Optimization Methods for the FA18 Mission Computer Memory Mapping Problem

1
Optimization Methods for the F/A-18 Mission
Computer Memory Mapping Problem

• Adam Sealey
• Masters Thesis Candidate
• Dr. David Sturgill
• Thesis Advisor

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Background

• Time-sliced mission computer
• Each task requires data elements
• Fixed amount of virtual memory available for each
  task
• Goal map data elements to virtual addresses so
  that all constraints are met

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Problem Illustration
Data 4
Data 3
Data 3
Data 4
Data 1
Data 2
Data 1
Data 1
Task 1
Task 2
Task 3
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Constraints

• Each task must have access to the data elements
  it needs
• Data elements cannot overlap in physical memory
• Each data element must be contiguous
• A data element must have the same virtual address
  in all tasks
• ...

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Computationally Challenging

• About 500 elements
• About 60 tasks
• 64K logical address space
• A large problem for brute-force techniques
• Is there a better way?

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NP-Completeness

• NP-Complete problem class
• Large set of computationally equivalent problems
• No known efficient solutions for any

TSP
Graph Color
Bin Pack
Memory Map
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Generalization

• Pretend we can have
• Any number of tasks
• Any number of data elements
• Any virtual memory size
• Facilitates proving NP-Completeness

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NP-Completeness Reduction

• Graph Coloring
• Construction
• Verification

A
C
B
D
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NP-Completeness Reduction

• Graph Coloring
• Construction
• Verification

A
C
B
A
A
C
B
B
B
C
D
D
C
D
B-D
B-C
A-B
A-C
C-D
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NP-Completeness Reduction

• Graph Coloring
• Construction
• Verification
• Does a valid mapping always generate a valid
  coloring?
• Is there a valid mapping for every valid coloring?

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Approaches

• NP-Complete no guaranteed good way to solve
  generalized problem
• Types of Approaches
• Incomplete Search
• Complete Search
• Approximation

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Incomplete Search

• Greedily try to build a map
• Place elements in virutal memory one after
  another
• Give each element the earliest possible memory
  address
• This isnt really going to work (unless we get
  really lucky)

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Incomplete Search

• Final mapping is determined by insertion order
• Number of unmapped elements quality of the
  ordering
• We want to learn the best insertion order
• Genetic algorithm
• Preliminary results!

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Complete Search

• Systematic - Ensure only inspect at each
  potential solution at most once
• Partial Ordering
• Pruning
• Conflict

A
B
C
D
E
F
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Approximation

• Approximation algorithms
• Find non-optimal solution in polynomial time
• Ex Guarantee finding solution that is no worse
  than 2x as bad as optimal solution in poly-time
• Goal Come up with useful approximation that will
  fit into memory
• Flavors
• Flavor Blending

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Conclusion/Future Work

• Incomplete Search
• Better methods for getting to good solutions
• Run preliminary result through validation tool
• Complete Search
• Developing search pruning based on partial order
• Developing additional search refinements
• Approximation
• Find an approximation that can be bound within
  memory

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Questions?