Preserving Proximity in Arrays

Efficiency of storage management in algorithms which use arrays is often enhanced if the arrays are stored in a proximity-preserving manner; that is, array positions which are close to one another in the array are stored close to one another. This paper is devoted to studying certain qualitative and quantitative questions concerning preservation of proximity by array storage schemes (or,realizations). It is shown that fully extendible array realizations cannot preserve proximity in any global sense, not even proximity along a single direction (say, along rows). They can, however, preserve proximity in certain local senses; and realizations which are optimal in various senses of local preservation are exhibited. Partially extendible array storage schemes can preserve proximity in a global way; bounds on their “diameters of preservation” are derived, and optimal schemes are exhibited.