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) ( d , f ) -cluttered orderings of various set systems, d,f?N 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 ? ? -labellings. In this paper, we investigate cluttered orderings for the complete bipartite graph. We adapt the concept of a wrapped ? ? -labelling to the bipartite case and introduce the notion of a (d,f) ( 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 ? ? -labellings leading to cluttered orderings for the corresponding bipartite graphs.
cluttered ordering bipartite graph raid wrapped ? ? -labelling ? ? ? ? ?