Tight Bounds for Dynamic Storage Allocation
SIAM Journal on Discrete Mathematics
Approximation algorithms for bin packing: a survey
Approximation algorithms for NP-hard problems
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Worst-case efficient priority queues
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
SIAM Journal on Computing
Theory of Computing Systems
Strip packing with precedence constraints and strip packing with release times
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
An adaptive packed-memory array
ACM Transactions on Database Systems (TODS)
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In this paper we consider methods for dynamically storing a set of different objects ("modules") in a physical array. Each module requires one free contiguous subinterval in order to be placed. Items are inserted or removed, resulting in a fragmented layout that makes it harder to insert further modules. It is possible to relocate modules, one at a time, to another free subinterval that is contiguous and does not overlap with the current location of the module. These constraints clearly distinguish our problem from classical memory allocation. We present a number of algorithmic results, including a bound of Θ(n2) on physical sorting if there is a sufficiently large free space and sum up NP-hardness results for arbitrary initial layouts. For online scenarios in which modules arrive one at a time, we present a method that requires O(1) moves per insertion or deletion and amortized cost O(mi lg m) per insertion or deletion, where mi is the module's size, m is the size of the largest module and costs for moves are linear in the size of a module.