Concepts inUnion-Find with Constant Time Deletions
Disjoint-set data structure
In computing, a disjoint-set data structure is a data structure that keeps track of a set of elements partitioned into a number of disjoint (nonoverlapping) subsets. A union-find algorithm is an algorithm that performs two useful operations on such a data structure: Find: Determine which subset a particular element is in. This can be used for determining if two elements are in the same subset. Union: Join two subsets into a single subset.
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Time complexity
In computer science, the time complexity of an algorithm quantifies the amount of time taken by an algorithm to run as a function of the size of the input to the problem. The time complexity of an algorithm is commonly expressed using big O notation, which suppresses multiplicative constants and lower order terms. When expressed this way, the time complexity is said to be described asymptotically, i.e. , as the input size goes to infinity.
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Time
Time is the indefinite continued progress of existence and events that occur in apparently irreversible succession from the past through the present to the future. Time is a component quantity of many measurements used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change of quantities in material reality or in the conscious experience.
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Robert Tarjan
Robert Endre Tarjan (born April 30, 1948) is an American computer scientist. He is the discoverer of several graph algorithms, including Tarjan's off-line least common ancestors algorithm, and co-inventor of both splay trees and Fibonacci heaps. Tarjan is currently the James S. McDonnell Distinguished University Professor of Computer Science at Princeton University, and is also a Senior Fellow at Hewlett-Packard.
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Amortized analysis
In computer science, amortized analysis is a method of analyzing algorithms that considers the entire sequence of operations of the program. It allows for the establishment of a worst-case bound for the performance of an algorithm irrespective of the inputs by looking at all of the operations.
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Set (abstract data type)
In computer science, a set is an abstract data structure that can store certain values, without any particular order, and no repeated values. It is a computer implementation of the mathematical concept of a finite set. Unlike most other collection types, rather than retrieving a specific element from a set, one typically tests a value for membership in a set. Some set data structures are designed for static or frozen sets that do not change after they are constructed.
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Deletion (genetics)
In genetics, a deletion (also called gene deletion, deficiency, or deletion mutation) is a mutation in which a part of a chromosome or a sequence of DNA is missing. Deletion is the loss of genetic material. Any number of nucleotides can be deleted, from a single base to an entire piece of chromosome. Deletions can be caused by errors in chromosomal crossover during meiosis. This causes several serious genetic diseases. Deletion also causes frameshift.
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Disjoint sets
In mathematics, two sets are said to be disjoint if they have no element in common. For example, {1, 2, 3} and {4, 5, 6} are disjoint sets.
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