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Table 1

From: An ILP solution for the gene duplication problem

Notation Definition
M(i, j) Taxon-cluster representation of (the) species tree: M(i, j) = 1 iff taxon i is in the cluster j. Additional constraints on M require the cluster set to form a binary hierarchy (tree).
C(p, q, xy) Compatibility: C(p, q, xy) = 1 exactly if the cluster pair (p, q) has the gamete xy {01, 10, 11}.
T(a, b, c, xyz) Rooted triple: T(a, b, c, xyz) = 1 exactly if the rooted triple with leaf set {a, b, c} and topology xyz is displayed in M. Topologies for xyz are 011, 101, and 110 and refer to the rooted triples bc|a, ac|b and ab|c respectively.
D(g) t-inconsistency: D(g) = 1 if the gene vertex g is t-inconsistent w.r.t. a tree represented by matrix M.
  1. Notation used in our ILP solution.