Linkless Octree Using Multi‐Level Perfect Hashing

Abstract

The standard C/C++ implementation of a spatial partitioning data structure, such as octree and quadtree, is often inefficient in terms of storage requirements particularly when the memory overhead for maintaining parentto-child pointers is significant with respect to the amount of actual data in each tree node. In this work, we present a novel data structure that implements uniform spatial partitioning without storing explicit parent-tochild pointer links. Our linkless tree encodes the storage locations of subdivided nodes using perfect hashing while retaining important properties of uniform spatial partitioning trees, such as coarse-to-fine hierarchical representation, efficient storage usage, and efficient random accessibility. We demonstrate the performance of our linkless trees using image compression and path planning examples.

Fast Generation of Pointerless Octree Duals

“…In particular, increasing b size may be delicate in the static strategy, since it would require two large blocks (of size 2 b ) of data for the hashtable. A solution to optimize the hashing is to use perfect hashing techniques, which are already used for pointerless octrees [LH06,BC08,CJC*09].…”

“…Pointerless representations of octrees [Gar82] have become popular for sparing memory [CJC*09] and for their ability to work on parallel [WS93] and GPU architectures [BC08]. The use of Morton codes [Mor66, SS09] for indexing the octree (see Section 2) is widely used, since they allow for efficient manipulation as dilated integers [Sch92,SS95] and optimized search [GDB03,CLL*08].…”

Data-Parallel Hashing Techniques for GPU Architectures

“…Choi et al [21] follow-up the work of Bastos and Celes [9] with a similar link-less octree design that avoids the need to store extra bitmaps for the sparsity encoding of empty grid cells in the sparse spatial domain. This encoding indicates whether a cell contains associated data that is stored within the hash table; if no data is present, then a query operation for the cell can be avoided.…”

2D Adaptive Grid-Based Image Analysis Approach for Biological Networks

“…2) Spatial hashing: This work applies the same hashing principle as in [16], [24], and [17]. We store the depth and the quadrant coordinates for each node using a hashing method, where the d is the level (depth) of the subdivision and C is a tuple, which defines the subdivision labeling of a certain image block, where C can be calculated recursively as follows:…”

“…We implemented a pointer-less quadtree partitioning based on [16], [24] and performed the graph analysis based on img2net [4], [6] and the Networkx Python library [28], using the same graph properties in img2net (as described in Table IV). We used the following packages to implement our work: Python 2.7.3, SciPy, NumPy, nested_dict 1.61, Cython and NetworkX.…”