CS 5220

Discrete events

Basic setup:

• Finite set of variables, updated via transition function
• Synchronous case: finite state machine
• Asynchronous case: event-driven simulation
• Synchronous example: Game of Life

Nice starting point — no discretization concerns!

Game of Life

Game of Life (John Conway):

1. Live cell dies with < 2 live neighbors
2. Live cell dies with > 3 live neighbors
3. Live cell lives with 2–3 live neighbors
4. Dead cell becomes live with exactly 3 live neighbors

Game of Life

Easy to parallelize by domain decomposition.

• Update work involves volume of subdomains
• Communication per step on surface (cyan)

Game of Life: Pioneers and Settlers

What if pattern is “dilute”?

• Few or no live cells at surface at each step
• Think of live cell at a surface as an “event”
• Only communicate events!
  • This is asynchronous
  • Harder with message passing — when do you receive?

Asynchronous Game of Life

How do we manage events?

• Could be speculative — assume no communication across boundary for many steps, back up if needed
• Or conservative — wait whenever communication possible
  • possible $\not \equiv$ guaranteed!
  • Deadlock: everyone waits for everyone else to send
  • Can get around this with NULL messages

How do we manage load balance?

• No need to simulate quiescent parts of the game!
• Maybe dynamically assign smaller blocks to processors?

High-Performance Game of Life

• Lots of implementations use fancy bit representations
• Ch 17 and Ch 18 of Abrash's Game Programmer's Black Book have an old, but still illuminating discussion of low-level (serial) optimizations
• HashLife is a triumph of algorithm design.

High-Performance Game of Life

How would I tackle this? Assuming matrix version, I might:

• Build a bit-packed representation
• Use a fast vectorized kernel to update small blocks
• Coarse blocking with generation skipping
• Dynamic scheduling of coarse block updates

What would you do?