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On an optimality property of ternary trees
1979
Information and Control
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The concept of effort is defined for rooted trees. The class of rooted trees with minimal effort is determined. The asymptotic behaviour of the minimal effort is calculated. ...
Various choices for the effort function are considered, as well as variations of the optimality, criterion. ...
For example, it seems that optimal trees for increasing values of N are ternary trees.
AN OPTIMALITY PROPERTY OF TERNARY Tm~ES W e recall that e(u) -~ u. ...
doi:10.1016/s0019-9958(79)90121-9
fatcat:fya43ma3ejehhn2enn7uc4e3hu
On Ternary Coding and Three-Valued Logic
[article]
2018
arXiv
pre-print
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In this paper we present a new comparison of binary and ternary coding and their relative efficiencies are computed both for number representation and decision trees. ...
The implications of our inability to use optimal representation through mathematics or logic are examined. ...
Ternary coding remains relevant in algorithms that use decision trees. Let's consider coding of numbers to an arbitrary base b. ...
arXiv:1807.06419v1
fatcat:aiysrus2wrcvxehtwrutcoqqxi
Page 2486 of Mathematical Reviews Vol. , Issue 80F
[page]
1980
Mathematical Reviews
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An upper bound on the tree diame- ter is given for a prescribed number of nodes. ...
We consider the properties of trees (particularly the diameter of trees) that realize a given gauge matrix (terminal capacity matrix) of a network. ...
Optimal 2,3-Trees
1979
SIAM journal on computing (Print)
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In this section we prepare the way for our study of optimal 2,3-trees. ...
Both have the property that a number of different representations for the same set of records are permissible within the limits of the definitions of the respective structures. ...
If /3 and r denote the number of binary and ternary nodes, respectively, at height one, then 2/3 + 3r n. An n-leaf 2,3-tree can be constructed by the following three-step procedure. ...
doi:10.1137/0208004
fatcat:vaflseayojd4xin7wbqtccdbvm
Optimizing AST Node for Java Script Compiler A lightweight Interpreter for Embedded Device
2013
Journal of Computers
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In this paper, we implement AST node optimization technique for a set of frequently used operators and statements on a JavaScript compiler, such as Identifiers, Function-calls, Dot-operator and If-then-else ...
Abstract Syntax Tree (AST) could be a better option for mobile codes as it is compiled only once. ...
ACKNOWLEDGMENT We are extremely grateful to the administration of SOA Deemed to be University, Bhubaneswar, India for extending the opportunity to us in preparing this manuscript. ...
doi:10.4304/jcp.8.2.349-355
fatcat:6rrxfo6fefaq3fsulpsrclddma
Approximately optimal trees for group key management with batch updates
2009
Theoretical Computer Science
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We design an O(n) heuristic algorithm for the sparse case and show that it produces a nearly 2-approximation to the optimal key tree. ...
Under this model, it was recently shown that an optimal key tree can be constructed in linear time when p is a constant and in O(n 4 ) time when p → 0. ...
In fact, their results implied that, for n = 3 t , the optimal key tree is a balanced ternary tree, and for many other values of n, the optimal tree is as close to a balanced ternary tree with n leaves ...
doi:10.1016/j.tcs.2008.10.034
fatcat:tssqi34oonh65eb2cwvnf4qfke
Searching large indexes on tiny devices
2008
Proceedingsc of the 13th international conference on Intelligent user interfaces - IUI '09
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The underlying index for our method is based on a ternary search tree that is optimal under certain user-oriented constraints. ...
The small physical size of mobile devices imposes dramatic restrictions on the user interface (UI). ...
We explained how an Optimal Binary Search Tree can be augmented with character pinning in the form of a Ternary Search Tree. ...
doi:10.1145/1502650.1502687
dblp:conf/iui/ShaniMPTV09
fatcat:6g5r6i2kxnhxhauy73a5hczn74
On the Area Requirements of Planar Straight-Line Orthogonal Drawings of Ternary Trees
[article]
2019
arXiv
pre-print
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Further, we present upper bounds, the outcomes of an experimental evaluation, and a conjecture on the area requirements of planar straight-line orthogonal drawings of complete ternary trees. ...
Finally, we present a polynomial lower bound on the length of the minimum side of any planar straight-line orthogonal drawing of a complete ternary tree. ...
In the following we show an inductive algorithm that takes in input an n-node ternary tree T and constructs a drawing Γ of T that satisfies the top-visibility property, i.e., the vertical half-line emanating ...
arXiv:1902.11044v1
fatcat:scqzf7xudfae7fwehqtykmmivu
Page 594 of Mathematical Reviews Vol. , Issue 2000a
[page]
2000
Mathematical Reviews
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A precision constraint is imposed on one of these estimates and the optimal design is found using the theory of canonical moments. ...
Robustness properties of the optimal designs to model assumptions and their performances relative to similar designs are studied.”
2000a:62178 62K05 62K15 Vijayan, K. ...
Page 1483 of Mathematical Reviews Vol. 58, Issue 2
[page]
1979
Mathematical Reviews
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She associates a tree with the equation and gives some
operations on trees which lead to one solution or all solutions of the equation. ...
B. 58 +9867
A design technique for an integrable ternary arithmetic unit. ...
Constrained optimal selection for multi-sensor robot navigation using plug-and-play factor graphs
2014
2014 IEEE International Conference on Robotics and Automation (ICRA)
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This mechanism constructs candidate subsets of sensors based on heuristic rules and a ternary tree expansion algorithm. ...
A novel constrained optimal selection mechanism is presented to identify the optimal subset of active sensors to use, during initialization and when any sensor condition changes. ...
Select Optimal Sensor Subset Upon the completely built ternary tree, our mechanism locates only a portion of tree nodes based on available resource and desired accuracy in real-time system. ...
doi:10.1109/icra.2014.6906925
dblp:conf/icra/ChiuZCDS014
fatcat:ilang5gdjndpvpwecnkoprry5a
Tree morphisms, transducers, and integer sequences
[article]
2006
arXiv
pre-print
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By definition, transducer integer sequences are integer sequences produced, under a suitable interpretation, by finite automata encoding tree morphisms (length and prefix preserving transformations of ...
The notion of transducer integer sequences is considered through a series of examples. ...
The graph on the left represents an invertible ternary transducer, denoted A H . ...
arXiv:math/0612080v1
fatcat:m5z53iz5grco7lg3tnqpqax5ze
On The Optimality Of Ternary Arithmetic For Compactness And Hardware Design
2016
Zenodo
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In this paper, the optimality of ternary arithmetic is investigated under strict mathematical formulation. ...
Using proper formulations for the optimization task, the universal constant e (base of natural logarithms) is proven as the most efficient radix and ternary is asserted as the closest integer choice. ...
one early ternary machine was built entirely from wood by Thomas Fowler in 1840 and it operated in balanced ternary [4] . the 2-D size of the associated tree, if a specic number (upper bound) C is treated ...
doi:10.5281/zenodo.164939
fatcat:w2j5stomxzhulkc63zhal7t3le
A reduction architecture for the optimal scheduling of binary trees
1988
Future generations computer systems
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An interconnection network that allows for scheduling of binary trees of arbitrary depth is presented. ...
Some issues related to the design of a machine based on this network are also discussed. ...
Average lif vs. level no. for a class of incomplete ternary trees on the network sizes 8-256. ...
doi:10.1016/0167-739x(88)90006-4
fatcat:6j7isesevvb3rkieztlzjk7qxu
On the optimality of ternary arithmetic for compactness and hardware design
[article]
2016
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
In this paper, the optimality of ternary arithmetic is investigated under strict mathematical formulation. ...
Using proper formulations for the optimization task, the universal constant 'e' (base of natural logarithms) is proven as the most efficient radix and ternary is asserted as the closest integer choice. ...
Such an example for the number 39 is presented in Figure 1 . In Figure 1 each node contains exactly three items and each one of them is the root for three similar sub-trees. ...
arXiv:1611.03715v1
fatcat:qq5meplybvhivdxqkvx27j2xje
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