Common intervals of trees

ved. In this paper we consider the problem of finding common intervals of trees, a generalization of the concept of common intervals in permutations. For a permutation π of [n] = {1,2, . . . , n}, an interval of π is a set of the form {π(i),π(i + 1), . . . , π(j)} for 1 i < j n, and any permutation of [n] has n(n−1)/2 intervals. Given a family Π = (π0, . . . , πk−1) of k 2 permutations of [n], a common interval of Π is a subset S of [n] such that S is an interval of πi for 0 i k−1. Common intervals have applications in many different fields. Some genetic algorithms using subtour exchange crossover based on common intervals have been proposed for sequencing problems such as the traveling salesman problem or the single machine

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