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  2. Sorting algorithm - Wikipedia

    en.wikipedia.org/wiki/Sorting_algorithm

    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:

  3. Stable roommates problem - Wikipedia

    en.wikipedia.org/wiki/Stable_roommates_problem

    In mathematics, economics and computer science, particularly in the fields of combinatorics, game theory and algorithms, the stable-roommate problem (SRP) is the problem of finding a stable matching for an even-sized set. A matching is a separation of the set into disjoint pairs ("roommates

  4. Assignment problem - Wikipedia

    en.wikipedia.org/wiki/Assignment_problem

    There is also a constant s which is at most the cardinality of a maximum matching in the graph. The goal is to find a minimum-cost matching of size exactly s. The most common case is the case in which the graph admits a one-sided-perfect matching (i.e., a matching of size r), and s=r. Unbalanced assignment can be reduced to a balanced assignment.

  5. Matching (graph theory) - Wikipedia

    en.wikipedia.org/wiki/Matching_(graph_theory)

    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 ...

  6. Algorithm - Wikipedia

    en.wikipedia.org/wiki/Algorithm

    Merge sorting is an example of divide and conquer, where an unordered list can be divided into segments containing one item and sorting of entire list can be obtained by merging the segments. A simpler variant of divide and conquer is called a decrease-and-conquer algorithm , which solves one smaller instance of itself, and uses the solution to ...

  7. Divide-and-conquer algorithm - Wikipedia

    en.wikipedia.org/wiki/Divide-and-conquer_algorithm

    An important application of divide and conquer is in optimization, [example needed] where if the search space is reduced ("pruned") by a constant factor at each step, the overall algorithm has the same asymptotic complexity as the pruning step, with the constant depending on the pruning factor (by summing the geometric series); this is known as ...

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  9. Bin packing problem - Wikipedia

    en.wikipedia.org/wiki/Bin_packing_problem

    The algorithm can be made much more effective by first sorting the list of items into decreasing order (sometimes known as the first-fit decreasing algorithm), although this still does not guarantee an optimal solution and for longer lists may increase the running time of the algorithm. It is known, however, that there always exists at least ...