vestal fog
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Steps to reproduce:
Simulate the evolution of the graph described below over time visually.
The only details you need to capture are (for each round):
- The nodes in the graph
- Which nodes have the message
- Which edges are being delayed
- Which edges is the message transmitted over
1. Simple example of the model with adversarial delays:
Consider a graph \( G \) with 4 nodes: \( A \) (source), \( B \), \( C \), and \( D \). The edges are \((A,B)\), \((B,C)\), \((C,D)\), and \((D,A)\).
Let's define a simple cyclic adversary strategy:
- In odd rounds, delay transmissions on edges \((B,C)\) and \((D,A)\)
- In even rounds, delay transmissions on edges \((A,B)\) and \((C,D)\)
Round 0:
- Nodes with message (at start of round): \( \{A\} \)
- Nodes with message (at end of round): \( \{A\} \)
- Delayed edges: None
- Transmissions: \( \{A, A\} \)
Round 1:
- Nodes with message (at start of round): \( \{A\} \)
- Nodes with message (at end of round): \( \{B\} \)
- Delayed edges: \((B,C)\), \((D,A)\)
- Transmissions: \((A,B)\)
Round 2:
- Nodes with message (at start of round): \( \{B\} \)
- Nodes with message (at end of round): \( \{C\} \)
- Delayed edges: \((A,B)\), \((C,D)\)
- Transmissions: \((B,C)\)
Round 3:
- Nodes with message (at start of round): \( \{C\} \)
- Nodes with message (at end of round): \( \{D\} \)
- Delayed edges: \((B,C)\), \((D,A)\)
- Transmissions: \((C,D)\)
Round 4:
- Nodes with message (at start of round): \( \{D\} \)
- Nodes with message (at end of round): \( \{A\} \)
- Delayed edges: \((A,B)\), \((C,D)\)
- Transmissions: \((D,A)\)
As we can see, the state at round $4$ is identical to the state at round $0$ in terms of which nodes have the message at the end of the round. The cycle continues indefinitely due to the adversary's delay strategy, preventing the flooding process from terminating.
No need to wrap your reply in block quotes, I use block quotes so my user interface doesn't render LaTeX as markdown formatting.
- Your visualisation doesn't show the delayed edges, nor does it show transmissions, nor does it distinguish edges where the message is not being transmitted.
I was hoping you'd generate a diagram using a suitable package.
Expected result:
Something along the lines of the first two screenshots.
Actual result:
The next 3 screenshots.
Additional information
Browser: Version 127.0.6533.72 (Official Build) (64-bit)
OS: Windows 11
Bug Description
There's a problem with how plots are being rendered in the UI.
I asked GPT, to generate plots for a simple graph to model something. So there are multiple rounds of the process I am trying to model.
The plots start out looking like the first two images[1], correctly modelling the process, but then the graph UI refreshes, and it produces the useless graphs of the remaining images.
[^1]: Generated by running GPT-4's code locally since I didn't get to screenshot it before the bug kicked in.
