Multiple choice hashing is named because it employs the implementation of multiple hash functions.On a high level, when there are multiple hash functions each item is mapped to multiple buckets and therefore the Algorithmdesigner has freedom to select in which of those the item would reside.It turns out that this freedom permits for Algorithms which obtain allocations that are much more balanced then that availed by implementing a single hash function.We will present the main Algorithmic ideas and the main mathematical tools that are implemented for proving bounds on the allocations these Algorithms produce.We will see that the analysis is ... Read More

DefinitionDynamic perfect hashing is defined as a programming method for resolving collisions in a hash table data structure.ApplicationWhile more memory-intensive than its hash table counterparts, this method is ideal for situations where fast queries, insertions, and deletions must be performed on a large set of elements.ImplementationDietzfelbinger et al. explain a dynamic dictionary Algorithm that, when a set of m items is incrementally appended to the dictionary, membership queries always consume constant time and therefore O(1) worst-case time, the total storage needed is O(m) (linear), and O(1) expected amortized insertion and deletion time (amortized constant time).In the dynamic case, when a ... Read More

Definition of Perfect HashingPerfect hashing is defined as a model of hashing in which any set of n elements can be stored in a hash table of equal size and can have lookups performed in constant time. It was specifically invented and discussed by Fredman, Komlos and Szemeredi (1984) and has therefore been nicknamed as "FKS Hashing".Definition of Static HashingStatic Hashing defines another form of the hashing problem which permits users to accomplish lookups on a finalized dictionary set (that means all objects in the dictionary are final as well as not changing).ApplicationSince static hashing needs that the database, its objects and ... Read More

A meldable DEPQ (MDEPQ) is defined as a DEPQ (Double Ended Priority Queue) that, in addition to the DEPQ operations listed above, includes the operation meld(p, q) ... meld the DEPQs p and q into a single DEPQ. The result of melding the double-ended priority queues p and q is a single double-ended priority queue that contains all elements of p and q. The meld operation is destructive in that following the meld, p and q do not remain as independent DEPQs.To meld two DEPQs in less than linear time, it is necessary that the DEPQs be represented implementing explicit ... Read More

Total and leaf correspondence are more sophisticated correspondence techniques. In both of these techniques, half the elements are located in the min PQ and the other half in the max PQ. When the number of elements is odd, one element is stored in a buffer. This buffered element is not the member of either PQ. In total correspondence technique, each element x in the min PQ is paired with a distinct element y of the max PQ. (x, y) is a corresponding pair of elements such that priority(x)

Existence of general methods to arrive at efficient DEPQ(Double Ended Priority Queue) data structures from single-ended priority queue (PQ) data structures that also provide an efficient implementation of the remove(bNode) operation (this operation eliminates the node bNode from the PQ). The simplest of these methods, dual structure method, maintains both a min PQ and a max PQ of all the DEPQ elements associated with correspondence pointers between the nodes of the min PQ and the max PQ that consist the same element.Figure D displays a dual heap structure for the elements 7, 8, 3, 6, 5. Correspondence pointers are displayed ... Read More

Dual HeapExistence of general methods to arrive at efficient DEPQ (Double Ended Priority Queue) data structures from single-ended priority queue (PQ) data structures that also provide an efficient implementation of the remove(aNode) operation (this operation eliminates the node aNode from the PQ). The simplest of these methods, dual structure method, keeps track of both a min PQ and a max PQ of all the DEPQ elements associated with correspondence pointers between the nodes of the min PQ and the max PQ consisting the same element.Figure A displays a dual heap structure for the elements 7, 8, 3, 6, 5. Correspondence ... Read More

Now we shall explain the technique for removing the min elements in the deap data structure. During deletion, our main target to delete the minimal value from deaps. As the height of the tree is always log n, it consumes time of order of log n. We can discuss deletion operation as follows −Procedure deap_deletion(b[],m): if(m

To insert element into deap data structure, we might need the procedures to calculate the minimum and maximum values as depicted below −Procedure min_value(m): //To calculate the minimum value in deap. return m-2log2((m-1) ;Procedure max_value(m): //To calculate the maximum value in deap. return m+2log2(m-1);The insertion operation in deap data structure can be done in following way −For any heap b[], we should check if m is a position within the maximum-heap of deap.We shall then calculate the minimum and maximum values in deap.Now, comparison is done between the key values at left sub-tree and right sub-tree.At last, we perform the ... Read More

A min-max heap is defined as a complete binary tree containing alternating min (or even) and max (or odd) levels. Even levels are denoted as for example 0, 2, 4, etc, and odd levels are denoted as 1, 3, 5, etc.We consider in the next points that the root element is at the first level, i.e., 0.Example of Min-max heapFeatures of Min-max heapEach node in a min-max heap is associated with a data member (usually called key) whose value is implemented to calculate the order of the node in the min-max heap.The root element is the minimum element in the ... Read More