The NIST Dictionary of Algorithms and Data Structures is a reference work maintained by the U.S. National Institute of Standards and Technology. It defines a large number of terms relating to algorithms and data structures.

Note: Many, but not all, of the definitions in the Dictionary of Algorithms and Data Structures are in the public domain, since they were written by employees of the U.S. Federal Government acting as agents of the government. However, some are contributed by outside contributors, and are therefore not in the public domain. Please only submit material from this work to Wikipedia when you have confirmed that this particular item is in the public domain.

This list of terms was originally derived from the index of this document, and should be in the public domain, as it was compiled by a Federal Government employee as part of a Federal Government work. Some of the terms defined are:

A

• absolute performance guarantee
• abstract data type
• (a,b)-tree
• accepting state
• Ackermann's function
• active data structure
• acyclic directed graph
• acyclic graph
• adaptive heap sort
• adaptive Huffman encoding
• adaptive k-d tree
• adaptive sort
• address-calculation sort
• adjacency-list representation
• adjacency-matrix representation
• adjacent
• admissible vertex
• ADT
• adversary
• algorithm
• algorithm B
• algorithm BSTW
• algorithm FGK
• algorithmically solvable
• algorithm V
• all pairs shortest path
• alphabet
• Alpha Skip Search algorithm
• alternating path
• alternating Turing machine
• alternation
• American flag sort
• amortized cost
• ancestor
• and
• ANSI
• antichain
• antisymmetric relation
• AP
• Apostolico-Crochemore
• Apostolico-Giancarlo algorithm
• approximate string matching
• approximation algorithm
• arborescence
• arc
• arithmetic coding
• array
• array index
• array merging
• array search
• articulation point
• assignment problem
• association list
• associative
• associative array
• asymptotically tight bound
• asymptotic bound
• asymptotic lower bound
• asymptotic space complexity
• asymptotic time complexity
• asymptotic upper bound
• augmenting path
• automaton
• average case
• average-case cost
• AVL tree
• axiomatic semantics

B

• backtracking
• bag
• balance
• balanced binary search tree
• balanced binary tree
• balanced k-way merge sort
• balanced merge sort
• balanced multiway merge
• balanced multiway tree
• balanced quicksort
• balanced tree
• balanced two-way merge sort
• BANG file
• Batcher sort
• Baum Welch algorithm
• BB α tree
• BDD
• BD-tree
• Bellman-Ford algorithm
• Benford's law
• best case
• best-case cost
• best-first search
• biconnected component
• biconnected graph
• bidirectional bubble sort
• big-O notation
• binary function
• binary GCD algorithm
• binary heap
• binary insertion sort
• binary knapsack problem
• binary priority queue
• binary relation
• binary search
• binary search tree
• binary tree
• binary tree representation of trees
• bingo sort
• binomial heap
• binomial tree
• bin packing problem
• bin sort
• bintree
• bipartite graph
• bipartite matching
• bisector
• bitonic sort
• bit vector
• Bk tree
• block
• block addressing index
• blocking flow
• block search
• Bloom filter
• blossom
• bogosort
• boogol
• boolean
• boolean expression
• boolean function
• border
• bottleneck traveling salesman
• bottom-up tree automaton
• boundary-based representation
• bounded error probability in polynomial time
• bounded queue
• bounded stack
• Boyer-Moore
• Boyer-Moore-Horspool
• bozo sort
• B+ tree
• BPP
• Bradford's law
• branch and bound
• branching
• breadth-first search
• Bresenham's algorithm
• brick sort
• bridge
• British Museum algorithm
• brute force
• brute force string search
• brute force string search with mismatches
• BSP-tree
• B*-tree
• B-tree
• bubble sort
• bucket
• bucket array
• bucketing method
• bucket sort
• bucket trie
• buddy system
• buddy tree
• build-heap
• Burrows-Wheeler transform
• busy beaver
• BV-tree
• BWT
• Byzantine generals

C

• cactus stack
• Calculus of Communicating Systems
• calendar queue
• candidate consistency testing
• candidate verification
• canonical complexity class
• capacitated facility location
• capacity
• capacity constraint
• cartesian tree
• cascade merge sort
• caverphone
• Cayley-Purser
• CCS
• C curve
• cell probe model
• cell tree
• cellular automaton
• centroid
• certificate
• chain
• chaining
• child
• Chinese postman problem
• Chinese remainder theorem
• Christofides algorithm
• Christofides heuristic
• chromatic index
• chromatic number
• Church-Turing thesis
• circuit
• circuit complexity
• circuit value problem
• circular list
• circular queue
• clique
• clique problem
• clustering
• clustering free
• coalesced hashing
• coarsening
• cocktail shaker sort
• codeword
• coding tree
• collective recursion
• collision
• collision resolution scheme
• Colussi
• combination
• comb sort
• Communicating Sequential Processes
• commutative
• compact DAWG
• compact trie
• comparison sort
• competitive analysis
• competitive ratio
• complement
• complete binary tree
• complete graph
• completely connected graph
• complete tree
• complexity
• complexity class
• computable
• concave function
• concurrent flow
• concurrent read, concurrent write
• concurrent read, exclusive write
• configuration
• confluently persistent data structure
• conjunction
• connected components
• connected graph
• co-NP
• constant function
• continuous knapsack problem
• Cook reduction
• Cook's theorem
• counting sort
• covering
• CRC
• CRCW
• Crew (algorithm)
• critical path problem
• CSP
• CTL
• cuckoo hashing
• cut
• cutting plane
• cutting stock problem
• cutting theorem
• cut vertex
• cycle
• cyclic redundancy check

D

• D-adjacent
• DAG
• DAG shortest paths
• data structure
• DAWG
• decidable
• decidable language
• decimation
• decision problem
• decision tree
• decomposable searching problem
• degree
• dense graph
• depoissonization
• depth
• depth-first search
• deque
• derangement
• descendant
• deterministic
• deterministic algorithm
• deterministic finite automata string search
• deterministic finite automaton
• deterministic finite state machine
• deterministic finite tree automaton
• deterministic pushdown automaton
• deterministic tree automaton
• Deutsch-Jozsa algorithm
• DFA
• DFS
• DFS forest
• DFTA
• diagonalization
• diameter
• dichotomic search
• dictionary
• diet (see discrete interval encoding tree below)
• difference
• digital search tree
• digital tree
• digraph
• Dijkstra's algorithm
• diminishing increment sort
• dining philosophers
• direct chaining hashing
• directed acyclic graph
• directed acyclic word graph
• directed graph
• discrete interval encoding tree
• discrete p-center
• disjoint set
• disjunction
• distributional complexity
• distribution sort
• divide and conquer
• divide and marriage before conquest
• division method
• domain
• don't care
• Doomsday rule
• double-direction bubble sort
• double-ended priority queue
• double hashing
• double left rotation
• double metaphone
• double right rotation
• doubly-chained tree
• doubly-ended queue
• doubly linked list
• DPDA
• Dragon curve
• dual
• dual linear program
• Dutch national flag
• dyadic tree
• dynamic
• dynamic array
• dynamic hashing
• dynamic programming
• dynamization transformation

E

• edge
• edge coloring
• edge connectivity
• edge crossing
• edge-weighted graph
• edit distance
• edit operation
• edit script
• efficiency
• 8 queens
• elastic-bucket trie
• element uniqueness
• end-of-string
• enfilade
• ERCW
• EREW
• Euclidean algorithm
• Euclidean distance
• Euclidean Steiner tree
• Euclidean traveling salesman problem
• Euclid's algorithm
• Euler cycle
• Eulerian graph
• Eulerian path
• exact string matching
• EXCELL
• exchange sort
• exclusive or
• exclusive read, concurrent write
• exclusive read, exclusive write
• exhaustive search
• existential state
• expandable hashing
• expander graph
• exponential
• extended binary tree
• extended Euclid's algorithm
• extended k-d tree
• extendible hashing
• external index
• external memory algorithm
• external memory data structure
• external merge
• external merge sort
• external node
• external quicksort
• external radix sort
• external sort
• extrapolation search
• extremal
• extreme point

F

• facility location
• factor
• factorial
• fast fourier transform
• fathoming
• feasible region
• feasible solution
• feedback edge set
• feedback vertex set
• Ferguson-Forcade algorithm
• FFT
• Fibonacci number
• Fibonacci search
• Fibonacci tree
• Fibonacci heap
• FIFO
• filial-heir chain
• Find
• find kth least element
• finitary tree
• finite Fourier transform
• finite state automaton
• finite state machine
• finite state machine minimization
• finite state transducer
• first child-next sibling binary tree
• first come, first served
• first-in, first-out
• fixed-grid method
• flash sort
• flow
• flow conservation
• flow function
• flow network
• Floyd-Warshall algorithm
• Ford-Bellman
• Ford-Fulkerson method
• forest
• forest editing problem
• formal language
• formal methods
• formal verification
• forward index
• fractal
• fractional knapsack problem
• fractional solution
• free edge
• free list
• free tree
• free vertex
• frequency count heuristic
• full array
• full binary tree
• full inverted index
• fully dynamic graph problem
• fully persistent data structure
• fully polynomial approximation scheme
• function (programming)
• function (mathematics)
• functional data structure

G

• Galil-Giancarlo
• Galil-Seiferas
• gamma function
• GBD-tree
• GCD
• geometric optimization problem
• global optimum
• gnome sort
• goobi
• graph
• graph coloring
• graph concentration
• graph drawing
• graph isomorphism
• graph partition
• Gray code
• greatest common divisor
• greedy algorithm
• greedy heuristic
• grid drawing
• grid file
• Grover's algorithm

H

• halting problem
• Hamiltonian cycle
• Hamiltonian path
• Hamming distance
• hash function
• hash heap
• hash table
• hash table delete
• Hausdorff distance
• hB-tree
• head
• heap
• heapify
• heap property
• heapsort
• heaviest common subsequence
• height
• height-balanced binary search tree
• height-balanced tree
• Herter-Heighway Dragon
• heuristic
• hidden Markov model
• highest common factor
• Hilbert curve
• histogram sort
• HMM
• homeomorphic
• horizontal visibility map
• Horner's rule
• Horspool
• Huffman encoding
• Hungarian algorithm
• hybrid algorithm
• hyperedge
• hypergraph

I

• ID
• ideal merge
• implication
• implies
• in-branching
• inclusion-exclusion principle
• inclusive or
• incompressible string
• in-degree
• independent set
• index file
• information theoretic bound
• in-order traversal
• in-place sort
• insertion sort
• instantaneous description
• integer linear program
• integer multi-commodity flow
• integer polyhedron
• interactive proof system
• interior-based representation
• internal node
• internal sort
• interpolation search
• interpolation-sequential search
• interpolation sort
• intersection
• interval tree
• intractable
• introsort
• introspective sort
• inverse Ackermann function
• inverted file index
• inverted index
• irreflexive
• isomorphic
• iteration

J

• Jaro-Winkler
• Johnson's algorithm
• Johnson-Trotter
• J sort
• jump list
• jump search

K

• Karmarkar's algorithm
• Karnaugh map
• Karp-Rabin
• Karp reduction
• k-ary heap
• k-ary Huffman encoding
• k-ary tree
• k-clustering
• k-coloring
• k-connected graph
• k-d-B-tree
• k-dimensional
• K-dominant match
• k-d tree
• key
• KMP
• KmpSkip Search
• knapsack problem
• knight's tour
• Knuth-Morris-Pratt algorithm
• Königsberg bridges problem
• Kolmogorov complexity
• Kraft's inequality
• Kripke structure
• Kruskal's algorithm
• kth order Fibonacci numbers
• kth shortest path
• kth smallest element
• KV diagram
• k-way merge
• k-way merge sort
• k-way tree

L

• labeled graph
• language
• last-in, first-out
• Las Vegas algorithm
• lattice
• layered graph
• LCM
• LCS
• leaf
• least common multiple
• leftist tree
• left rotation
• Lempel-Ziv-Welch
• level-order traversal
• Levenshtein distance
• lexicographical order
• LIFO
• linear
• linear congruential generator
• linear hash
• linear insertion sort
• linear order
• linear probing
• linear probing sort
• linear product
• linear program
• linear quadtree
• linear search
• link
• linked list
• list
• list contraction
• little-o notation
• Lm distance
• load factor
• local alignment
• local optimum
• logarithmic
• longest common subsequence
• longest common substring
• Lotka's law
• lower bound
• lower triangular matrix
• lowest common ancestor
• l-reduction
• lucky sort
• LZW

M

• Malhotra-Kumar-Maheshwari blocking flow
• Manhattan distance
• many-one reduction
• Markov chain
• Marlena
• marriage problem
• Master theorem
• matched edge
• matched vertex
• matching
• matrix
• matrix-chain multiplication problem
• max-heap property
• maximal independent set
• maximally connected component
• Maximal Shift
• maximum bipartite matching
• maximum-flow problem
• MAX-SNP
• MBB
• Mealy machine
• mean
• median
• meld
• memoization
• merge
• merge sort
• meromorphic function
• metaheuristic
• metaphone
• midrange
• Miller-Rabin
• min-heap property
• minimal perfect hashing
• minimum bounding box
• minimum cut
• minimum path cover
• minimum spanning tree
• minimum vertex cut
• mixed integer linear program
• mode
• model checking
• model of computation
• moderately exponential
• MODIFIND
• monotone priority queue
• monotonically decreasing
• monotonically increasing
• Monte Carlo algorithm
• Moore machine
• Morris-Pratt
• move
• move-to-front heuristic
• move-to-root heuristic
• MST
• multi-commodity flow
• multigraph
• multilayer grid file
• multiplication method
• multiprefix
• multiprocessor model
• multiset
• multi suffix tree
• multiway decision
• multiway merge
• multiway search tree
• multiway tree
• Munkres' assignment algorithm

N

• naive string search
• nand
• n-ary function
• NC
• NC many-one reducibility
• nearest neighbor
• negation
• network flow
• network flow problem
• next state
• NFA
• NFTA
• NIST
• node
• nonbalanced merge
• nonbalanced merge sort
• nondeterministic
• nondeterministic algorithm
• nondeterministic finite automaton
• nondeterministic finite state machine
• nondeterministic finite tree automaton
• nondeterministic polynomial time
• nondeterministic tree automaton
• nondeterministic Turing machine
• nonterminal node
• nor
• not
• Not So Naive
• NP
• NP-complete
• NP-complete language
• NP-hard
• n queens
• nullary function
• null tree
• NYSIIS

O

• OBDD
• objective function
• occurrence
• octree
• off-line algorithm
• offset
• omega
• omicron
• one-based indexing
• one-dimensional
• online algorithm
• open addressing
• optimal
• optimal cost
• optimal hashing
• optimal merge
• optimal mismatch
• optimal polygon triangulation problem
• optimal polyphase merge
• optimal polyphase merge sort
• optimal solution
• optimal triangulation problem
• optimal value
• optimization problem
• or
• oracle set
• oracle tape
• oracle Turing machine
• order
• ordered array
• ordered binary decision diagram
• ordered linked list
• ordered tree
• order preserving hash
• order preserving minimal perfect hashing
• oriented acyclic graph
• oriented graph
• oriented tree
• orthogonal drawing
• orthogonal lists
• orthogonally convex rectilinear polygon
• oscillating merge sort
• out-branching
• out-degree
• overlapping subproblems

P

• packing
• padding argument
• pagoda
• pairing heap
• PAM
• parallel computation thesis
• parallel prefix computation
• parallel random-access machine
• parametric searching
• parent
• partial function
• partially decidable problem
• partially dynamic graph problem
• partially ordered set
• partially persistent data structure
• partial order
• partial recursive function
• partition
• passive data structure
• patience sorting
• path
• path cover
• path system problem
• Patricia tree
• pattern
• pattern element
• P-complete
• PCP
• PDA
• Peano curve
• Pearson's hash
• perfect binary tree
• perfect hashing
• perfect k-ary tree
• perfect matching
• perfect shuffle
• performance guarantee
• performance ratio
• permutation
• persistent data structure
• phonetic coding
• pile
• pipelined divide and conquer
• planar graph
• planarization
• planar straight-line graph
• PLOP-hashing
• point access method
• pointer jumping
• pointer machine
• poissonization
• polychotomy
• polyhedron
• polylogarithmic
• polynomial
• polynomial approximation scheme
• polynomial hierarchy
• polynomial time
• polynomial-time Church-Turing thesis
• polynomial-time reduction
• polyphase merge
• polyphase merge sort
• polytope
• poset
• postfix traversal
• Post machine
• postman's sort
• postorder traversal
• Post's correspondence problem
• potential function
• PRAM
• predicate
• prefix
• prefix code
• prefix computation
• prefix sums
• prefix traversal
• preorder traversal
• primary clustering
• primitive recursive
• Prim's algorithm
• principle of optimality
• priority queue
• prisoner's dilemma
• PRNG
• probabilistic algorithm
• probabilistically checkable proof
• probabilistic Turing machine
• probe sequence
• procedure
• process algebra
• proper
• proper binary tree
• proper coloring
• proper subset
• property list
• prune and search
• pseudo-random number generator
• PTAS
• pth order Fibonacci numbers
• P-tree
• purely functional language
• pushdown automaton
• pushdown transducer
• p-way merge sort

Q

• qm sort
• q sort
• quadratic probing
• quadtree
• quadtree complexity theorem
• quad trie
• quantum computation
• queue
• quick search
• quicksort

R

• Rabin-Karp
• radix quicksort
• radix sort
• ragged matrix
• Raita
• random access machine
• randomization
• randomized algorithm
• randomized binary search tree
• randomized complexity
• randomized polynomial time
• randomized rounding
• randomized search tree
• Randomized-Select
• random number generator
• random sampling
• range
• range sort
• rank
• Ratcliff/Obershelp pattern recognition
• RBST
• reachable
• rebalance
• recognizer
• rectangular matrix
• rectilinear
• rectilinear Steiner tree
• recurrence equations
• recurrence relation
• recursion
• recursion termination
• recursion tree
• recursive
• recursive data structure
• recursive doubling
• recursive language
• recursively enumerable language
• recursively solvable
• red-black tree
• reduced basis
• reduced digraph
• reduced ordered binary decision diagram
• reduction
• reflexive relation
• regular decomposition
• rehashing
• relation
• relational structure
• relative performance guarantee
• relaxation
• relaxed balance
• rescalable
• restricted universe sort
• result cache
• Reverse Colussi
• Reverse Factor
• R-file
• Rice's method
• right rotation
• right-threaded tree
• RNG
• ROBDD
• root
• root balance
• rooted tree
• rotate left
• rotate right
• rotation
• rough graph
• RP
• [[R+-tree]]
• R*-tree
• R-tree
• run time

S

• saguaro stack
• saturated edge
• SBB tree
• scan
• scapegoat tree
• search
• search tree
• search tree property
• secant search
• secondary clustering
• segment
• Select
• select and partition
• selection problem
• selection sort
• select kth element
• select mode
• self-loop
• self-organizing heuristic
• self-organizing list
• self-organizing sequential search
• semidefinite programming
• separate chaining hashing
• separation theorem
• sequential search
• set
• set cover
• set packing
• shadow heap
• shadow merge
• shadow merge insert
• shaker sort
• Shannon-Fano coding
• shared memory
• Shell sort
• Shift-Or
• Shor's algorithm
• shortcutting
• shortest common supersequence
• shortest common superstring
• shortest path
• shortest spanning tree
• shuffle
• shuffle sort
• sibling
• Sierpinski curve
• Sierpinski triangle
• sieve of Eratosthenes
• sift up
• signature
• Simon's algorithm
• simple merge
• simple path
• simple uniform hashing
• simplex communication
• simulated annealing
• simulation theorem
• single-destination shortest-path problem
• single-pair shortest-path problem
• single program multiple data
• single-source shortest-path problem
• singly linked list
• singularity analysis
• sink
• sinking sort
• skd-tree
• skew symmetry
• skip list
• skip search
• slope selection
• Smith algorithm
• Smith-Waterman algorithm
• smoothsort
• solvable
• sort
• sorted array
• sorted list
• sort in place
• sort merge
• soundex
• source
• space-constructible function
• spanning tree
• sparse graph
• sparse matrix
• sparsification
• sparsity
• spatial access method
• spectral test
• splay tree
• SPMD
• square matrix
• square root
• SST
• stable
• stack
• stack tree
• star-shaped polygon
• start state
• state
• state machine
• state transition
• static
• static Huffman encoding
• s-t cut
• st-digraph
• Steiner minimum tree
• Steiner point
• Steiner ratio
• Steiner tree
• Steiner vertex
• Steinhaus-Johnson-Trotter
• Stirling's approximation
• Stirling's formula
• stooge sort
• straight-line drawing
• strand sort
• strictly decreasing
• strictly increasing
• strictly lower triangular matrix
• strictly upper triangular matrix
• string
• string editing problem
• string matching
• string matching on ordered alphabets
• string matching with errors
• string matching with mismatches
• string searching
• strip packing
• strongly connected component
• strongly connected graph
• strongly NP-hard
• subadditive ergodic theorem
• subgraph
• subgraph isomorphism
• sublinear time algorithm
• subsequence
• subset
• substring
• subtree
• suffix
• suffix array
• suffix automaton
• suffix tree
• superimposed code
• superset
• supersink
• supersource
• symmetric relation
• symmetrically linked list
• symmetric binary B-tree
• symmetric set difference
• symmetry breaking

T

• tail
• tail recursion
• target
• temporal logic
• terminal
• terminal node
• ternary search tree
• text
• text searching
• theta
• threaded binary tree
• threaded tree
• three-dimensional
• three-way merge sort
• three-way radix quicksort
• time-constructible function
• time/space complexity
• top-down radix sort
• top-down tree automaton
• topological order
• topological sort
• topology tree
• total function
• totally decidable language
• totally decidable problem
• totally undecidable problem
• total order
• tour
• tournament
• towers of Hanoi
• tractable
• transducer
• transition
• transition function
• transitive relation
• transitive closure
• transitive reduction
• transpose sequential search
• traveling salesman
• treap
• tree
• tree automaton
• tree contraction
• tree editing problem
• tree sort
• tree traversal
• triangle inequality
• triconnected graph
• trie
• trinary function
• tripartition
• TSP
• TST
• Turbo-BM
• Turbo Reverse Factor
• Turing machine
• Turing reduction
• Turing transducer
• twin grid file
• two-dimensional
• two-level grid file
• 2-3-4 tree
• 2-3 tree
• Two Way algorithm
• two-way linked list
• two-way merge sort

U

• UKP
• unary function
• unbounded knapsack problem
• uncomputable function
• uncomputable problem
• undecidable
• undecidable language
• undecidable problem
• undirected graph
• uniform circuit complexity
• uniform circuit family
• uniform hashing
• uniform matrix
• union
• union of automata
• universal hashing
• universal state
• universal Turing machine
• universe
• UnShuffle sort
• unsolvable problem
• unsorted list
• upper triangular matrix

V

• Van Emde Boas priority queue
• vehicle routing problem
• Veitch diagram
• Venn diagram
• vertex
• vertex coloring
• vertex connectivity
• vertex cover
• vertical visibility map
• virtual hashing
• visibility map
• visible
• Viterbi algorithm
• VRP

W

• walk
• weak-heap
• weak-heap sort
• weight-balanced tree
• weighted, directed graph
• weighted graph
• window
• witness
• work
• work-depth model
• work-efficient
• work-preserving
• worst case
• worst-case cost
• worst-case minimum access

X

• xor

Y

• Yule distribution

Z

• Zeller's congruence
• 0-ary function
• 0-based indexing
• 0/1 knapsack problem
• Zhu-Takaoka
• Zipfian distribution
• Zipf's law
• zipper
• ZPP