same variable.
Network Topologies
- Bisection Bandwidth represents the minimum number of links needed to cut a network into two equal halves.
- Diameter determines the longest shortest path between any two nodes in a network.
Array Topology
- Processors are arranged in a straight line.
- Bisection Bandwidth: 1 because cutting one link divides the network in half.
- Diameter: P - 1, where P represents the number of processors.
Mesh (2D) Topology
- Processors form a grid structure.
- Bisection Bandwidth: P, where P represents the number of processors in each side of the mesh.
- Diameter: 2 * (square root of P - 1).
Tree Topology
- Processor arrangement resembles a hierarchical tree structure.
- Bisection Bandwidth: 1 for a balanced binary tree.
- Diameter: 2 * log 2 (P), where P represents the number of processors and log 2 denotes the base-2 logarithm.
Hypercube Topology
- Connections are based on binary representations of processor IDs.
- Bisection Bandwidth: 2^(d-1), where d represents the hypercube dimension.
- Diameter: log 2 (P), where P represents the number of processors.
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Description
This quiz focuses on understanding Bernstein's conditions for concurrent process execution and explores various network topologies, including array and mesh configurations. Key concepts such as bisection bandwidth and diameter are examined to evaluate network performance. Test your knowledge of these essential computer science principles!
