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Lexographic Ordering

  • The lexographic ordering of sets of objects is given by:
    • for A,B ⊆ G, i ∈ G = {1, ..., n} to order the objects
    • A ≺ i B iff i ∈ B – A and A ∩ {1,...,i-1} = B ∩ {1,...,i-1}
    • A ≺ B iff ∃ i such that A ≺ i B (and there is only one i)
  • The ≺ denotes a lexographic ordering and thus, every two distinct sets A, B ⊆ G are comparable
  • B ⊆ G can also be represented in terms of a characteristics vector:
    • G = {1,2,3,4,5}, B={1,2,5}
    • characteristics vector of B = 11001

Speaker notes:

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