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In computer programming, an unrolled linked list is a variation on the linked list which stores multiple elements in each node. It can dramatically increase cache performance, while decreasing the memory overhead associated with storing list metadata such as references. It is related to the B-tree.
A typical unrolled linked list node looks like this:
record node { node next // reference to next node in listint numElements // number of elements in this node, up to maxElementsarray elements // an array of numElements elements,// with space allocated for maxElements elements }Each node holds up to a certain maximum number of elements, typically just large enough so that the node fills a single cache line or a small multiple thereof. A position in the list is indicated by both a reference to the node and a position in the elements array. It is also possible to include a previous pointer for an unrolled doubly linked list.
To insert a new element, we find the node the element should be in and insert the element into the elements array, incrementing numElements. If the array is already full, we first insert a new node either preceding or following the current one and move half of the elements in the current node into it.
To remove an element, we find the node it is in and delete it from the elements array, decrementing numElements. If this reduces the node to less than half-full, then we move elements from the next node to fill it back up above half. If this leaves the next node less than half full, then we move all its remaining elements into the current node, then bypass and delete it.
One of the primary benefits of unrolled linked lists is decreased storage requirements. All nodes (except at most one) are at least half-full. If many random inserts and deletes are done, the average node will be about three-quarters full, and if inserts and deletes are only done at the beginning and end, almost all nodes will be full. Assume that:
maxElements, the maximum number of elements in each elements array;Then, the space used for n elements varies between and . For comparison, ordinary linked lists require space, although v may be smaller, and arrays, one of the most compact data structures, require space. Unrolled linked lists effectively spread the overhead v over a number of elements of the list. Thus, we see the most significant space gain when overhead is large, maxElements is large, or elements are small.
If the elements are particularly small, such as bits, the overhead can be as much as 64 times larger than the data on many machines. Moreover, many popular memory allocators will keep a small amount of metadata for each node allocated, increasing the effective overhead v. Both of these make unrolled linked lists more attractive.
Because unrolled linked list nodes each store a count next to the next field, retrieving the kth element of an unrolled linked list (indexing) can be done in n/m + 1 cache misses, up to a factor of m better than ordinary linked lists. Additionally, if the size of each element is small compared to the cache line size, the list can be traversed in order with fewer cache misses than ordinary linked lists. In either case, operation time still increases linearly with the size of the list.
In computer science, a B-tree is a self-balancing tree data structure that maintains sorted data and allows searches, sequential access, insertions, and deletions in logarithmic time. The B-tree generalizes the binary search tree, allowing for nodes with more than two children. Unlike other self-balancing binary search trees, the B-tree is well suited for storage systems that read and write relatively large blocks of data, such as databases and file systems.
In computing, a hash table, also known as hash map, is a data structure that implements an associative array or dictionary. It is an abstract data type that maps keys to values. A hash table uses a hash function to compute an index, also called a hash code, into an array of buckets or slots, from which the desired value can be found. During lookup, the key is hashed and the resulting hash indicates where the corresponding value is stored.
In computer science, a heap is a specialized tree-based data structure that satisfies the heap property: In a max heap, for any given node C, if P is a parent node of C, then the key of P is greater than or equal to the key of C. In a min heap, the key of P is less than or equal to the key of C. The node at the "top" of the heap is called the root node.
In computer science, a linked list is a linear collection of data elements whose order is not given by their physical placement in memory. Instead, each element points to the next. It is a data structure consisting of a collection of nodes which together represent a sequence. In its most basic form, each node contains data, and a reference to the next node in the sequence. This structure allows for efficient insertion or removal of elements from any position in the sequence during iteration. More complex variants add additional links, allowing more efficient insertion or removal of nodes at arbitrary positions. A drawback of linked lists is that data access time is a linear function of the number of nodes for each linked list because nodes are serially linked so a node needs to be accessed first to access the next node. Faster access, such as random access, is not feasible. Arrays have better cache locality compared to linked lists.
In computer science, merge sort is an efficient, general-purpose, and comparison-based sorting algorithm. Most implementations produce a stable sort, which means that the relative order of equal elements is the same in the input and output. Merge sort is a divide-and-conquer algorithm that was invented by John von Neumann in 1945. A detailed description and analysis of bottom-up merge sort appeared in a report by Goldstine and von Neumann as early as 1948.
In computer science, a priority queue is an abstract data-type similar to a regular queue or stack data structure. Each element in a priority queue has an associated priority. In a priority queue, elements with high priority are served before elements with low priority. In some implementations, if two elements have the same priority, they are served in the same order in which they were enqueued. In other implementations, the order of elements with the same priority is undefined.
A splay tree is a binary search tree with the additional property that recently accessed elements are quick to access again. Like self-balancing binary search trees, a splay tree performs basic operations such as insertion, look-up and removal in O(log n) amortized time. For random access patterns drawn from a non-uniform random distribution, their amortized time can be faster than logarithmic, proportional to the entropy of the access pattern. For many patterns of non-random operations, also, splay trees can take better than logarithmic time, without requiring advance knowledge of the pattern. According to the unproven dynamic optimality conjecture, their performance on all access patterns is within a constant factor of the best possible performance that could be achieved by any other self-adjusting binary search tree, even one selected to fit that pattern. The splay tree was invented by Daniel Sleator and Robert Tarjan in 1985.
A binary heap is a heap data structure that takes the form of a binary tree. Binary heaps are a common way of implementing priority queues. The binary heap was introduced by J. W. J. Williams in 1964, as a data structure for heapsort.
A Bloom filter is a space-efficient probabilistic data structure, conceived by Burton Howard Bloom in 1970, that is used to test whether an element is a member of a set. False positive matches are possible, but false negatives are not – in other words, a query returns either "possibly in set" or "definitely not in set". Elements can be added to the set, but not removed ; the more items added, the larger the probability of false positives.
In computing, a persistent data structure or not ephemeral data structure is a data structure that always preserves the previous version of itself when it is modified. Such data structures are effectively immutable, as their operations do not (visibly) update the structure in-place, but instead always yield a new updated structure. The term was introduced in Driscoll, Sarnak, Sleator, and Tarjans' 1986 article.
A van Emde Boas tree, also known as a vEB tree or van Emde Boas priority queue, is a tree data structure which implements an associative array with m-bit integer keys. It was invented by a team led by Dutch computer scientist Peter van Emde Boas in 1975. It performs all operations in O(log m) time, or equivalently in O(log log M) time, where M = 2m is the largest element that can be stored in the tree. The parameter M is not to be confused with the actual number of elements stored in the tree, by which the performance of other tree data-structures is often measured.
A B+ tree is an m-ary tree with a variable but often large number of children per node. A B+ tree consists of a root, internal nodes and leaves. The root may be either a leaf or a node with two or more children.
In computer science, a scapegoat tree is a self-balancing binary search tree, invented by Arne Andersson in 1989 and again by Igal Galperin and Ronald L. Rivest in 1993. It provides worst-case lookup time and amortized insertion and deletion time.
In computer science, a dynamic array, growable array, resizable array, dynamic table, mutable array, or array list is a random access, variable-size list data structure that allows elements to be added or removed. It is supplied with standard libraries in many modern mainstream programming languages. Dynamic arrays overcome a limit of static arrays, which have a fixed capacity that needs to be specified at allocation.
In computational geometry, the bin is a data structure that allows efficient region queries. Each time a data point falls into a bin, the frequency of that bin is increased by one.
In computer science, a linked data structure is a data structure which consists of a set of data records (nodes) linked together and organized by references. The link between data can also be called a connector.
In computer science, a min-max heap is a complete binary tree data structure which combines the usefulness of both a min-heap and a max-heap, that is, it provides constant time retrieval and logarithmic time removal of both the minimum and maximum elements in it. This makes the min-max heap a very useful data structure to implement a double-ended priority queue. Like binary min-heaps and max-heaps, min-max heaps support logarithmic insertion and deletion and can be built in linear time. Min-max heaps are often represented implicitly in an array; hence it's referred to as an implicit data structure.
Skip graphs are a kind of distributed data structure based on skip lists. They were invented in 2003 by James Aspnes and Gauri Shah. A nearly identical data structure called SkipNet was independently invented by Nicholas Harvey, Michael Jones, Stefan Saroiu, Marvin Theimer and Alec Wolman, also in 2003.
In computing, sequence containers refer to a group of container class templates in the standard library of the C++ programming language that implement storage of data elements. Being templates, they can be used to store arbitrary elements, such as integers or custom classes. One common property of all sequential containers is that the elements can be accessed sequentially. Like all other standard library components, they reside in namespace std.
Approximate Membership Query Filter (AMQ-Filter) is a group of space-efficient probabilistic data structures that supports approximate membership queries. An approximate membership query answers if an element is in a set or not with a false positive rate of .
