US 2025/0298806 and other countries
Method and system for optimization and personalization of search results according to preferences and mandatory constraints
Comparison with State-of-the-Art Methods
See how our Preference-DAG Optimality Scoring compares to existing approaches across key dimensions.
| Approach | Fast at Web Scale? | Gaming-Resistant? | Explainable? | Provably Optimal? | Streaming-Compatible?1 | Algorithmic Complexity2 |
|---|---|---|---|---|---|---|
| Traditional ML Ranking Google, Amazon, Bing | ✅ Yes | ⚠️ SEO arms race | ⚠️ Opaque | ❌ No proofs | ⚠️ System-level only | O(N log N) Fixed candidate set |
| Recommendation Engines Netflix, Spotify, Amazon Recs | ✅ Yes | ⚠️ Fraud detection | ⚠️ Black-box | ❌ Engagement proxy | ⚠️ Session-level only | O(N) Retrieval, not optimality |
| MCDA / Pareto / Skyline AHP, TOPSIS, ELECTRE | ⚠️ Limited scale | ⚠️ Gameable | ✅ Yes | ✅ Pareto-optimal | ❌ No | O(N²×V) Dominance-testing based |
| LLM-Enhanced Search Perplexity, ChatGPT+Search | ⚠️ Slower (seconds) | ⚠️ Prompt injection | ⚠️ Citations only | ❌ No guarantees | ⚠️ Conversational only | O(N log N + T) Retrieval + generation |
| Generic Preference-Based Pareto, CP-Net, Utility | ⚠️ Moderate | ⚠️ Data gameable | ✅ Yes | ✅ Under model | ❌ No | NP-hard CP-net dominance testing |
| Preference-DAG (US 2025/0298806) PerfectFinder | ✅ Yes | ✅ Yes | ✅ Full audit | ✅ Guaranteed | ✅ Full streaming | O(N×V + N log N) No dominance testing |
Notation:
1 Streaming-Compatible: Can solutions be evaluated and ranked as they arrive from multiple sources, without requiring the full solution set upfront? ✅ = algorithmically progressive; ⚠️ = UI/system-level only; ❌ = requires full dataset.
2 Algorithmic Complexity: Worst-case per-query cost (Big O notation) for computing optimal ranking, excluding offline training, index building, and caching.
Practical Example: What These Numbers Mean
Scenario:
- • V = 10 preference nodes (e.g., color, brand, price range...)
- • E = 15 edges in the preference DAG
- • N = 10,000 candidate products (streaming from multiple sources)
- • CPU speed: ~1 billion simple operations/second
Computation Time:
| Method | Operations | Time |
|---|---|---|
| MCDA/Pareto O(N²×V) | 10,000² × 10 = 1B | ~1 second |
| CP-Net (NP-hard) | Exponential | seconds–minutes |
| PerfectFinder O(N×V + N log N) | 100K + 133K ≈ 233K | ~0.2 ms |
PerfectFinder is ~4,300× faster than dominance-testing approaches for this scenario.
Detailed Analysis by Approach
Traditional ML Ranking
Google, Amazon Search, Bing
Train a model that scores items using weighted relevance signals.
Pros:
- • Extremely fast at web scale (ms latency)
- • Mature infrastructure (indexes, caching)
Cons:
- • Opaque: limited explainability
- • Vulnerable to SEO/spam manipulation
- • No formal guarantee of optimality
Recommendation Engines
Netflix, Spotify, Amazon Recs
Predict user-item affinity from past behavior using CF/content/hybrid methods.
Pros:
- • Highly personalized
- • Great for browsing or discovery
Cons:
- • Optimizes engagement, not explicit preferences
- • Vulnerable to review/interaction fraud
- • Not suitable for multi-criteria decisions
MCDA Methods
AHP, TOPSIS, ELECTRE, Skyline
Weighted criteria, dominance testing, or Pareto ranking.
Pros:
- • Transparent and explainable
- • Can compute Pareto-optimal solutions
Cons:
- • Requires O(N²) dominance tests
- • Scaling difficult for large N or streaming
- • Preference models usually rigid
LLM-Augmented Search
Perplexity, You.com, ChatGPT+Search, Google AI Overviews
Retrieve documents then use LLMs to synthesize answers.
Pros:
- • Understands natural language needs
- • Conversational refinement
Cons:
- • Ranking logic remains opaque
- • Vulnerable to prompt injection
- • No formal optimality guarantee
- • Slower than traditional search
Generic Preference-Based
Utility, CP-Nets, Pareto
Explicit preference modeling; score or compare based on rules.
Pros:
- • Explainable preference structure
- • Can provide formal guarantees
Cons:
- • Pareto/CP-Net can be NP-hard
- • O(N²) overhead common
- • Difficult to scale across sources
Preference-DAG Optimality
US 2025/0298806 / PerfectFinder
DAG weights with parallel scoring and streaming results.
Key Advantages:
- ✅ Scales efficiently: Avoids O(N²) dominance tests
- ✅ Parallel by design: Independent source scoring
- ✅ Strict priority: Higher preferences always dominate
- ✅ Fully explainable: Direct, inspectable influence
- ✅ Gaming-resistant: Prevents feature stacking
- ✅ Incremental: Score without recomputing
- ✅ Formal guarantees: Top scores are optimal
Abstract
This invention provides a breakthrough method for finding truly optimal solutions from large datasets based on user preferences and mandatory requirements. It solves critical problems that plague traditional search and ranking systems: gaming through feature manipulation, computational infeasibility at scale, and lack of explainability.
The Core Innovation: The system represents user preferences as a directed acyclic graph (DAG) and computes an optimality score for each candidate solution using a novel scoring mechanism. This score can be calculated using only the current solution and the preference structure—without comparing against other solutions. This eliminates the need for expensive pairwise dominance testing that grows quadratically with dataset size.
Key Capabilities:
- Gaming-Resistant: Higher-priority preferences always dominate any combination of lower-priority ones, preventing manipulation through feature stacking
- Progressive Processing: Solutions arriving incrementally from multiple data sources can be scored immediately without waiting for the complete dataset
- Provably Optimal: Maximum-score solutions are guaranteed to be Pareto-optimal with respect to the preference DAG
- Computationally Efficient: Near-linear scaling (O(N × V + N log N)) instead of quadratic (O(N² × V)), enabling real-time performance on millions of candidates
- Fully Explainable: Every ranking decision includes a complete audit trail showing which preferences were satisfied and why
- Parallel & Distributed: Independent scoring enables massive parallelization across multiple processors and data sources
Impact: This technology transforms decision-making in e-commerce, supplier selection, personalized recommendations, and any domain requiring optimal choices from complex preference structures. It delivers millisecond response times while maintaining mathematical guarantees of optimality and full regulatory auditability.
Why Traditional Approaches Fail
Problem 1: Computationally Expensive Dominance Testing
Traditional multi-objective optimization systems must perform pairwise dominance testing: comparing each solution against all other solutions to determine if one dominates another.
- • Computational Complexity: O(N² × V) — quadratic in solution count
- • Each new solution requires comparison with all existing solutions
- • Cannot process solutions incrementally or in parallel without re-testing
- • Requires all solutions to be available before optimization begins
This approach is impractical for real-world use cases with large datasets, multiple data sources, or streaming results.
Problem 2: Linear Weighting Produces Incorrect Results
A naive approach might assign linear or additive weights to preferences (e.g., Rank Sum or Rank Reciprocal methods). This is mathematically incorrect for preference DAGs.
With linear weights, multiple lower-level preferences can accumulate a higher score than a single higher-level preference, violating the dominance hierarchy.
This means lower-priority preferences can incorrectly overwhelm higher-priority ones, producing falsely optimal solutions.
This produces falsely optimal solutions that violate user preferences. Such solutions would be dominated by others but incorrectly labeled as optimal.
Our Solution: Direct Optimality Scoring
This patent introduces a novel scoring mechanism that assigns weights to DAG nodes in a way that preserves the dominance hierarchy, ensuring:
Higher-level preferences in the DAG always dominate any combination of lower-level preferences, preventing gaming through feature stacking.
- ✅ No dominance testing needed — each solution gets a single, stable optimality score
- ✅ Pareto-optimality guaranteed — maximum-score solutions are provably optimal
- ✅ Incremental processing — new solutions can be scored without recomputing existing scores
- ✅ Parallel computation — independent scoring enables distributed processing
Technical Highlights
Computational Complexity
Time Complexity: O((V+E) + N×V + N log N)
- V = number of DAG nodes (preference criteria)
- E = number of DAG edges
- N = number of feasible solutions (satisfying mandatory constraints)
- • (V+E): Initialize DAG weights via topological sort
- • N×V: Score each feasible solution against DAG preferences
- • N log N: Sort solutions by optimality score
Key advantage: No pairwise dominance testing needed (which would be O(N² × V)). Our novel scoring mechanism ensures optimality through direct scoring of each solution.
Space: O(V + E + N×V/w) with bitset optimization
Use Cases
- Personalized recommendations
- E-commerce product search
- Vendor/supplier selection
- Regulatory-compliant decisioning
Prior Art Distinctions
Unlike ML-based ranking (opaque, trainable), multi-objective optimization (NP-hard, slow), or weighted sum models (gameable), this approach provides provable optimality, polynomial-time execution, and full auditability.