Table of contents
1.
Introduction
2.
Characteristics of the Hashing Technique
3.
What are Hash Functions?
4.
Examples of commonly used hash functions are
5.
Applications of Hashing
6.
What is Static Hashing?
6.1.
Key characteristics of static hashing
6.2.
Operations Provided by Static Hashing
6.2.1.
1. Insertion
6.2.2.
2. Search
6.2.3.
3. Deletion
6.2.4.
4. Resize
6.3.
Advantages of Static Hashing
6.4.
Disadvantages of Static Hashing
7.
What is Dynamic Hashing?
7.1.
Key characteristics of dynamic hashing are
7.2.
Operations Provided by Dynamic Hashing
7.2.1.
1. Insertion
7.2.2.
2. Search
7.2.3.
3. Deletion
7.2.4.
4. Resizing
7.3.
Advantages of Dynamic Hashing
7.4.
Disadvantages of Dynamic Hashing
8.
Differences between static and dynamic hashing
9.
Frequently Asked Questions
9.1.
How does dynamic hashing handle the growth of the dataset?
9.2.
Can static hashing be resized if the initial table size is insufficient?
9.3.
Which hashing technique is more suitable when the dataset size is unknown?
10.
Conclusion
Last Updated: Oct 23, 2024
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Difference Between Static Hashing and Dynamic Hashing

Author Rinki Deka
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Introduction

Hashing is a technique in computer science that helps quickly store and get data back from places like arrays or databases. It uses special functions, which are known as hash functions to assign keys to particular spots in an array, which makes it faster to find the data later. This array is called a hash table. Hashing is very useful for operations like speeding up how quickly we can find information in databases, keeping data secure in cryptography, and even in caching, which keeps often-used data ready to use quickly. 

Difference Between Static Hashing and Dynamic Hashing

In this article, we'll look at different ways to do hashing, what they're good for, their advantages, and their disadvantages. We'll also compare how these methods differ from each other.

Characteristics of the Hashing Technique

Hashing is a technique for providing fast and efficient access to data stored in a hash table. Let’s look at the important characteristics of Hashing in a little more detail : 

1. Deterministic: Hashing is a deterministic process, meaning that for a given input (key), the hash function will always produce the same output (hash value). This deterministic nature ensures that the same key will always map to the same index in the hash table.


2. Efficiency: Hashing offers constant-time average-case complexity for insertion, deletion, and lookup operations. This means that regardless of the size of the dataset, these operations can be performed quickly, making hashing highly efficient for large amounts of data.


3. Collision resolution: Since multiple keys can potentially map to the same hash value (known as a collision), hashing techniques employ collision resolution strategies. Common techniques include chaining (storing colliding elements in a linked list) and open addressing (probing the hash table for an empty slot).


4. Load factor: The load factor of a hash table represents the ratio of the number of occupied slots to the total number of slots. A well-designed hash table aims to maintain a balanced load factor to ensure efficient operations and minimize collisions.
 

5. Hash distribution: A good hash function should distribute the keys evenly across the hash table. An even distribution reduces the likelihood of collisions and improves the overall performance of the hashing technique.

What are Hash Functions?

Hash functions are the core component of hashing techniques. A hash function is a mathematical function that takes an input (or "key") and returns a fixed-size output, typically an integer, known as the hash value or hash code. The purpose of a hash function is to map the input data to an index in the hash table.

Some important properties of hash functions are


1. Deterministic: A hash function always produces the same hash value for the same input key. This ensures that the mapping between keys and hash values remains consistent.


2. Uniformity: A good hash function should distribute the hash values evenly across the range of possible outputs. This helps minimize collisions and ensures efficient utilization of the hash table.


3. Efficiency: Hash functions should be computationally efficient and quickly calculated. Since hashing is used for quick data access, the hash function itself should not become a performance blocker.


4. Avalanche effect: A small change in the input key should result in a significantly different hash value. This property ensures that similar keys will likely have different hash values, reducing the chances of collisions.

Examples of commonly used hash functions are

1. Division method: In this method, the hash value is calculated by taking the modulo of the key with the size of the hash table. For example, `hash(key) = key % tableSize`.


2. Multiplication method: This method multiplies the key by a constant value, then extracts a portion of the result as the hash value. For example, `hash(key) = floor(tableSize * (key * constant - floor(key * constant)))`.


3. Cryptographic hash functions: Functions like SHA-256 and MD5 are cryptographic hash functions that produce fixed-size hash values. They are designed to be one-way functions, meaning it is infeasible to determine the original input given only the hash value.

Applications of Hashing

1. Databases: Hashing is extensively used in database systems for efficient indexing and quick data retrieval. Hash indexes allow for constant-time lookup of records based on their key values, greatly improving search performance compared to linear search or tree-based indexes.


2. Password Storage: Hashing is commonly used to store passwords securely. Instead of storing plain-text passwords, the password is hashed using a cryptographic hash function, and the resulting hash value is stored. When a user enters their password, it is hashed and compared with the stored hash value for authentication.


3. Caching: Hashing is employed in caching mechanisms to quickly retrieve previously computed or frequently accessed data. The data is stored in a hash table with a unique key, allowing for fast retrieval when needed. Caching helps improve performance by reducing the need for expensive computation or database queries.


4. Symbol Tables: Compilers and interpreters use hash tables to implement symbol tables, which store information about identifiers, variables, and their attributes. Hashing enables fast lookup of symbols during the compilation or interpretation process.


5. Data Integrity: Hashing generates unique fingerprints or checksums for files or large datasets. By comparing the hash values, one can quickly determine if two files or datasets are identical, making it useful for data integrity checks and file comparisons.


6. Bloom Filters: Bloom filters are probabilistic data structures that use hashing to test whether an element is a member of a set. They provide fast membership tests with a small probability of false positives, making them useful in various applications, such as spell checkers, web caches, and network routers.


7. Cryptographic Applications: Hashing is fundamental to various cryptographic protocols and algorithms. It is used in digital signatures, message authentication codes (MACs), and blockchain technologies to ensure data integrity, authenticity, and non-repudiation.

What is Static Hashing?

Static hashing, also known as closed hashing, is a type of hashing technique where the size of the hash table is fixed and determined in advance. In static hashing, the hash table is divided into a fixed number of buckets, and each bucket is associated with a specific range of hash values.

Key characteristics of static hashing


1. Fixed Table Size: The size of the hash table remains constant throughout the lifetime of the data structure. Once the table size is determined, it cannot be changed dynamically.
 

2. Direct Addressing: Static hashing uses a direct addressing scheme, where each bucket in the hash table corresponds to a unique hash value. The hash function maps the keys directly to the corresponding buckets.
 

3. Collision Resolution: Since multiple keys can hash to the same bucket, static hashing employs collision resolution techniques to handle collisions. Common methods include chaining (storing colliding elements in a linked list within the bucket) and open addressing (probing the hash table for an empty slot).
 

4. Load Factor: The load factor of a static hash table is the ratio of the number of occupied buckets to the total number of buckets. A high load factor indicates a densely populated hash table, which can lead to increased collisions and reduced performance.
 

5. Bucket Overflow: If a bucket becomes full and cannot accommodate more elements, it leads to bucket overflow. Static hashing techniques need to handle bucket overflow efficiently, either by using overflow chains or by probing for empty buckets.


Static hashing is suitable for scenarios where the number of keys and the expected size of the dataset are known in advance. It provides fast average-case performance for search, insertion, and deletion operations, with a time complexity of O(1) on average.

Operations Provided by Static Hashing

The different operations that static hashing does are : 
 

1. Insertion

   - To insert a key-value pair into the hash table, the hash function is applied to the key to compute the corresponding bucket index.

   - If the bucket is empty, the key-value pair is stored directly in that bucket.

   - If the bucket is already occupied (collision), a collision resolution technique is applied:

     - Chaining: The key-value pair is appended to the linked list associated with the bucket.

     - Open Addressing: The hash table is probed for the next empty slot using techniques like linear probing, quadratic probing, or double hashing.

 

2. Search

   - To search for a value associated with a given key, the hash function is applied to the key to determine the bucket index.

   - If the bucket is empty, the search terminates, indicating that the key is not present in the hash table.

   - If the bucket is not empty, the search process depends on the collision resolution technique:

     - Chaining: The linked list in the bucket is traversed to find a match for the key.

     - Open Addressing: The hash table is probed until the key is found or an empty slot is encountered.
 

3. Deletion

   - To delete a key-value pair from the hash table, the search operation is performed to locate the key.

   - If the key is found, the corresponding key-value pair is removed from the hash table.

   - In the case of chaining, the key-value pair is unlinked from the linked list.

   - In the case of open addressing, the slot is marked as deleted to avoid disrupting the probing sequence.
 

4. Resize

   - Static hashing does not typically support dynamic resizing of the hash table.

   - However, if the load factor becomes too high and the performance degrades, the hash table can be manually resized.

   - Resizing involves creating a new hash table with a larger size and rehashing all the existing key-value pairs into the new table.

Advantages of Static Hashing

1. Fast Average-Case Performance: Static hashing provides excellent average-case performance for search, insertion, and deletion operations, with an average time complexity of O(1) when using a well-designed hash function and appropriate load factor. This constant-time performance makes static hashing highly efficient for large datasets that require quick access to data.
 

2. Simple Implementation: Static hashing is relatively simple to implement compared to other data structures like balanced trees or dynamic hashing techniques. The basic operations, such as computing the hash function and resolving collisions, are straightforward to understand, making it a good choice for scenarios prioritizing quick implementation and maintainability.
 

3. Efficient Memory Utilization: When the size of the dataset is known in advance, and the hash table is appropriately sized, static hashing can be space-efficient. Static hashing minimizes wasted memory space by selecting a suitable table size and load factor, making it more memory-friendly compared to other data structures that may require additional memory for balancing or resizing.
 

4. Deterministic Behavior: Static hashing exhibits deterministic behavior, meaning that the same input key always produces the same hash value and maps to the same bucket. This deterministic nature enables predictable and repeatable results, which can be advantageous in certain applications and allows for efficient caching and lookup optimizations.
 

5. Good for Distributed Systems: Static hashing is well-suited for distributed systems where data is partitioned across multiple nodes. By using a consistent hashing scheme, data can be evenly distributed among the nodes based on their hash values, which facilitates efficient data retrieval and load balancing in distributed environments.

Disadvantages of Static Hashing

1. Fixed Table Size: One of the main drawbacks of static hashing is that the size of the hash table is fixed and determined in advance. Once the table size is set, it cannot be dynamically resized to accommodate changes in the dataset. If the actual number of keys exceeds the predetermined table size, the performance can degrade due to increased collisions and bucket overflows.
 

2. Inefficient Space Utilization: If the hash table is not properly sized or the load factor is too low, static hashing can lead to inefficient space utilization. When the number of keys is significantly smaller than the table size, a large portion of the hash table remains empty, resulting in wasted memory space. This can be a concern when dealing with large hash tables or when memory is a scarce resource.
 

3. Performance Degradation with High Collision Rates: The performance of static hashing heavily relies on the quality of the hash function and the distribution of keys. If the hash function is poorly designed or if the keys have a non-uniform distribution, it can lead to a high number of collisions. As the number of collisions increases, the performance of search, insertion, and deletion operations can degrade, as the collision resolution mechanism (e.g., chaining or open addressing) introduces additional overhead.
 

4. Limited Scalability: Static hashing is not inherently scalable, as it does not provide a built-in mechanism for resizing the hash table when the dataset grows. If the initial table size is not chosen carefully, and the dataset expands beyond the capacity of the hash table, the performance will suffer. Resizing the hash table requires manual intervention and can be a costly operation, as it involves rehashing all the existing key-value pairs.
 

5. Not Suitable for Unknown or Changing Dataset Sizes: Static hashing is not well-suited for scenarios where the size of the dataset is unknown or subject to frequent changes. If the dataset size is not known in advance or if it can grow or shrink dynamically, static hashing may not be the best choice. In such cases, dynamic hashing techniques or other data structures that support automatic resizing, such as hash tables with load factor thresholds or balanced trees, may be more appropriate.

What is Dynamic Hashing?

Dynamic hashing, also known as extendible hashing, is a type of hashing technique that allows the hash table to grow or shrink dynamically based on the number of elements stored in it. Unlike static hashing, where the hash table size is fixed, dynamic hashing provides a mechanism to adapt the table size as needed.

Key characteristics of dynamic hashing are

1. Extendible Hash Table: In dynamic hashing, the hash table is organized as a directory of buckets. Each bucket can hold multiple key-value pairs and is identified by a unique hash prefix.
 

2. Hash Function: Dynamic hashing uses a hash function to map keys to hash values. The hash function is designed to distribute the keys evenly across the buckets.
 

3. Directory: The directory is an array of pointers, where each pointer refers to a bucket. The size of the directory is determined by the current global depth of the hash table.
 

4. Local Depth: Each bucket has its own local depth, which indicates the number of bits used from the hash value to determine the bucket's location in the directory.
 

5. Bucket Splitting: When a bucket becomes full and needs to accommodate more elements, dynamic hashing employs a bucket-splitting mechanism. The full bucket is split into two buckets, and the local depth of the new buckets is increased.
 

6. Directory Expansion: If the local depth of a bucket exceeds the global depth of the directory, the directory size is doubled, and the pointers are updated accordingly. This expansion allows the hash table to grow dynamically.

 

7. Bucket Merging: In some implementations of dynamic hashing, when the load factor of the hash table falls below a certain threshold, buckets can be merged to reduce the table size and improve space utilization.

Operations Provided by Dynamic Hashing

Dynamic hashing supports the same basic operations as static hashing, but with the added flexibility of dynamic resizing. Let's look at the common operations provided by dynamic hashing:

1. Insertion

   - To insert a key-value pair, the hash function is applied to the key to compute the hash value.

   - The hash value determines the corresponding bucket in the directory.

   - If the bucket has sufficient space, the key-value pair is inserted into the bucket.

   - If the bucket is full, a bucket-splitting operation is performed:

     - The local depth of the bucket is increased.

     - If the local depth exceeds the global depth, the directory size is doubled (directory expansion).

     - The key-value pairs in the original bucket are redistributed between the two resulting buckets based on their hash values.

   - The insertion operation is then performed on the appropriate bucket.
 

2. Search

   - To search for a value associated with a given key, the hash function is applied to the key to compute the hash value.

   - The hash value determines the corresponding bucket in the directory.

   - The bucket is searched for the key-value pair.

   - If the key is found, the associated value is returned.

   - If the key is not found, the search terminates, indicating that the key is not present in the hash table.
 

3. Deletion

   - To delete a key-value pair, the search operation is performed to locate the key.

   - If the key is found, the corresponding key-value pair is removed from the bucket.

   - In some implementations, if the load factor of the hash table falls below a certain threshold after the deletion, bucket merging may be performed to reduce the table size and improve space utilization.
 

4. Resizing

   - Dynamic hashing automatically handles the resizing of the hash table as the number of elements changes.

   - When a bucket becomes full and needs to be split, the local depth of the bucket is increased, and the directory size is expanded if necessary.

   - Bucket splitting redistributes the key-value pairs among the resulting buckets based on their hash values.

   - The resizing operation is transparent to the user and ensures that the hash table remains efficient as the dataset grows or shrinks.


Note: Dynamic hashing efficiently performs these operations, adapting the hash table size as needed. The average time complexity of insertion, search, and deletion operations in a well-designed dynamic hash table is O(1), similar to static hashing.

Advantages of Dynamic Hashing

1. Automatic Resizing: One of the main advantages of dynamic hashing is its ability to automatically resize the hash table based on the number of elements stored. As the dataset grows or shrinks, dynamic hashing adjusts the table size accordingly, eliminating the need for manual resizing. This adaptive behavior ensures that the hash table remains efficient and optimized for the current dataset size.
 

2. Efficient Space Utilization: Dynamic hashing aims to maintain a balanced load factor by dynamically adjusting the number of buckets. When the load factor exceeds a certain threshold, the hash table is expanded through bucket splitting. Conversely, if the load factor falls below a threshold, buckets can be merged to reduce the table size. This dynamic resizing mechanism helps optimize space utilization and minimizes wasted memory compared to static hashing with fixed table sizes.
 

3. Handles Unknown or Changing Dataset Sizes: Dynamic hashing is particularly useful when the size of the dataset is unknown or subject to frequent changes. It adapts to the growth or shrinkage of the dataset without requiring prior knowledge of the data distribution. This makes dynamic hashing suitable for scenarios where the data size is unpredictable or where the dataset undergoes significant modifications over time.
 

4. Efficient Collision Resolution: Dynamic hashing employs a bucket-splitting mechanism to resolve collisions efficiently. When a bucket becomes full and needs to accommodate more elements, it is split into two buckets, and the local depth is increased. This splitting process helps maintain a low collision rate and ensures that the hash table remains efficient even as the number of elements grows.
 

5. Good Average-Case Performance: Dynamic hashing provides good average-case performance for search, insertion, and deletion operations. With a well-designed hash function and appropriate load factor thresholds, the average time complexity of these operations is O(1). The automatic resizing and efficient collision resolution mechanisms contribute to the overall performance of dynamic hashing.

 

6. Flexibility and Adaptability: Dynamic hashing offers flexibility and adaptability to different dataset characteristics. It can handle datasets with non-uniform key distributions and adapt to changes in the data over time. The dynamic resizing feature allows the hash table to evolve and maintain efficiency regardless of the dataset's growth pattern.
 

7. Simplified User Experience: From a user's perspective, dynamic hashing provides a simplified experience compared to static hashing. Users don't need to worry about manually resizing the hash table or handling bucket overflows. The dynamic hashing algorithm takes care of these aspects automatically, allowing users to focus on performing operations on the hash table without concerning themselves with low-level details.

Disadvantages of Dynamic Hashing

1. Overhead of Directory Management: Dynamic hashing introduces an additional level of complexity with its directory structure. The directory is an array of pointers that refer to the buckets, and it needs to be managed and updated as the hash table grows or shrinks. This overhead of directory management can add some computational and memory costs compared to simpler hashing techniques.
 

2. Increased Complexity: Dynamic hashing algorithms are generally more complex than static hashing. The mechanisms for bucket splitting, directory expansion, and pointer management contribute to the increased complexity. Implementing and maintaining a dynamic hashing system requires a deeper understanding of the underlying concepts and data structures.
 

3. Potential for Bucket Imbalance: Although dynamic hashing aims to maintain a balanced load factor, there is still a potential for bucket imbalance. Depending on the hash function and the distribution of keys, some buckets may become more heavily loaded than others. This can lead to performance degradation in certain scenarios, as the collision resolution mechanism may need to handle more elements in those buckets.
 

4. Additional Memory Overhead: Dynamic hashing requires additional memory to store the directory and manage the pointers. The size of the directory grows as the hash table expands, consuming more memory. While dynamic hashing aims to optimize space utilization, the overhead of the directory structure should be considered, especially when dealing with large datasets or memory-constrained environments.
 

5. Performance Overhead for Resizing: Although dynamic hashing automatically handles resizing, the resizing process itself can introduce some performance overhead. When a bucket needs to be split, or the directory needs to be expanded, it requires additional operations and memory allocations. This overhead can impact the performance of the hash table during the resizing phase.
 

6. Not Suitable for Certain Distribution Patterns: Dynamic hashing assumes a relatively uniform distribution of keys across the buckets. If the dataset has a highly skewed or non-uniform distribution, dynamic hashing may not perform optimally. In such cases, alternative hashing techniques or data structures specifically designed for skewed distributions may be more appropriate.
 

7. Limited Ability to Handle Extreme Growth: While dynamic hashing can handle dataset growth, it may face challenges in extremely rapid or massive growth scenarios. If the dataset size increases too quickly, the resizing process may not be able to keep up, leading to performance degradation. Other scalable data structures or distributed hashing techniques may be necessary in such cases.
 

8. Potential for Higher Worst-Case Complexity: Although dynamic hashing provides good average-case performance, the worst-case complexity for operations like search, insertion, and deletion can be higher than static hashing. This is because the collision resolution mechanism and the potential for bucket imbalance can impact the worst-case behavior.

Differences between static and dynamic hashing

Static HashingDynamic Hashing
The size of the hash table is fixed and determined in advance; cannot change dynamically.The hash table can grow or shrink dynamically based on the number of elements.
No built-in mechanism for resizing; manual resizing is required if the initial table size is insufficient.Automatically adjusts the size of the hash table based on the number of elements, without manual intervention.
May lead to inefficient space utilization if the table is not properly sized, resulting in wasted memory.Optimizes space utilization by dynamically adjusting the number of buckets to maintain a balanced load factor.
Performance degrades if the number of keys exceeds the table size, leading to collisions and bucket overflows.Handles collisions and maintains good performance through bucket splitting and directory expansion mechanisms as the dataset grows.
Simpler to implement with straightforward collision resolution techniques.More complex to implement due to bucket splitting, directory management, and resizing mechanisms.
Suitable when the dataset size is known in advance and can fit within the predetermined table size.Suitable when the dataset size is unknown or frequently changes, allowing for dynamic growth.

Frequently Asked Questions

How does dynamic hashing handle the growth of the dataset?

Dynamic hashing automatically adjusts the size of the hash table by splitting buckets and expanding the directory when the number of elements increases, ensuring efficient performance as the dataset grows.

Can static hashing be resized if the initial table size is insufficient?

Static hashing does not provide a built-in mechanism for resizing. If the initial table size is insufficient, manual resizing is required, which involves creating a new hash table and rehashing all the elements.

Which hashing technique is more suitable when the dataset size is unknown?

Dynamic hashing is more suitable when the dataset size is unknown or subject to frequent changes. It can adapt to the growth or shrinkage of the dataset without requiring prior knowledge of the data size.

Conclusion

In this article, we discussed the fundamental concepts of hashing, like hash functions, collision resolution techniques, and the differences between static and dynamic hashing. We looked into the characteristics, advantages, and disadvantages of each approach. Static hashing provides simplicity and efficiency for fixed-size datasets, while dynamic hashing offers flexibility and adaptability for datasets with unknown or changing sizes. 

You can also check out our other blogs on Code360.

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