Approximation algorithms for dynamic storage allocation

Abstract

We present a new O(n log n)-time 5-approximation algorithm for the NP-hard dynamic storage allocation problem (DSA). The two previous approximation algorithms for DSA are based on on-line coloring of interval graphs and have approximation ratios of 6 and 80 [6, 7, 16]. Our result gives an affirmative answer to the important open question of whether the approximation ratio of DSA can be improved below the bound implied by on-line coloring of interval graphs [7, 16]. Our approach is based on the novel concept of a 2-allocation and on the design of an efficient transformation of a 2-allocation to an at most 5/2 times larger memory allocation. For the NP-hard variant of DSA with only two sizes of blocks allowed, we give a simpler 2-approximation algorithm. Further, by means of a tighter analysis of the widely used First Fit strategy, we show how the competitive ratio of on-line DSA can be improved to Θ(max{1, log(nk/M)}) where M, k, and n are upper bounds on the maximum number of simultaneously occupied cells, the maximum number of blocks simultaneously in the storage, and the maximum size of a block.