Myopic‑Hybrid Algorithm

Overview

A concise academic animation that walks through the deterministic Myopic‑Hybrid algorithm for selecting seed nodes in influence outreach. The viewer sees a dark‑background social network, the step‑by‑step computation of degrees, influence probabilities, underserved node identification, and the degree‑based tiebreaker, culminating in the final seed set and performance metrics.

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Phases

#	Phase Name	Duration	Description
1	Scene 1 – Network & Goal	~4 s	Show a dark‑background graph of ~35 nodes, highlight the goal equation $\text{Goal: Select } k \text{ seed nodes}$.
2	Scene 2 – Initial Seed	~5 s	Compute degrees, highlight the highest‑degree node, display $s_0=\arg\max_i d_i$ and seed set $S=\{s_0\}$, then animate a diffusion wave from that seed.
3	Scene 3 – Influence Probabilities	~5 s	After diffusion, assign probabilities $p_i$, colour‑code nodes (strong colour = high probability, faint colour = low).
4	Scene 4 – Underserved Nodes	~5 s	Compute $p_{\min}=\min_{i otin S} p_i$, highlight the least‑influenced nodes, show candidate set $C=\{i otin S : p_i \le p_{\min}+\epsilon\}$ with $\epsilon=0.01$.
5	Scene 5 – Degree‑Based Tiebreaker	~5 s	Show average degree $\bar d = \frac{1}{n}\sum_i d_i$, list candidate nodes with their degrees, highlight the node $v^* = \arg\min_{i\in C}|\bar d - d_i|$ as the next seed.
6	Scene 6 – Add Seed & Diffuse	~4 s	Update seed set $S \leftarrow S \cup \{v^*\}$, animate a second diffusion wave from the enlarged seed set.
7	Scene 7 – Iterative Loop	~8 s	Briefly show the loop of steps (estimate $p_i$ → find $p_{\min}$ → build $C$ → compute $\bar d$ → select $v^*$ → add seed) with a fast‑forward visual, repeating until $|S|=k$. The network updates after each iteration (node colours change).
8	Scene 8 – Final Evaluation	~5 s	Display final seed set $S^{*}=\{s_1,\dots,s_k\}$, animate influence spreading from all seeds, and show performance metrics $\mu = \frac{1}{n}\sum_i p_i$, $\operatorname{Var}(p)$, and Jain’s Fairness Index $JFI = \frac{(\sum_i p_i)^2}{n\sum_i p_i^2}$ together with min probability, influence gap, and disparity.
9	Final Scene – Message	~3 s	Fade in the title MYOPIC‑HYBRID and tagline "Target the underserved. Choose a structurally reliable seed."

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Layout

┌─────────────────────────────────────────────┐
│                                             │
│                MAIN (graph)                 │
│                                             │
├─────────────────────────────────────────────┤
│  Caption / equation (small, persistent)      │
└─────────────────────────────────────────────┘

Area Descriptions

Area	Content	Notes
Main	Dark‑background network graph, diffusion waves, highlighted nodes, candidate sets, and any dynamic visual cues.	Occupies ~85 % of frame height.
Caption	Current key equation or short label (e.g., "Goal: Select k seeds", "Initial seed", "Candidate set C", etc.).	Small footer; updates each phase.

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Notes

• Assumptions made due to missing specifics:
  1. Number of nodes = 35, edge density moderate to keep the graph readable.
  2. Diffusion is visualised as a radial colour‑pulse expanding from seed nodes.
  3. Probability values are abstract; colour intensity is used instead of numeric labels.
  4. The loop in Scene 7 is shown as a fast‑forward montage rather than a full‑length repetition to keep total runtime ≈ 45 s.
  5. All equations are displayed in LaTeX format in the caption area; no additional on‑screen text is used.
• Dark background with light‑coloured nodes for high contrast.
• Smooth easing for all transitions (fade‑in, highlight, diffusion pulse).
• The entire animation fits within a single Manim Scene class.
• No audio or interactive elements are required.
• The final message uses bold typography and stays on screen for a brief pause before fading out.