On-the-Fly Array Initialization in Less Space
Torben Hagerup, Frank Kammer

TL;DR
This paper introduces a space-efficient data structure that supports fast array initialization and access, optimizing memory usage and operation times in word RAM models for various tradeoffs.
Contribution
It presents a novel array representation method that achieves constant-time initialization and access with significantly reduced space compared to prior solutions.
Findings
Supports constant-time array initialization and access with minimal space overhead.
Provides a flexible tradeoff between initialization time, access time, and memory usage.
Achieves near-optimal space complexity for arbitrary access times with fast initialization.
Abstract
We show that for all given with , an array of entries of bits each can be represented on a word RAM with a word length of bits in at most bits of uninitialized memory to support constant-time initialization of the whole array and -time reading and writing of individual array entries. At one end of this tradeoff, we achieve initialization and access (i.e., reading and writing) in constant time with bits for arbitrary fixed , to be compared with bits for the best previous solution, and at the opposite end, still with constant-time initialization, we support -time access with just bits, which is optimal for arbitrary access times if the initialization executes fewer than steps.
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Taxonomy
TopicsAntenna Design and Optimization · Radio Astronomy Observations and Technology · Electromagnetic Compatibility and Measurements
