Various search relevance algorithms have been developed over the years to improve the quality of search results. Some of these methods are foundational, while others are cutting-edge and have arisen from advancements in machine learning and natural language processing. Here’s a list of some popular search relevance algorithms and methods:

1. Vector Space Model (VSM): Represents documents and queries as vectors in a high-dimensional space. Cosine similarity is typically used to measure the similarity between a document and a query.
2. Boolean Model: Uses boolean operations like AND, OR, and NOT to retrieve relevant documents. It doesn’t rank documents but rather returns a set of documents that satisfy the boolean expression.
3. Probabilistic Models: Assigns a probability to each document being relevant to the query. The BM25 model, which was already mentioned, is one of the most popular in this category.
4. Latent Semantic Indexing (LSI): Uses singular value decomposition (SVD) to identify patterns in the relationships between the terms and concepts in unstructured text.
5. Latent Dirichlet Allocation (LDA): A generative probabilistic model used for topic modeling. It assumes that documents are mixtures of topics and that topics generate words.
6. Neural IR Models: With the rise of deep learning, various neural network architectures have been proposed for information retrieval tasks. Examples include:

• DRMM (Deep Relevance Matching Model)
• KNRM (Kernelized Neural Ranking Model)
• BERT and its derivatives for search: Using pre-trained models like BERT (Bidirectional Encoder Representations from Transformers) to understand the context and semantics of search queries and documents.

1. Learning to Rank (L2R): An approach where machine learning is used to train models to rank documents based on features extracted from them. Common algorithms include:

• RankNet
• LambdaMART
• RankBoost

1. Query Expansion: Augments the original query with additional terms to improve the retrieval performance. This could be done using techniques like pseudo-relevance feedback.
2. Distributed Representations: Using word embeddings like Word2Vec or FastText to understand the semantic meaning of words, then leveraging that semantic understanding to improve search relevance.
3. Graph-based Models: These use graph structures to represent relationships between entities (like documents, terms, or concepts). Personalized PageRank and HITS (Hypertext Induced Topic Search) are examples.
4. Collaborative Filtering and Content-Based Filtering: These methods are especially popular for recommendation systems but can be adapted for search as well. Collaborative filtering is based on user-item interactions, whereas content-based filtering focuses on the properties of items.

Remember, search systems often don’t rely on just one of these algorithms or methods. They combine multiple strategies and continuously tweak and refine them to achieve the best search experience.