[For the entire collection see Zbl 0527.00031.] We study parallel solutions to the connected component problem, which arises as a subproblem in many graph problem and whose information flow requirements seem to be a paradigm for other graph problems. Our solutions are for networks that do not have enough storage capacity to store an adjacency matrix of the edges of graph explicitly for the entire computation. Our first algorithm finds the connected components of an n- vertex graph on a 2-dimensional mesh of processors in time $O(n\sp{3/2})$ when the input is in the form of unordered edges. The mesh reads every edge once, and we assume that the time elapsing between the reading of the i-th and $(i+1)$-st input wave can depend on the data (i.e., is when- indeterminate). When the graph is given in the form of an adjacency matrix (i.e., the i-th input wave is the i-the row of the matrix) the algorithm can be modified to find the connected components in $O(n\sp{3/2})$ time by a when-determinate algorithm. Both algorithms can be generalized to higher dimensional meshes to achieve an area-time tradeoff of $AT\sp 2=O(n\sp 4)$ in the range $Ω(n)\le A

Keywords: parallel computation; graph algorithm; meshes; connected component problem; networks; verification problem; adjaceny matrix