This is a study of a model for sub-optimal linear ordering of rooms to be allocated along a linear communication path. The pattern of communication path, such as linear, loop, T-shape and cross, tends to be imaged as a basic form of architectural plan at the beginning of design. Criteria for the sub-optimum ordering of rooms are those that follow. 1) Maximizing or minimizing the maximum or minimum number of communication movements passing through between each possible subset of rooms and its complementary set of rooms. 2) Maximizing or minimizing the total length of communication movents between rooms. The study is also developed in this paper to deal with allocation when rooms are different in size and some rooms are fixed at the given place in advance. The problem to find the sub-optimum ordering turns out to be equivalent to find the shortest directed path from the start vertex to the goal vertex in a state-space graph. Each vertex of this graph consists of subsets of rooms. The start vertex and the end vertex consists of empty set and universal set respectively.