Exact Analyses of a Simple Heuristic Employed In Array Compression

... this paper is to precisely analyse the behaviour of one such extremely simple heuristic which is known to give modest compression in practice. For the heuristic we prove that the expected asymptotic space requirement is, at worst, a(k)n+ b(k)x and that although its dependency on n is inherent, it can be made arbitrarily small. Here k is a parameter and a(k) and b(k) are, respectively, monotonically decreasing and increasing functions. Thus k allows a trade-off between dependency on n and x;for example, pairs (a(k), b(k)) can be (0.1, 3.26), (0.03, 5.57) and (6 10 -4 , 33). We also show that for some applications the dependency of the space requirement on n canbemadesublinear. The heuristic allows constant time access to any element. Our analyses are over two different models for the uniform probability distribution and we derive exact formulae for the expected space used. We prove that the heuristic gives the same asymptotic performance in both model