An off-line storage allocation algorithm

Abstract

We investigate the off-line dynamic storage allocation (DSA, for short) problem, as defined in [3, p.226] and [7]. Its basic version is NP-hard in the strong sense as well as many subproblems [3,6]. In this paper we analyze a strongly restricted version of the DSA problem in which block sizes form a divisible sequence and arrivals of larger blocks follow arrivals of smaller ones. We devise a polynomial-time algorithm which finds an optimal allocation for any such instance. This optimum appears to be equal to the maximal amount of busy store at any time in the instance. Hence, the last quantity can be replaced by OPT in Robson's [5] and Krogdahl's [4] lower bounds for the performance of on-line algorithms for the DSA problem. From the obtained estimation it easily follows that no on-line polynomial approximation strategy for DSA achieves a constant worst-case performance ratio. To be precise in discussing on-line and off-line properties of algorithms we formulate the definition of the DSA problem in the way which follows earlier approaches to the problem [5]. This definition is equivalent to that of [3], hence all DSA complexity features remain unchanged. Denote by