Function combsum 

pub fn combsum<I: Clone + Eq + Hash>(
    results_a: &[(I, f32)],
    results_b: &[(I, f32)],
) -> Vec<(I, f32)>

Sum of min-max normalized scores (CombSUM).

CombSUM normalizes each list to [0, 1] using min-max normalization, then sums the normalized scores. This preserves score magnitudes while handling different scales.

Formula

For each list: normalized = (score - min) / (max - min) Final score: score(d) = Σ normalized_scores(d)

Arguments

• results_a - First ranked list: Vec<(document_id, score)>
• results_b - Second ranked list: Vec<(document_id, score)>

Returns

Fused ranking sorted by combined score (descending). Documents with higher normalized scores across lists rank higher.

Example

use rankops::combsum;

// Both lists use cosine similarity (0-1 scale)
let sparse = vec![
    ("doc1", 0.9),
    ("doc2", 0.8),
    ("doc3", 0.7),
];

let dense = vec![
    ("doc2", 0.95),
    ("doc1", 0.85),
    ("doc3", 0.75),
];

let fused = combsum(&sparse, &dense);
// doc2 ranks highest (0.8 + 0.95 = 1.75 after normalization)

Performance

Time complexity: O(n log n) where n = total items across all lists. For typical workloads (100-1000 items per list), fusion completes in <1ms.

When to Use

• ✅ Scores are on similar scales (e.g., all cosine similarities 0-1)
• ✅ You trust score magnitudes (scores represent true relevance)
• ✅ Need better accuracy than RRF (CombSUM typically 3-4% higher NDCG)

When NOT to Use

• ❌ Incompatible score scales (BM25: 0-100 vs embeddings: 0-1) - use RRF
• ❌ Score distributions differ significantly - use standardized or dbsf
• ❌ Unknown score scales - use RRF

Trade-offs

• Accuracy: Typically 3-4% higher NDCG than RRF (OpenSearch benchmarks)
• Robustness: Less robust to outliers than RRF (min-max is sensitive)
• Speed: Similar to RRF (~1-2% faster due to simpler computation)