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arXiv · 1101.5407

Maintaining Arrays of Contiguous Objects

Michael A. Bender·Sándor P. Fekete·Tom Kamphans·Nils Schweer
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Abstract

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 Theta(n^2) 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(m_i log M) per insertion or deletion, where m_i 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.

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Michael A. Bender, Sándor P. Fekete, Tom Kamphans, Nils Schweer. 2011-01-27. Maintaining Arrays of Contiguous Objects. https://arxiv.org/abs/1101.5407

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