Cluttered orderings for the complete bipartite graph

To minimize the access cost in large disk arrays (RAID) Cohen, Colbourn, and Froncek introduced and investigated in a series of papers the concept of (d,f)-cluttered orderings of various set systems, d,f∈N. In case of a graph this amounts to an ordering of the edge set such that the number of points contained in any d consecutive edges is bounded by the number f. For the complete graph, Cohen et al. gave some optimal solution for small parameters d and introduced some general construction principle based on wrapped Δ-labellings. In this paper, we investigate cluttered orderings for the complete bipartite graph. We adapt the concept of a wrapped Δ-labelling to the bipartite case and introduce the notion of a (d,f)-movement for subgraphs. From this we get a general existence theorem for cluttered orderings. The main result of this paper is the explicit construction of several infinite families of wrapped Δ-labellings leading to cluttered orderings for the corresponding bipartite graphs.