Abstract
In the final phase of Omega experiment, you no longer control a single signal. You are tasked with commanding a Quantum Swarm of Mnanobots through a high-fidelity neural network. To suceed, you must reach the Event Horizon ( Target Node ) with maximum collective energy while maintaining swarm cohesion and evading an autonomous predatory AI.
Key Mechanics
1.Swarm Cohesion & Centroid Constraints
The swarm consists of Mindividual agents. At any time T, the Centroid (C) of the swarm is defined as the geometric mean of all active agent's position:
  • Cohesion Limit: If any agent i moves to a position where , that agent is instantly neutralized ( Energy = 0 ).
  • Movement Cost: Energy consumption for a jump is scaled by the agent's distance from the Centroid.
2.Dynamic Edge Saturation
The neural pathways exhibit Ion Saturation. Every time an agent traverses an edge between Node Uand Node V, the resistance of that specific path increases:
Subsequent agents ( or the same agent returning ) will consume significantly more ATP to cross the same path.
3.Relativistic Time Dilation
Nodes with high Mass distort the local temporal flow. If a swarm occupies a node with mass m, the local time relative to the global clock is:
  • Resonance Windows: Nodes only accept incoming signals if
4. The Shadow Predator ( Adversarial AI )
An autonomous Predator Signal spawns at a designated node. It uses a Breath-First Search (BFS) to move toward the swarm's Centroid.
  • Detection: If the swarm's Centroid enters the Line-of-Sight (LoS) of the Predator (a clear linear path with no obstructing nodes with a radius r), the swarm's energy is drained at a rate of 10 units/sec.
Input / Output Specifications
Inputs:
  • nodes: A struct array containing x, y, z (coordinates), mass (0 to 1), and initial_res (base resistance)
  • predator_start: The index of the node where the Shadow Predator begins.
  • params: A struct containing: ( .M: Number of agents in the swarm ;
  • .R_max: Maximum allowed distance from Centroid
  • .ATP_total: Initial energy pool shared by the swarm.
  • .target: The destination Node ID. )
Outputs:
  • max_energy: The remaining total ATP when the first agent reaches the target (or -1 if the swarm is neutralized ).
  • best_strategy: A cell array, where each cell contains the sequence of Node IDs visited by that specific agent.
Solve

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Last Solution submitted on Mar 20, 2026

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Hoang Minh Tri

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