Hash Compression: Concepts and Techniques

This reading introduces hash functions and hash compression, explaining how keys are converted into numeric table indices and why this process is fundamental to data structures like hash tables used in everyday applications such as phone contacts and compilers.

This reading explains how modular arithmetic (the division method) is used as a compression strategy to map arbitrary keys into valid hash table indices, covering its mechanics, advantages, and practical considerations for achieving efficient average-case performance.

This reading covers folding and other compression techniques—such as digit folding and shift folding—that break large keys like social security numbers or product codes into smaller parts and combine them to produce a hash table index within a manageable range.

This reading examines the distribution properties of hash functions, explaining what uniform distribution means, why it matters for minimizing collisions, and how to evaluate whether a hash function spreads keys evenly across a table's available slots.

This reading compares multiple hash compression methods—such as modular, MAD, and bit-masking approaches—discussing their trade-offs in terms of distribution quality, computational cost, and suitability for different data types to guide method selection.

An opening reading that explains why hash functions must map values from a huge key space down into a small table of slots, establishing compression as a distinct step in hashing and giving learners the vocabulary and motivation needed before studying specific techniques.

A lesson on the modulo operation as the standard compression method, covering the index = hash(key) % M formula, why table size M matters (prime versus power-of-two choices), and its cost and distribution tradeoffs; learners use it to master the most common compression strategy.

A survey reading on compression techniques beyond modular arithmetic, including folding methods that split a key into equal segments and combine them, plus related approaches such as mid-square and digit extraction; used to broaden a learner's toolkit of index-generation methods.

An explanatory reading on how well hash functions spread keys across a table, introducing uniform distribution as the ideal benchmark and examining how real compression techniques deviate from it, so learners can reason about clustering and collision behavior.

A decision-making guide that compares modular arithmetic, mid-square, digit extraction, and folding against criteria such as compression efficiency, computational cost, and distribution quality, giving learners a framework for choosing an appropriate method for a given application.

A consolidated version of the full module that strings together all five topic readings—introduction, modular arithmetic, folding and other techniques, distribution properties, and method selection—in one continuous document for review or printing.

This reading compares multiple hash compression methods—such as modular, MAD, and bit-masking approaches—discussing their trade-offs in terms of distribution quality, computational cost, and suitability for different data types to guide method selection.