Cost-Oblivious Storage Reallocation

Abstract

Databases allocate and free blocks of storage on disk. Freed blocks introduce holes where no data is stored. Allocation systems attempt to reuse such deallocated regions in order to minimize the footprint on disk. When previously allocated blocks cannot be moved, this problem is called the memory allocation problem. The competitive ratio for this problem has matching upper and lower bounds that are logarithmic in the number of requests and in the ratio of the largest to smallest requests. This article defines the storage reallocation problem, where previously allocated blocks can be moved, or reallocated , but at some cost. This cost is determined by the allocation/reallocation cost function . The objective is to minimize the storage footprint, that is, the largest memory address containing an allocated object, while simultaneously minimizing the reallocation costs. This article gives asymptotically optimal algorithms for storage reallocation, in which the storage footprint is at most (1+ ϵ) times optimal, and the reallocation cost is O ((1/ϵ)log (1/ϵ)) times the original allocation cost, that is, it is within a constant factor of optimal when ϵ is a constant. The algorithms are cost oblivious , which means they achieve these bounds with no knowledge of the allocation/reallocation cost function, as long as the cost function is subadditive.

Cost-Oblivious Reallocation for Scheduling and Planning

“…Being cost oblivious means that the scheduler does not use any knowledge of f . Cost obliviousness was introduced in [8], motivated by the practical problem of storage reallocation in database systems. Cost obliviousness is desirable, because the true cost of reallocation may be complex or even unknown.…”

“…Cost oblivious reallocation is a relatively new concept that we recently introduced [8]. In that paper, the goal was to minimize the total space footprint of the data being stored; this is analogous to minimizing the makespan (i.e., the maximum time that any job completes) in scheduling.…”

“…In the current paper, we focus on minimizing the sum of completion times, which imposes different constraints on the ordering of jobs. The storage reallocator [8] relied on different tools, e.g., cascading buffers, that would not help for minimizing sum of completion times; by contrast, the main tool here is the k-cursor sparse table.…”

“…8 These claims are useful for proving both the desired prefix density and bounds on the cost of rebuilding buffers. We show that the data structure achieves constant prefix density.…”

“…In our own research, we have modelled FPGA reorganization as a reallocation problem, minimizing reconfiguration costs [17]. We have also explored reallocation problems in database resource management with respect to crash safety and transactional support [8]. One of our long-term goals is to understand which scheduling objectives are amenable to efficient reallocation, and which ones are brittle.…”