### 3.7.47. Compulsory part

A constraint for which the filtering algorithm may use the notion of compulsory part. The notion of compulsory part was introduced by A. Lahrichi within the context of cumulative scheduling problems [Lahrichi79], [Lahrichi82], [Lahrichi82a] as well as within the context of rectangles placement problems [LahrichiGondran84]. Within these two contexts, the compulsory part respectively corresponds to the intersection of all feasible instances of a task or to the intersection of all feasible instances of a rectangle.

Figure 3.7.12 illustrates the notion of compulsory part in the context of scheduling and placement problems. The first, second and third rows respectively corresponds to the $\mathrm{𝚌𝚞𝚖𝚞𝚕𝚊𝚝𝚒𝚟𝚎}$ [AggounBeldiceanu93], the $\mathrm{𝚌𝚞𝚖𝚞𝚕𝚊𝚝𝚒𝚟𝚎}_\mathrm{𝚝𝚛𝚊𝚙𝚎𝚣𝚎}$ [Poder02], [PoderBeldiceanuSanlaville04] and the $\mathrm{𝚍𝚒𝚏𝚏𝚗}$ [BeldiceanuGuoThiel01] constraints. The first, second and third columns respectively correspond to the shape of the object for which we compute the compulsory part, to the extreme positions of the object and to the corresponding compulsory part.