Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Dynamic programming: deterministic and stochastic models
Dynamic programming: deterministic and stochastic models
Combinatorial analysis of ramified patterns and computer imagery of trees
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
The algorithmic beauty of plants
The algorithmic beauty of plants
Efficient antialiased rendering of 3-D linear fractals
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
The object instancing paradigm for linear fractal modeling
Proceedings of the conference on Graphics interface '92
Ordered and Unordered Tree Inclusion
SIAM Journal on Computing
Improved approximation algorithms for tree alignment
Journal of Algorithms
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Variations on the Common Subexpression Problem
Journal of the ACM (JACM)
Identifying approximately common substructures in trees based on a restricted edit distance
Information Sciences: an International Journal
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Introduction to Discrete Structures for Computer Science and Engineering
Introduction to Discrete Structures for Computer Science and Engineering
An efficient instantiation algorithm for simulating radiant energy transfer in plant models
ACM Transactions on Graphics (TOG)
A New Editing based Distance between Unordered Labeled Trees
CPM '93 Proceedings of the 4th Annual Symposium on Combinatorial Pattern Matching
Selected topics on assignment problems
Discrete Applied Mathematics
Local similarity between quotiented ordered trees
Journal of Discrete Algorithms
IEEE Transactions on Computers
Journal of Graph Theory
Approximate labelled subtree homeomorphism
Journal of Discrete Algorithms
Sketchpad: a man-machine graphical communication system
AFIPS '63 (Spring) Proceedings of the May 21-23, 1963, spring joint computer conference
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In this paper, we are interested in the problem of approximating trees by trees with a particular self-nested structure. Self-nested trees are such that all their subtrees of a given height are isomorphic. We show that these trees present remarkable compression properties, with high compression rates. In order to measure how far a tree is from being a self-nested tree, we then study how to quantify the degree of self-nestedness of any tree. For this, we define a measure of the self-nestedness of a tree by constructing a self-nested tree that minimizes the distance of the original tree to the set of self-nested trees that embed the initial tree. We show that this measure can be computed in polynomial time and depict the corresponding algorithm. The distance to this nearest embedding self-nested tree (NEST) is then used to define compression coefficients that reflect the compressibility of a tree. To illustrate this approach, we then apply these notions to the analysis of plant branching structures. Based on a database of simulated theoretical plants in which different levels of noise have been introduced, we evaluate the method and show that the NESTs of such branching structures restore partly or completely the original, noiseless, branching structures. The whole approach is then applied to the analysis of a real plant (a rice panicle) whose topological structure was completely measured. We show that the NEST of this plant may be interpreted in biological terms and may be used to reveal important aspects of the plant growth.