Refined Buneman Trees

Algorithm 7 The DISCARD-RIGHT algorithm
Require: σ = U 1 |V 1 and σ ′ = U 2 |V 2 are incompatible splits.
Ensure: return true if μ σ ′ ≤ 0, false otherwise.
1: A = U1 ∩ U2, B = U1 ∩ V 2, C = V 1 ∩ U2, D = V 1 ∩ V 2
2: Q = ∅
3: for a =1to|A| do
4: for b =1to|B| do
5: for c =1to|C| do
6: for d =1to|D| do
7: determine permutations q 1 and q 2 of A[a], B[b], C[c] andD[d] such
that q 1 ∈ q(σ) andq 2 ∈ q(σ ′ )
8: Q = Q ∪ q 2
9: if |Q| = n − 3 then
10: goto sum
11: end if
12: end for
13: end for
14: end for
15: end for
16: sum:
17: if ∑ n−3
i=1 β Q[i] ≤ 0 then
18: return TRUE
19: end if
20: return FALSE
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