For n ∈ N , we consider the problem of partitioning the interval [ 0 , n ) into k subintervals of positive integer lengths ℓ 1 , … , ℓ k such that the lengths satisfy a set of simple constraints of the form ℓ i ⋄ i j ℓ j where ⋄ i j is one of <, >, or =. In the full information case, ⋄ i j is given for all 1 ⩽ i , j ⩽ k . In the sequential information case, ⋄ i j is given for all 1 < i < k and j = i ± 1 . That is, only the relations between the lengths of consecutive intervals are specified. The cyclic information case is an extension of the sequential information case in which the relationship ⋄ 1 k between ℓ 1 and ℓ k is also given. We show that all three versions of the problem can be solved in time polynomial in k and log n .