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Efficient sorting is important for optimizing the efficiency of other algorithms (such as search and merge algorithms) that require input data to be in sorted lists. Sorting is also often useful for canonicalizing data and for producing human-readable output. Formally, the output of any sorting algorithm must satisfy two conditions:
An important variant is where each clause has exactly three literals (3SAT), since it is used in the proof of many other NP-completeness results. [3]: p. 48 Circuit satisfiability problem; Conjunctive Boolean query [3]: SR31 Cyclic ordering [36] Exact cover problem. Remains NP-complete for 3-sets.
In mathematics, economics, and computer science, the stable marriage problem (also stable matching problem) is the problem of finding a stable matching between two equally sized sets of elements given an ordering of preferences for each element. A matching is a bijection from the elements
If the sort key values are totally ordered, the sort key defines a weak order of the items: items with the same sort key are equivalent with respect to sorting. See also stable sorting. If different items have different sort key values then this defines a unique order of the items. Workers sorting parcels in a postal facility
A third important topology in this spirit is the Lawson topology. There are close connections between these topologies and the concepts of order theory. For example, a function preserves directed suprema if and only if it is continuous with respect to the Scott topology (for this reason this order theoretic property is also called Scott ...
A matching M of a graph G is maximal if every edge in G has a non-empty intersection with at least one edge in M. The following figure shows examples of maximal matchings (red) in three graphs. A maximum matching (also known as maximum-cardinality matching [2]) is a matching that contains the largest possible number of edges. There may be many ...
Why playful people are better at coping with life's challenges, according to a new study. ... Telling people in your life that you want to be more playful can feel a bit silly — which might ...
Matching is a statistical technique that evaluates the effect of a treatment by comparing the treated and the non-treated units in an observational study or quasi-experiment (i.e. when the treatment is not randomly assigned).