Algorithmically, strong or weak anchor points are treated by DIALIGN in the same way as fragments ( = segment pairs) in the greedy procedure for multi-alignment. By transitivity, a set Anc of anchor points defines a quasi partial order relation ≤Anc on the set X of all positions of the input sequences – in exactly the same way as an alignment Ali induces a quasi partial order relation ≤Ali on X as described in [16,25]. Formally, we consider an alignment Ali as well as a set of anchor points Anc as an equivalence relation defined on the set X of all positions of the input sequences. Next, we consider the partial order relation ≤ on X that is given by the 'natural' ordering of positions within the sequences. In order-theoretical terms, ≤ is the direct sum of the linear order relations defined on the individual sequences. The partial order relation ≤Anc is then defined as the transitive closure of the union ≤ ∪ Anc. In other words, we have x ≤Anc y if and only if there is a chain x0, ..., xk of positions with x0 = x and xk = y such that for every i ∈ {1,..., k}, position xi-1 is either anchored with xi or xi-1 and xi belong to the same sequence, and xi-1 is on the left-hand side of xi in that sequence.