Complexity analysis of the discrete sequential search problem with group activities

This paper studies the computational complexity of the discrete sequential search problem with group activities, in which a set of boxes is given and a single object is hidden in one of these boxes. Each box is characterized by a probability that it contains that object and the cost of searching that box. Furthermore, each box may be related to one or more `group activities'. For `conjunctive' group activities, a box can be searched only when all the associated group activities have been performed whereas for `disjunctive' group activities, a box can be searched as soon as at least one of the associated group activities has been executed. A cost is also incurred when performing a group activity. The goal is to find a sequence in which the boxes are to be searched and the group activities will be executed to minimize the expected total cost while satisfying the precedence constraints imposed by the group activities. In this paper, we prove that this problem is strongly NP-hard both for conjunctive group activities and for disjunctive group activities, and we discuss some special cases that can be solved in polynomial time.