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Algorithm characteristic in computations
In 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
Measures of how efficiently algorithms use resources
The worst-case analysis is related to the worst-case complexity. Many algorithms with bad worst-case performance have good average-case performance
Best,_worst_and_average_case
Amount of resources to perform an algorithm
worst-case complexity is the maximum of the complexity over all inputs of size n, and the average-case complexity is the average of the complexity over
Computational_complexity
Upper bound on resources required by an algorithm
complexity of an algorithm should be contrasted with its average-case complexity, which is an average measure of the amount of resources the algorithm uses
Worst-case_complexity
Inherent difficulty of computational problems
following complexities: Best-case complexity: This is the complexity of solving the problem for the best input of size n {\displaystyle n} . Average-case complexity:
Computational complexity theory
Computational_complexity_theory
probabilistic complexity estimates are the average-case complexity and the almost-always complexity. To obtain the average-case complexity, given an input
Probabilistic analysis of algorithms
Probabilistic_analysis_of_algorithms
Estimate of time taken for running an algorithm
Less common, and usually specified explicitly, is the average-case complexity, which is the average of the time taken on inputs of a given size (this makes
Time_complexity
Soviet-American mathematician
his work in randomness in computing, algorithmic complexity and intractability, average-case complexity, foundations of mathematics and computer science
Leonid_Levin
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
Equivalence of average-case and expected complexity
be obtained by a deterministic algorithm on a random input (its average-case complexity), for a probability distribution on inputs chosen to be as hard
Yao's_principle
Sorting algorithm which uses multiple comparison intervals
unknown whether Shellsort can reach this asymptotic order of average-case complexity, which is optimal for comparison sorts. The lower bound was improved
Shellsort
Algorithm analysis method
worst-case complexity. Average-case analysis was first introduced to overcome the limitations of worst-case analysis. However, the resulting average-case complexity
Smoothed_analysis
Unsolved problem in computer science
JSTOR 2580891. R. Impagliazzo, "A personal view of average-case complexity", p. 134, 10th Annual Structure in Complexity Theory Conference (SCT'95), 1995. "Tentative
P_versus_NP_problem
Software size estimation technique
complexity of the use cases for the system. To find the UUCW for a system, each of the use cases must be identified and classified as Simple, Average
Use_case_points
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
Counterintuitive mathematical object
atypical behavior from the algorithm, such as a violation of its average case complexity, or even its correctness. For example, hash tables generally have
Pathological_(mathematics)
Method of searching a sorted array
On average, Fibonacci search performs about 4% more comparisons than binary search, and it has an average-case complexity and worst-case complexity of
Fibonacci_search_technique
Computational problem used in cryptography
applications, worst case complexity is not sufficient, and we need to guarantee cryptographic construction are hard based on average case complexity. A full rank
Short integer solution problem
Short_integer_solution_problem
String search algorithm
for time in order to obtain an average-case complexity of O(n) on random text, although it has O(nm) in the worst case, where the length of the pattern
Boyer–Moore–Horspool algorithm
Boyer–Moore–Horspool_algorithm
American computer scientist
started to work on various aspects of computational complexity theory including average case complexity. He became one of the founders of the emerging field
Yuri_Gurevich
Algorithm for linear programming
worst-case complexity has led to the development of other measures of complexity. The simplex algorithm has polynomial-time average-case complexity under
Simplex_algorithm
Problem of inverting exponentiation in groups
algorithm known for the worst case, but the average-case complexity can be shown to be about as hard as the worst case using random self-reducibility
Discrete_logarithm
Numerical linear algebra algorithm
O(n) complexity. However, this will happen on average only once per rotation. Thus, each rotation has O(n) and one sweep O(n3) average-case complexity, which
Jacobi_eigenvalue_algorithm
Sorting algorithm
values form a single pile and both phases run in O(n) time. The average-case complexity is still O(n log n): any uniformly random sequence of values will
Patience_sorting
Number taken as representative of a list of numbers
In mathematics, an average of a collection or group is a value that is most central, common, or typical in some sense, and represents its overall position
Average
Sorting algorithm
having constant size). This allows O ( n ) {\displaystyle O(n)} average time complexity even without uniformly distributed input. The most common variant
Bucket_sort
Impagliazzo, Russell (1995), "A personal view of average-case complexity", Proc. Tenth Annual Structure in Complexity Theory Conference (SCT'95), pp. 134–147,
Glossary of mathematical jargon
Glossary_of_mathematical_jargon
American computer scientist
17. Impagliazzo, Russell (April 17, 1995). "A Personal View of Average-Case Complexity". Klarreich, Erica (April 18, 2022). "Which Computational Universe
Russell_Impagliazzo
Divergent sum of positive unit fractions
its average-case complexity (with the assumption that all input permutations are equally likely) or in its expected time analysis of worst-case inputs
Harmonic_series_(mathematics)
Type of cryptographic software obfuscation
situations about average-case complexity: Algorithmica: In this case P = NP, but iO exists. Heuristica: In this case NP problems are easy on average; iO does
Indistinguishability obfuscation
Indistinguishability_obfuscation
Algorithm for the kth smallest element in an array
This reduces the average complexity from O ( n log n ) {\displaystyle O(n\log n)} to O ( n ) {\displaystyle O(n)} , with a worst case of O ( n 2 ) {\displaystyle
Quickselect
French computer scientist (1948–2011)
methods for analyzing the computational complexity of algorithms, including the theory of average-case complexity. He introduced the theory of analytic
Philippe_Flajolet
Associative array for storing key–value pairs
according to a probing sequence. In a well-dimensioned hash table, the average time complexity for each lookup is independent of the number of elements stored
Hash_table
Fast approximate median algorithm
asymptotic worst-case complexity quite well, it is typically outperformed in practice by instead choosing random pivots for its average O ( n ) {\displaystyle
Median_of_medians
Binary tree selected at random
these trees. Random binary trees have been used for analyzing the average-case complexity of data structures based on binary search trees. For this application
Random_binary_tree
Data structure for storing non-overlapping sets
also developed one-pass Find algorithms that retain the same worst-case complexity but are more efficient in practice. These are called path splitting
Disjoint-set_data_structure
American mathematician
in 2011 his Ph.D. with advisor Madhu Sudan from MIT with thesis Average-Case Complexity of Detecting Cliques. From 2010 to 2013 Rossman was a postdoc at
Benjamin_Rossman
Hypothesis in computational complexity theory
Computational Complexity: A Modern Approach. Cambridge University Press. pp. 362–363. ISBN 9780521424264.. Feige, Uriel (2002). "Relations between average case complexity
Computational hardness assumption
Computational_hardness_assumption
Information-based complexity (IBC) studies optimal algorithms and computational complexity for the continuous problems that arise in physical science,
Information-based_complexity
Task of transforming a deterministic finite automaton
solving the problem, and for certain distributions of inputs its average-case complexity is even better, O(n log log n). Once Hopcroft's algorithm has been
DFA_minimization
Optimization problem in computer science
NP-hard and discovered some connections between the worst-case complexity and average-case complexity of some lattice problems. Building on these results,
Lattice_problem
Rooted binary tree data structure
guaranteed worst-case performance. The basic operations include: search, traversal, insert and delete. BSTs with guaranteed worst-case complexities perform better
Binary_search_tree
Search algorithm finding the position of a target value within a sorted array
Therefore, the space complexity of binary search is O ( 1 ) {\displaystyle O(1)} in the word RAM model of computation. The average number of iterations
Binary_search
Technique for reducing number of solutions
of Valiant-Vazirani in their search-to-decision reduction for average-case complexity. Avi Wigderson used the isolation lemma in 1994 to give a randomized
Isolation_lemma
Measure of complexity of real-valued functions
learning theory (machine learning and theory of computation), Rademacher complexity, named after Hans Rademacher, measures richness of a class of sets with
Rademacher_complexity
Simple sorting algorithm using comparisons
cases where the list is already mostly sorted (having a small number of inversions), despite the fact that it has worse average-case time complexity.
Bubble_sort
Hungarian-American computer scientist
Almanach, 1986, Budapest. Ajtai, Miklós (1998). "Worst-case complexity, average-case complexity and lattice problems". Documenta Mathematica: 421–428.
Miklós_Ajtai
Probabilistic data structure
{\mathcal {O}}(\log n)} average complexity for search as well as O ( log n ) {\displaystyle {\mathcal {O}}(\log n)} average complexity for insertion within
Skip_list
Binary tree derived from a sequence of numbers
In particular, Vuillemin used these structures to analyze the average-case complexity of concatenation and splitting operations on binary search trees
Cartesian_tree
Data structure used for indexing spatial information
tree, inspired by the concept of balancing a B-tree. Worst case query and delete complexity are thus identical to the R-Tree. The insertion strategy to
R*-tree
Algorithm that arranges lists in order
Sorting algorithms can be classified by: Computational complexity Best, worst and average case behavior in terms of the size of the list. For typical
Sorting_algorithm
Divide and conquer sorting algorithm
terms of moves, merge sort's worst case complexity is O(n log n) - the same complexity as quicksort's best case. Merge sort is more efficient than quicksort
Merge_sort
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
Relaxed variant of the sorting problem
sequence of calls has average-case complexity O(n + k log k), which is asymptotically equivalent to O(n + k log n). The worst-case time is quadratic, but
Partial_sorting
Multidimensional search tree for points in k dimensional space
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 ) ) {\displaystyle
K-d_tree
the average with respect to the induced distribution on yi, the average-case complexity of f is the same (within polynomial factors) as the worst-case randomized
Random_self-reducibility
hard worst-case or average-case complexity. Worst-case complexity measures the difficulty of solving pathological cases rather than typical cases of the underlying
Security of cryptographic hash functions
Security_of_cryptographic_hash_functions
Sorting algorithm
sorted are distinct, the expected number of comparisons performed in the average case by randomized bogosort is asymptotically equivalent to ( e − 1 ) n !
Bogosort
conclusions. Woźniakowski's 1991 paper, showing the connection between average case complexity of integration and QMC, led to new interest in QMC. Woźniakowski's
Quasi-Monte Carlo methods in finance
Quasi-Monte_Carlo_methods_in_finance
Russian-American mathematician
Myasnikov, Alexei; Schupp, Paul; Shpilrain, Vladimir (2005). "Average-case complexity and decision problems in group theory". Advances in Mathematics
Ilya_Kapovich
Topics referred to by the same term
military armoured vehicle. AVGP may refer to: AvgP (mathematics) in average-case complexity AV-GP (contest), the AV Grand Prix, a Japanese adult video contest
AVGP_(disambiguation)
Self-balancing binary search tree
Additionally, after finding a node for insertion and deletion, the amortized complexity of the tree restructuring operations is constant. Adding or deleting the
WAVL_tree
Sorting algorithm
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 worse
Selection_sort
String searching algorithm
the combined length of the pattern and text, although its worst-case time complexity is the product of the two lengths. To find multiple matches, the
Rabin–Karp_algorithm
Relative value assigned to a diagnosis-related group of patients
system. The relative average value assigned to each group is its CMI. The CMI of a hospital reflects the diversity, clinical complexity and the needs for
Case_mix_index
Professor of operations research at MIT
introduced Overlap Gap Property, a new method for understanding average-case complexity, based on theory of spin glasses. He has served in editorial roles
David_Gamarnik
Method for algorithm analysis in computer science
analysis is that looking at the worst-case run time can be too pessimistic. Instead, amortized analysis averages the running times of operations in a sequence
Amortized_analysis
Self-balancing binary search tree data structure
Rebalancing (i.e. color changes) has a worst-case time complexity of O ( log n ) {\displaystyle O(\log n)} and average of O ( 1 ) {\displaystyle O(1)} , though
Red–black_tree
Unit hypercube of variable dimension whose corners have been perturbed
have polynomial-time complexity for linear optimization. The Klee–Minty cube has also inspired research on average-case complexity. When eligible pivots
Klee–Minty_cube
Proof method
average-case complexity of Shellsort", Journal of the ACM (JACM), 47:5(2000) 905–911. doi:10.1145/355483.355488 P.M.B. Vitanyi (2018), On the average‐case
Incompressibility_method
Data structure
the key, the system concludes that the key doesn't exist. Point lookup complexity is O ( L ) {\displaystyle O(L)} without Bloom filters, as each level must
Log-structured_merge-tree
Largest independent set of paired elements
{\displaystyle k} , and applying Yao's principle relating expected and average-case complexity, one can show that any deterministic or randomized algorithm for
Matroid_parity_problem
Divide and conquer sorting algorithm
lowers the average complexity to linear or O(n) time, which is optimal for selection, but the selection algorithm is still O(n2) in the worst case. A variant
Quicksort
Concept in computer science
In complexity theory, ZPP (zero-error probabilistic polynomial time) is the complexity class of problems for which a probabilistic Turing machine exists
ZPP_(complexity)
American computer scientist
random variate generation; prediction and machine learning; and average-case complexity. Vitter is a Fellow of the National Academy of Inventors (NAI)
Jeffrey_Vitter
Data structure
insert or delete an element as half of the array will need to be shifted on average. To overcome this problem, elements inside a node can be organized in a
B+_tree
Tree data structure that partitions a 2D area
in an area may be stored as a quadtree, with each leaf node storing the average temperature over the subregion it represents. The point quadtree is an
Quadtree
Number of bits that differ between two strings
strings over an alphabet of size q ≥ 2 the Hamming distance is applied in case of the q-ary symmetric channel, while the Lee distance is used for phase-shift
Hamming_distance
Computational benchmark
Michael J.; Montanaro, Ashley; Shepherd, Dan J. (2016-08-18). "Average-case complexity versus approximate simulation of commuting quantum computations"
Quantum_supremacy
Data structures used in spatial indexing
variant of the R-tree is worst-case optimal, but due to its increased complexity it has remained confined to theoretical study and has not received much
R-tree
Hybrid sorting algorithm based on insertion sort and merge sort
Peter McIlroy's 1993 paper "Optimistic Sorting and Information Theoretic Complexity". Timsort was designed to take advantage of runs of consecutive ordered
Timsort
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 \Theta
Floyd–Warshall_algorithm
Search tree data structure
has the complexity of O ( m ) {\displaystyle O(m)} , whereas an imperfect hash function may have numerous colliding keys, and the worst-case lookup speed
Trie
Abstract data type
first one only achieves O ( 1 ) {\displaystyle O(1)} per operation on average. That is, the amortized time is O ( 1 ) {\displaystyle O(1)} , but individual
Queue_(abstract_data_type)
Sorting algorithm
The complexity of the cocktail shaker sort in big O notation is O ( n 2 ) {\displaystyle O(n^{2})} for both the worst case and the average case, but
Cocktail_shaker_sort
Function for sorting in C++ standard library
language standard and may vary across implementations, but the worst-case asymptotic complexity of the function is specified: a call to sort must perform no more
Sort_(C++)
Algorithm that employs a degree of randomness as part of its logic or procedure
guide its behavior, in the hope of achieving good performance in the "average case" over all possible choices of random determined by the random bits; thus
Randomized_algorithm
Data structure
Development of operations it supports were primarily motivated by use in that case.[citation needed] A Fenwick tree is an implicit tree where nodes are consecutively
Fenwick_tree
Sequentially looking in an array
likely to be searched, then linear search has an average case of n+1/2 comparisons, but the average case can be affected if the search probabilities for
Linear_search
Concept in computational complexity theory
time; that is, if they lie in the complexity class P. In modern terms, it identifies tractable problems with the complexity class P. Formally, to say that
Cobham's_thesis
Study of resources used by an algorithm
the analysis of algorithms is the process of finding the computational complexity of algorithms—the amount of time, storage, or other resources needed to
Analysis_of_algorithms
Data structure for a string
rebuilding a new suffix array from scratch. Even if the theoretical worst-case time complexity is O ( n log n ) {\displaystyle {\mathcal {O}}(n\log n)} , it appears
Suffix_array
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
Code-breaking game
for the codebreaker gives the minimal number of moves for worst and average case and in the sense of a minimax value of a zero-sum game in game theory
Mastermind_(board_game)
Data structure in computer science
size can be continually reduced by seeking out a bottom-level node and averaging its bit data up into a leaf node, pruning part of the tree. Once sampling
Octree
Self-balancing binary search tree data structure
is a variant of the red–black tree and guarantees the same asymptotic complexity for operations, but is designed to be easier to implement. A left-leaning
Left-leaning_red–black_tree
Parallel sorting algorithm
j\leq 2n} . Case 1: If a n ≤ a 2 n {\displaystyle a_{n}\leq a_{2n}} then every element of the two subsequences are smaller. In this case d i = a i {\displaystyle
Bitonic_sorter
Probabilistic primality test
2307/2008231. JSTOR 2008231. I. Damgård; P. Landrock; C. Pomerance (1993). "Average case error estimates for the strong probable prime test". Mathematics of Computation
Solovay–Strassen primality test
Solovay–Strassen_primality_test
Type of sorting algorithm
better worst case complexity when a self-balancing tree is used, but even more overhead. Adding one item to a binary search tree is on average an O(log n)
Tree_sort
Random search tree data structure
for intersection is similar, but requires the join helper routine. The complexity of each of union, intersection and difference is O(m log n/m) for treaps
Treap
AVERAGE CASE-COMPLEXITY
AVERAGE CASE-COMPLEXITY
Male
English
Short form of English Caleb, CALE means "dog" or "rabid."
Surname or Lastname
English
English : from Anglo-Norman French cas(s)e ‘case’, ‘container’ (from Latin capsa), hence a metonymic occupational name for a maker of boxes or chests.Americanized spelling of French Caisse.Americanized spelling of Kaas.Americanized spelling of German Käse, a metonymic occupational name for a maker or seller of cheese. Compare Kaeser.
Boy/Male
Muslim
Moderate, Average
Boy/Male
Irish English
Observant; alert; vigorous.
Boy/Male
Tamil
Moderate, Average
Male
English
Middle English surname (of Norman French origin) transferred to forename use, CHASE means "hunter."Â
Boy/Male
Arabic, Muslim, Sindhi
Moderate; Average
Boy/Male
American, Australian, British, Dutch, English, French, Irish
Bringer of Peace; Box
Boy/Male
American, Australian, British, English, Irish
Rope-maker; A Cape
Female
English
English short form of Latin Cassandra, CASS means "she who entangles men."Â
Surname or Lastname
English
English : from a Middle English personal name, Cade, a survival of the Old English personal name or byname Cada, which is probably from a Germanic root meaning ‘lump’, ‘swelling’.English : metonymic occupational name for a cooper, from Middle English, Old French cade ‘cask’, ‘barrel’ (of Germanic origin, probably akin to the root mentioned in 1).English : nickname for a gentle or inoffensive person, from Middle English cade ‘domestic animal’, ‘pet’ (of unknown origin).French (Cadé) : topographic name from cade ‘juniper’ (from Latin catanus).Bearers of the name Caddé, from Amiens, were documented in Quebec city by 1670.
Surname or Lastname
Reduced form of Irish McCage, a variant of McCaig.English (East Anglia)
Reduced form of Irish McCage, a variant of McCaig.English (East Anglia) : from Middle English, Old French cage ‘cage’, ‘enclosure’ (Latin cavea ‘container’, ‘cave’), hence a metonymic occupational name for a maker and seller of small cages for animals or birds, or a keeper of the large public cage in which petty criminals were confined for short periods of imprisonment.
Female
English
Variant spelling of English Cassie, CASEY means "she who entangles men." Compare with masculine Casey.Â
Surname or Lastname
German
German : nickname for a swift runner or a timorous person, from Middle High German, Middle Low German hase ‘hare’.Jewish (Ashkenazic) : ornamental name from German Hase ‘hare’.English : from a Middle English nickname, Hase, from Old English hÄs ‘harsh, raucous, or hoarse voice’.Japanese : usually written with characters meaning ‘long valley’; habitational name from a place in Yamato (now Nara prefecture). Listed in the Shinsen shÅjiroku. Some bearers are descended from the Taira clan; they are found mainly in eastern Japan. Also pronounced Nagaya and Nagatani; the original pronunciation was Hatsuse, meaning ‘beginning of the strait’.
Boy/Male
Muslim/Islamic
Moderate average
Boy/Male
Hindu
Moderate, Average
Surname or Lastname
English
English : metonymic occupational name for a huntsman, or rather a nickname for an exceptionally skilled huntsman, from Middle English chase ‘hunt’ (Old French chasse, from chasser ‘to hunt’, Latin captare).Southern French : topographic name for someone who lived in or by a house, probably the occupier of the most distinguished house in the village, from a southern derivative of Latin casa ‘hut’, ‘cottage’, ‘cabin’.Thomas Chase came to MA from Chesham, Buckinghamshire, England, in the 1640s, and had many prominent descendants. Samuel Chase, born in Somerset Co., MD, in 1741, was one of the first members of the U.S. Supreme Court; Philander Chase, born in Cornish, NH, in 1741 was a prominent Episcopal clergyman, and his nephew Salmon Portland Chase (1808–73), also born in Cornish, was governor of OH, a U.S. senator, and secretary of the U.S. Treasury during the Civil War.
Female
English
Variant spelling of English Kate, CATE means "pure."
Surname or Lastname
Americanized spelling of German Kast.English (Essex, Kent)
Americanized spelling of German Kast.English (Essex, Kent) : possibly a nickname from Norman caste ‘chaste’, ‘virtuous’ (from Old French chaste).Possibly an altered spelling of French Caste, cognate with 2.
Surname or Lastname
English
English : variant spelling of Everidge.
AVERAGE CASE-COMPLEXITY
AVERAGE CASE-COMPLEXITY
Boy/Male
Danish, German, Scandinavian, Swedish
Ing's Warrior; Ing's Army
Girl/Female
Muslim
Friendly, Of good company
Boy/Male
Tamil
One who grants wishes
Boy/Male
Indian
Freed slave of sulaym
Girl/Female
Tamil
Humble, Unassuming, Obedience, Knowledge, Venus, Requester
Girl/Female
Arabic
Blessed; Auspicious
Boy/Male
Muslim/Islamic
Wise
Boy/Male
Arabic
Form of Muhammad
Boy/Male
Arabic
Grandeur; Glory
Boy/Male
Indian, Punjabi, Sikh
Embodiment of Reality
AVERAGE CASE-COMPLEXITY
AVERAGE CASE-COMPLEXITY
AVERAGE CASE-COMPLEXITY
AVERAGE CASE-COMPLEXITY
AVERAGE CASE-COMPLEXITY
v. t.
To do, accomplish, get, etc., on an average.
n.
A box and its contents; the quantity contained in a box; as, a case of goods; a case of instruments.
imp. & p. p.
of Average
n.
An inclosing frame; a casing; as, a door case; a window case.
n.
An average.
v. i.
To form, or exist in, a mean or medial sum or quantity; to amount to, or to be, on an average; as, the losses of the owners will average twenty five dollars each; these spars average ten feet in length.
v. t.
To strip the skin from; as, to case a box.
v. t.
To supply or impregnate with common air; as, to aerate soil; to aerate water.
n.
That which befalls, comes, or happens; an event; an instance; a circumstance, or all the circumstances; condition; state of things; affair; as, a strange case; a case of injustice; the case of the Indian tribes.
n.
A mean proportion, medial sum or quantity, made out of unequal sums or quantities; an arithmetical mean. Thus, if A loses 5 dollars, B 9, and C 16, the sum is 30, and the average 10.
n.
Acres collectively; as, the acreage of a farm or a country.
a.
According to the laws of averages; as, the loss must be made good by average contribution.
v. i.
To propose hypothetical cases.
n.
A box, sheath, or covering; as, a case for holding goods; a case for spectacles; the case of a watch; the case (capsule) of a cartridge; a case (cover) for a book.
p. pr. & vb. n.
of Average
a.
Pertaining to an average or mean; medial; containing a mean proportion; of a mean size, quality, ability, etc.; ordinary; usual; as, an average rate of profit; an average amount of rain; the average Englishman; beings of the average stamp.
v. t.
To divide among a number, according to a given proportion; as, to average a loss.
v. t.
To cause to fall; to shed; to reflect; to throw; as, to cast a ray upon a screen; to cast light upon a subject.
imp. & p. p.
of Case
v. t.
To cover or protect with, or as with, a case; to inclose.