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Estimate of time taken for running an algorithm
science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly
Time_complexity
Set of problems in computational complexity theory
complexity". The two most commonly analyzed resources are time and memory. In general, a complexity class is defined in terms of a type of computational problem
Complexity_class
Unproven computational hardness assumption
In computational complexity theory, the exponential time hypothesis (ETH) states that satisfiability of 3-CNF Boolean formulas (3-SAT) cannot be solved
Exponential_time_hypothesis
Amount of resources to perform an algorithm
computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally
Computational_complexity
Data structure for storing non-overlapping sets
by Bernard A. Galler and Michael J. Fischer in 1964. In 1973, their time complexity was bounded to O ( log ∗ ( n ) ) {\displaystyle O(\log ^{*}(n))}
Disjoint-set_data_structure
Computer memory needed by an algorithm
the input influencing space complexity. Analogously to time complexity classes DTIME(f(n)) and NTIME(f(n)), the complexity classes DSPACE(f(n)) and NSPACE(f(n))
Space_complexity
Class of problems solvable in polynomial time
In computational complexity theory, P, also known as PTIME or DTIME(nO(1)), is a fundamental complexity class. It contains all decision problems that can
P_(complexity)
Measurement of computational complexity
With respect to computational resources, asymptotic time complexity and asymptotic space complexity of computational algorithms and programs are commonly
Asymptotic computational complexity
Asymptotic_computational_complexity
Inherent difficulty of computational problems
their computational complexity, i.e., the amount of resources needed to solve them, such as time and storage. Other measures of complexity are also used, such
Computational complexity theory
Computational_complexity_theory
Model of computational complexity
In theoretical computer science, circuit complexity is a branch of computational complexity theory in which Boolean functions are classified according
Circuit_complexity
Complexity class used to classify decision problems
problems in computer science In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems
NP_(complexity)
Feature of systems that defy description
time. Warren Weaver posited in 1948 two forms of complexity: disorganized complexity, and organized complexity. Phenomena of 'disorganized complexity'
Complexity
Algorithm for the kth smallest element in an array
the side with the element it is searching for. This reduces the average complexity from O ( n log n ) {\displaystyle O(n\log n)} to O ( n ) {\displaystyle
Quickselect
Study of resources used by an algorithm
algorithms is the process of finding the computational complexity of algorithms—the amount of time, storage, or other resources needed to execute them.
Analysis_of_algorithms
Algorithm to multiply two numbers
number by every digit in the second and adding the results. This has a time complexity of O(n2), where n is the number of digits. When done by hand, this
Multiplication_algorithm
Computational complexity class
computational complexity theory and the analysis of algorithms, an algorithm is said to take quasi-polynomial time if its time complexity is quasi-polynomially
Quasi-polynomial_time
Tree searching strategy
depth-first search, which does not produce intermediate results. The time complexity of IDDFS in a (well-balanced) tree works out to be the same as breadth-first
Iterative deepening depth-first search
Iterative_deepening_depth-first_search
Decomposition of a number into a product
"Computational Complexity Blog: Complexity Class of the Week: Factoring". Goldreich, Oded; Wigderson, Avi (2008), "IV.20 Computational Complexity", in Gowers
Integer_factorization
Theoretical model of computation
a NTM, and vice versa. However, it is believed that in general the time complexity may not be the same. NTMs include DTMs as special cases, so every computation
Nondeterministic Turing machine
Nondeterministic_Turing_machine
Method for finding minimum spanning trees
to find the minimum spanning forest. In terms of their asymptotic time complexity, these three algorithms are equally fast for sparse graphs, but slower
Prim's_algorithm
Aho-Corasick to the Commentz-Walter Algorithm yields results with the idea of time complexity. Aho-Corasick is considered linear O(m+n+k) where k is the number of
Commentz-Walter_algorithm
Transformation of one computational problem to another
required computational resources in a given context (e.g., higher time complexity, greater memory requirement, need for extra hardware processor cores
Reduction_(complexity)
Ancient algorithm for generating prime numbers
+1)^{2}>(k+1)\Delta } . If Δ is chosen to be √n, the space complexity of the algorithm is O(√n), while the time complexity is the same as that of the regular sieve. For
Sieve_of_Eratosthenes
Clustering and community detection algorithm
other sources claim the time complexity is "essentially linear in the number of links in the graph," meaning the time complexity would instead be O ( m
Louvain_method
Consumption of resources that is indirectly required to achieve a goal
space overhead, but at the cost of slow performance (space/time tradeoff). Algorithmic complexity is generally specified using Big O notation. This makes
Overhead_(computing)
Algorithm for computing convex hulls in a set of points
finding the convex hull of a finite set of points in the plane with time complexity O(n log n). It is named after Ronald Graham, who published the original
Graham_scan
Type of image
computational time of histogram is O ( N ) {\displaystyle O(N)} time complexity. This saliency map algorithm has O ( N ) {\displaystyle O(N)} time complexity
Saliency_map
Algorithm that arranges lists in order
almost always based on an algorithm with average time complexity (and generally worst-case complexity) O(n log n), of which the most common are heapsort
Sorting_algorithm
Algorithms to generate prime numbers
time complexity would indicate because they have large negative constant offsets in their complexity and thus don't reach that asymptotic complexity until
Generation_of_primes
Bioinformatics computer program
alignment score order. This heuristic is necessary to restrict the time- and memory-complexity required to find the globally optimal solution. First, the algorithm
Clustal
Time used by a computer
are more commonly compared using measures of time complexity and space complexity. Typically, the CPU time used by a program is measured by the operating
CPU_time
Retrieval system algorithm
will reflect being closer to the centroid of related documents. The time complexity for training and testing the algorithm are listed below and followed
Rocchio_algorithm
Polynomial-time algorithm for the assignment problem
as the Kuhn–Munkres algorithm or Munkres assignment algorithm. The time complexity of the original algorithm was O ( n 4 ) {\displaystyle O(n^{4})} ,
Hungarian_algorithm
Heuristic pathfinding algorithm
only linear in the length of the solution that it constructs. Its time complexity is analyzed by Korf et al. under the assumption that the heuristic
Iterative_deepening_A*
Algorithmic runtime requirements for common math procedures
the computational complexity of various algorithms for common mathematical operations. Here, complexity refers to the time complexity of performing computations
Computational complexity of mathematical operations
Computational_complexity_of_mathematical_operations
Algorithm for integer multiplication
{\displaystyle \Omega (n^{2})\,\!} conjecture and other problems in the complexity of computation. Within a week, Karatsuba, then a 23-year-old student,
Karatsuba_algorithm
Associative array for storing key–value pairs
a probing sequence. In a well-dimensioned hash table, the average time complexity for each lookup is independent of the number of elements stored in
Hash_table
Rooted binary tree data structure
node's left subtree and less than the ones in its right subtree. The time complexity of operations on the binary search tree is linear with respect to the
Binary_search_tree
Given more time, a Turing machine can solve more problems
In computational complexity theory, the time hierarchy theorems are important statements about time-bounded computation on Turing machines. Informally
Time_hierarchy_theorem
Data structure for storing strings
S2, into a single rope. Time complexity: O ( 1 ) {\displaystyle O(1)} (or O ( log N ) {\displaystyle O(\log N)} time to compute the root weight)
Rope_(data_structure)
Complexity class in computer science
Logarithmic-space Polynomial-time), is the complexity class of computational complexity theory problems solvable in logarithmic space and polynomial time with probabilistic
RL_(complexity)
Upper bound on resources required by an algorithm
science (specifically computational complexity theory), the worst-case complexity measures the resources (e.g. running time, memory) that an algorithm requires
Worst-case_complexity
Measures of how efficiently algorithms use resources
respectively. Usually the resource being considered is running time, i.e. time complexity, but could also be memory or some other resource. Best case is
Best,_worst_and_average_case
Problem in computer science
Unsolved problem in computer science What is the Turing run-time complexity of the square-root sum problem? More unsolved problems in computer science
Square-root_sum_problem
Sorting algorithm
selection sort is an in-place comparison sorting algorithm. It has a O(n2) time complexity, which makes it inefficient on large lists, and generally performs
Selection_sort
Abstract data type in computer science
average time complexity of O ( 1 ) {\displaystyle O(1)} to test adjacency of two given vertices and to remove an edge and an amortized average time complexity
Graph_(abstract_data_type)
Unsolved problem in computer science
or linear time, and posited that if so, then the discovery of mathematical proofs could be automated. The relation between the complexity classes P and
P_versus_NP_problem
Topics referred to by the same term
complexity, the most widely used such measure. In computational complexity theory, although it would be a non-formal usage of the term, the time/space
Algorithmic_complexity
Measure of algorithmic complexity
theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is the length of a shortest computer
Kolmogorov_complexity
fields. For a fixed ground field, its time complexity is polynomial, but, for general ground fields, the complexity is exponential in the size of the ground
Factorization of polynomials over finite fields
Factorization_of_polynomials_over_finite_fields
Algorithm for visible surface determination in 3D graphics
pixel that p covers: paint p.color on pixel The painter's algorithm's time-complexity depends on the sorting algorithm used to order the polygons. Assuming
Painter's_algorithm
Stream ciphers
on Salsa20/6 with estimated time complexity of 2177, and a related-key attack on Salsa20/7 with estimated time complexity of 2217. In 2007, Tsunoo et
Salsa20
Agglomerative hierarchical clustering method
{\displaystyle O(n^{3})} time complexity, and using a heap for each cluster to keep its distances from other cluster reduces its time to O ( n 2 log n )
UPGMA
Method for partitioning partial orders into levels
state the time complexity of the Coffman–Graham algorithm, on an n-element partial order, to be O(n2). However, this analysis omits the time for constructing
Coffman–Graham_algorithm
Simplicial complex in Euclidean geometry
process of adding one point of 𝒫 at a time until all of 𝒫 has been processed. The following table reports time complexity results for the construction of triangulations
Point-set_triangulation
Concept of fault-tolerance
incorrect state or is corrupted by an intruder. Moreover, because of their complexity, it is very hard to debug and to analyze distributed systems. Hence, it
Self-stabilization
Algorithm to search the nodes of a graph
graph of German cities (upper diagram) starting from Frankfurt. The time complexity can be expressed as O(|V|+|E|), as every vertex and every edge will
Breadth-first_search
Tree data structure for metric spaces
nodes with the smallest distance from the root. This will lead to a time complexity of . However, this algorithm is very accurate and can find every substrings
BK-tree
Method for finding loopless paths
it is possible for each path to have N {\displaystyle N} nodes. The time complexity of Yen's algorithm is dependent on the shortest path algorithm used
Yen's_algorithm
Mathematical problem
algorithm is a sorting algorithm whose time complexity is currently an open problem. The worst case complexity has an upper bound which can be given in
Coin_problem
Solving an optimization problem with a quadratic objective function
can be done using O(L n3) arithmetic operations, for a total runtime complexity of O(L2 n4). Kapoor and Vaidya present another algorithm, which requires
Quadratic_programming
UNIX program for lexical analysis
nondeterministic finite automaton. A Flex lexical analyzer usually has time complexity O ( n ) {\displaystyle O(n)} in the length of the input. That is, it
Flex (lexical analyzer generator)
Flex_(lexical_analyzer_generator)
Branch of mathematical logic
Descriptive complexity is a branch of computational complexity theory and of finite model theory that characterizes complexity classes by the type of logic
Descriptive_complexity_theory
Algorithm in mathematical optimization
algorithms achieve even lower time complexities. The variant based on the highest label node selection rule has O(V 2√E) time complexity and is generally regarded
Push–relabel maximum flow algorithm
Push–relabel_maximum_flow_algorithm
American computer scientist (born 1969)
is an American theoretical computer scientist working in computational complexity theory and algorithms. Williams graduated from the Alabama School of Mathematics
Ryan Williams (computer scientist)
Ryan_Williams_(computer_scientist)
Computational complexity of quantum algorithms
Quantum complexity theory is the subfield of computational complexity theory that deals with complexity classes defined using quantum computers, a computational
Quantum_complexity_theory
Decision problem in computer science
of the knapsack problem and of the multiple subset sum problem. The time complexity of SSP depends on two parameters: n - the number of input integers
Subset_sum_problem
Parsing technique
grammars, and top-down parsing with backtracking may have exponential time complexity with respect to the length of the input for ambiguous CFGs. However
Top-down_parsing
Search tree data structure
for a node with an associated key of size m {\displaystyle m} has the complexity of O ( m ) {\displaystyle O(m)} , whereas an imperfect hash function may
Trie
Test if a Mersenne number is prime
to square a p-bit number. Since this happens O(p) times, the total time complexity is O(p3). A more efficient multiplication algorithm is the Schönhage–Strassen
Lucas–Lehmer_primality_test
Generic-case complexity is a subfield of computational complexity theory that studies the complexity of computational problems on "most inputs". Generic-case
Generic-case_complexity
Polynomial function with logarithm terms
quasi-polynomial growth, and algorithms with this as their time complexity are said to take quasi-polynomial time. All polylogarithmic functions of n are o(nε) for
Polylogarithmic_function
Algorithm in graph theory
having a cost of Θ ( n 2 ) {\displaystyle \Theta (n^{2})} , the total time complexity of the algorithm is n ⋅ Θ ( n 2 ) = Θ ( n 3 ) {\displaystyle n\cdot
Floyd–Warshall_algorithm
Computational problem of graph theory
Heiligman, Mark; Høyer, Peter; Mhalla, Mehdi (January 2006). "Quantum query complexity of some graph problems". SIAM Journal on Computing. 35 (6): 1310–1328
Shortest_path_problem
Self-balancing binary search tree data structure
hashcodes, a red–black tree is used. This results in the improvement of time complexity of searching such an element from O(m) to O(logm) where m is the number
Red–black_tree
Variant of heap data structure
worst-case time complexity of O(log n). For a random heap, and for repeated insertions, the insertion operation has an average-case complexity of O(1).
Binary_heap
Algorithm for finding shortest paths
Θ(|V|2) time, where |V| is the number of nodes. Fredman & Tarjan 1984 proposed a Fibonacci heap priority queue to optimize the running time complexity to Θ(|E|+|V|log|V|)
Dijkstra's_algorithm
Abstract data type
time is O(1), but individual operations can take O(n) where n is the number of elements in the queue. The second implementation is called a real-time
Queue_(abstract_data_type)
Algorithm for finding the convex hull of a set of points
time complexity for 2-dimensional and 3-dimensional space is O(n2), but when the input precision is restricted to O(logn) bits, its worst case time complexity
Quickhull
Distance Matrix's time complexity is O(N^2L^2) where N is the number of sequences and L is the length of the sequence. This time complexity is because the
MAFFT
Concept in computational complexity theory
Logarithmic-space Polynomial-time), is the complexity class of problems solvable in logarithmic space and polynomial time with probabilistic Turing machines
BPL_(complexity)
Abstract data type
sliding window over a sequence in a linear time complexity. The complexity of a naive solution is O(n.k) time and O(1) space, where n is the length of the
Double-ended_queue
Sorting algorithm
efficient for data sets that are already substantially sorted: the time complexity is O(kn) when each element in the input is no more than k places away
Insertion_sort
Algorithm characteristic in computations
computational complexity theory, the average-case complexity of an algorithm is the amount of some computational resource (typically time) used by the
Average-case_complexity
Inefficient recursive sorting algorithm
recursive sorting algorithm. It is notable for its exceptionally poor time complexity of O ( n log 3 / log 1.5 ) {\displaystyle O(n^{\log 3/\log 1.5})}
Stooge_sort
Data structure in tree form sorted for fast lookup
These subtrees must all qualify as binary search trees. The worst-case time complexity for searching a binary search tree is the height of the tree, which
Search_tree
Class of algorithms in computational geometry
the convex hull of a finite set of points, with various computational complexities. Computing the convex hull means that a non-ambiguous and efficient representation
Convex_hull_algorithms
List of unsolved computational problems
log n) time? What is the fastest algorithm for multiplication of two n-digit numbers? What is the lowest possible average-case time complexity of Shellsort
List of unsolved problems in computer science
List_of_unsolved_problems_in_computer_science
Type of cryptanalytic attack
n} unknown coefficients in p ( x ) {\displaystyle p(x)} . Then the time complexity for this attack is n {\displaystyle n} , requiring n {\displaystyle
Interpolation_attack
the analysis of algorithms, where they give rise to sub-exponential time complexity, and in the growth rate of groups, where a subexponential growth rate
Infra-exponential
Topics referred to by the same term
Quasi-polynomial time, relating to time complexity in computer science QP or EQP, Exact Quantum Polynomial time in computational complexity theory Akasa Air
QP
Topics referred to by the same term
parte, for a type of synonymy in taxonomy PP (complexity), a probabilistic polynomial time complexity class PP-format (Post Processing Format), a file
PP
Equivalence of average-case and expected complexity
In computational complexity theory, Yao's principle (also called Yao's minimax principle or Yao's lemma) relates the performance of randomized algorithms
Yao's_principle
Subfield of computational complexity theory
Fine-grained complexity is a subfield of computational complexity theory that studies the time required to solve computational problems, especially those
Fine_grained_complexity
Computational complexity class
computational complexity theory, the complexity class E is the set of decision problems that can be solved by a deterministic Turing machine in time 2O(n) and
E_(complexity)
Algorithmic complexity class
exponential time, i.e., in O(2p(n)) time, where p(n) is a polynomial function of n. EXPTIME is one intuitive class in an exponential hierarchy of complexity classes
EXPTIME
elements, the time complexities for the various functions are formulated in the table below. For pairing heaps, it is an amortized complexity. One example
Double-ended_priority_queue
Measure of the structural complexity of a software program
Cyclomatic complexity is a software metric used to indicate the complexity of a program. It is a quantitative measure of the number of linearly independent
Cyclomatic_complexity
Seasonal change of clock settings
clock shifts have the disadvantage of complexity. People must remember to change their clocks; this can be time-consuming, particularly for mechanical
Daylight_saving_time
Multidimensional search tree for points in k dimensional space
{\displaystyle O(n\log n)} time in the best case. An algorithm that builds a balanced k-d tree to sort points has a worst-case complexity of O ( k n log ( n
K-d_tree
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