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On an optimality property of ternary trees

F. Göbel, C. Hoede
1979 Information and Control  
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]

Subhash Kak
2018 arXiv   pre-print
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  
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

Raymond E. Miller, Nicholas Pippenger, Arnold L. Rosenberg, Lawrence Snyder
1979 SIAM journal on computing (Print)  
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

Binod Kumar Pattanayak, Sambit Kumar Patra, Bhagabat Puthal
2013 Journal of Computers  
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

Minming Li, Ze Feng, Nan Zang, Ronald L. Graham, Frances F. Yao
2009 Theoretical Computer Science  
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

Guy Shani, Christopher Meek, Tim Paek, Bo Thiesson, Gina Danielle Venolia
2008 Proceedingsc of the 13th international conference on Intelligent user interfaces - IUI '09  
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]

Barbara Covella, Fabrizio Frati, Maurizio Patrignani
2019 arXiv   pre-print
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  
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  
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

Han-Pang Chiu, Xun S. Zhou, Luca Carlone, Frank Dellaert, Supun Samarasekera, Rakesh Kumar
2014 2014 IEEE International Conference on Robotics and Automation (ICRA)  
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]

Zoran Sunic
2006 arXiv   pre-print
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

Harris Georgiou
2016 Zenodo  
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

K. Ravikanth, P.S. Sastry, K.R. Ramakrishnan, Y.V. Venkatesh
1988 Future generations computer systems  
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]

Harris V. Georgiou
2016 arXiv   pre-print
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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