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  2. Partition refinement - Wikipedia

    en.wikipedia.org/wiki/Partition_refinement

    When a set S i that has already been chosen is split by a refinement, only one of the two resulting sets (the smaller of the two) needs to be chosen again; in this way, each state participates in the sets X for O(s log n) refinement steps and the overall algorithm takes time O(ns log n), where n is the number of initial states and s is the size ...

  3. Disjoint sets - Wikipedia

    en.wikipedia.org/wiki/Disjoint_sets

    Disjoint-set data structures [9] and partition refinement [10] are two techniques in computer science for efficiently maintaining partitions of a set subject to, respectively, union operations that merge two sets or refinement operations that split one set into two. A disjoint union may mean one of two things. Most simply, it may mean the union ...

  4. Set splitting problem - Wikipedia

    en.wikipedia.org/wiki/Set_splitting_problem

    In computational complexity theory, the set splitting problem is the following decision problem: given a family F of subsets of a finite set S, decide whether there exists a partition of S into two subsets S 1, S 2 such that all elements of F are split by this partition, i.e., none of the elements of F is completely in S 1 or S 2.

  5. 3-partition problem - Wikipedia

    en.wikipedia.org/wiki/3-partition_problem

    Therefore, the remaining 3-sets can be partitioned into two groups: n 3-sets containing the items u ij, and n 3-sets containing the items u ij '. In each matching pair of 3-sets, the sum of the two pairing items u ij +u ij ' is 44T+4, so the sum of the four regular items is 84T+4. Therefore, from the four regular items, we construct a 4-set in ...

  6. Partition of a set - Wikipedia

    en.wikipedia.org/wiki/Partition_of_a_set

    If D is the set of cards in a standard 52-card deck, the same-color-as relation on D – which can be denoted ~ C – has two equivalence classes: the sets {red cards} and {black cards}. The 2-part partition corresponding to ~ C has a refinement that yields the same-suit-as relation ~ S , which has the four equivalence classes {spades ...

  7. How world leaders are reacting to Jimmy Carter’s death - AOL

    www.aol.com/world-leaders-reacting-jimmy-carter...

    In recent years I had the pleasure of calling him and thanking him for his historic efforts to bring together two great leaders, Begin and Sadat, and forging a peace between Israel and Egypt that ...

  8. Dichotomy - Wikipedia

    en.wikipedia.org/wiki/Dichotomy

    In this image, the universal set U (the entire rectangle) is dichotomized into the two sets A (in pink) and its complement A c (in grey). A dichotomy / d aɪ ˈ k ɒ t ə m i / is a partition of a whole (or a set) into two parts (subsets). In other words, this couple of parts must be

  9. Taking This Daily Vitamin Could Slash Dementia Risk By 40 ...

    www.aol.com/lifestyle/taking-daily-vitamin-could...

    $20.99 at Amazon. Orange Vitamin D3. Rated at 4.7 stars by over 6,000 happy customers on Amazon, this daily vitamin is a tried-and-true product that's affordable and even offers a refreshing ...