scholarly journals Dual-split trees

2019 ◽  
Author(s):  
Daqi Lin ◽  
Konstantin Shkurko ◽  
Ian Mallett ◽  
Cem Yuksel
Keyword(s):  
Split Trees

Hardware-Accelerated Dual-Split Trees

2020 ◽  
Vol 3 (2) ◽  
pp. 1-21
Author(s):  
Daqi Lin ◽  
Elena Vasiou ◽  
Cem Yuksel ◽  
Daniel Kopta ◽  
Erik Brunvand
Keyword(s):  
Ray Tracing ◽  
Hardware Acceleration ◽  
Memory Storage ◽  
Compact Representation ◽  
Space Partitioning ◽  
Data Movement ◽  
Bounding Volume ◽  
Bounding Boxes ◽  
Split Trees ◽  
Bounding Volume Hierarchies

Bounding volume hierarchies (BVH) are the most widely used acceleration structures for ray tracing due to their high construction and traversal performance. However, the bounding planes shared between parent and children bounding boxes is an inherent storage redundancy that limits further improvement in performance due to the memory cost of reading these redundant planes. Dual-split trees can create identical space partitioning as BVHs, but in a compact form using less memory by eliminating the redundancies of the BVH structure representation. This reduction in memory storage and data movement translates to faster ray traversal and better energy efficiency. Yet, the performance benefits of dual-split trees are undermined by the processing required to extract the necessary information from their compact representation. This involves bit manipulations and branching instructions which are inefficient in software. We introduce hardware acceleration for dual-split trees and show that the performance advantages over BVHs are emphasized in a hardware ray tracing context that can take advantage of such acceleration. We provide details on how the operations needed for decoding dual-split tree nodes can be implemented in hardware and present experiments in a number of scenes with different sizes using path tracing. In our experiments, we have observed up to 31% reduction in render time and 38% energy saving using dual-split trees as compared to binary BVHs representing identical space partitioning.

Construction of optimal binary split trees in the presence of bounded access probabilities

1988 ◽  
Vol 9 (2) ◽  
pp. 245-253 ◽  
Author(s):  
J.H Hester ◽  
D.S Hirschberg ◽  
L.L Larmore
Keyword(s):  
Split Trees

scholarly journals A weakly 1-stable distribution for the number of random records and cuttings in split trees

2011 ◽  
Vol 43 (01) ◽  
pp. 151-177 ◽  
Author(s):  
Cecilia Holmgren
Keyword(s):  
Classical Limit ◽  
Stable Distribution ◽  
Search Tree ◽  
Binary Search ◽  
Binary Search Tree ◽  
Search Trees ◽  
Infinitely Divisible ◽  
Digital Search Trees ◽  
Split Trees ◽  
Digital Search

In this paper we study the number of random records in an arbitrary split tree (or, equivalently, the number of random cuttings required to eliminate the tree). We show that a classical limit theorem for the convergence of sums of triangular arrays to infinitely divisible distributions can be used to determine the distribution of this number. After normalization the distributions are shown to be asymptotically weakly 1-stable. This work is a generalization of our earlier results for the random binary search tree in Holmgren (2010), which is one specific case of split trees. Other important examples of split trees includem-ary search trees, quad trees, medians of (2k+ 1)-trees, simplex trees, tries, and digital search trees.

scholarly journals The total path length of split trees

2012 ◽  
Vol 22 (5) ◽  
pp. 1745-1777 ◽  
Author(s):  
Nicolas Broutin ◽  
Cecilia Holmgren
Keyword(s):  
Path Length ◽  
Total Path Length ◽  
Split Trees

Optimum split trees

1984 ◽  
Vol 5 (3) ◽  
pp. 367-374 ◽  
Author(s):  
Yehoshua Perl
Keyword(s):  
Split Trees

Optimal multiway generalized split trees

1991 ◽  
Vol 41 (1-2) ◽  
pp. 39-47
Author(s):  
Gen-Huey Chen ◽  
Lung-Tien Liu
Keyword(s):  
Split Trees

scholarly journals Random Records and Cuttings in Split Trees: Extended Abstract

2008 ◽  
Vol DMTCS Proceedings vol. AI,... (Proceedings) ◽  
Author(s):  
Cecilia Holmgren
Keyword(s):  
Search Tree ◽  
Binary Search ◽  
Binary Search Tree ◽  
Search Trees ◽  
Digital Search Trees ◽  
International Audience ◽  
Split Trees ◽  
Digital Search

International audience We study the number of records in random split trees on $n$ randomly labelled vertices. Equivalently the number of random cuttings required to eliminate an arbitrary random split tree can be studied. After normalization the distributions are shown to be asymptotically $1$-stable. This work is a generalization of our earlier results for the random binary search tree which is one specific case of split trees. Other important examples of split trees include $m$-ary search trees, quadtrees, median of $(2k+1)$-trees, simplex trees, tries and digital search trees.

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