Scheduling complete binary tree with constant cost task on heterogeneous processors

2017 ◽  
Author(s):  
Issam Troudi ◽  
Mounir Marrakchi
Keyword(s):  
Binary Tree ◽  
Complete Binary Tree ◽  
Heterogeneous Processors ◽  
Constant Cost

Binary Trees and the n-Cutset Property

1991 ◽  
Vol 34 (1) ◽  
pp. 23-30 ◽  
Author(s):  
Peter Arpin ◽  
John Ginsburg
Keyword(s):  
Positive Integer ◽  
Partially Ordered Set ◽  
Binary Tree ◽  
Ordered Set ◽  
Maximal Chain ◽  
Binary Trees ◽  
Complete Binary Tree ◽  
Maximal Elements ◽  
Extremal Case ◽  
Result Theorem

AbstractA partially ordered set P is said to have the n-cutset property if for every element x of P, there is a subset S of P all of whose elements are noncomparable to x, with |S| ≤ n, and such that every maximal chain in P meets {x} ∪ S. It is known that if P has the n-cutset property then P has at most 2n maximal elements. Here we are concerned with the extremal case. We let Max P denote the set of maximal elements of P. We establish the following result. THEOREM: Let n be a positive integer. Suppose P has the n-cutset property and that |Max P| = 2n. Then P contains a complete binary tree T of height n with Max T = Max P and such that C ∩ T is a maximal chain in T for every maximal chain C of P. Two examples are given to show that this result does not extend to the case when n is infinite. However the following is shown. THEOREM: Suppose that P has the ω-cutset property and that |Max P| = 2ω. If P — Max P is countable then P contains a complete binary tree of height ω

Two Models of Additional Adjacencies between the Root and Descendants in a Complete Binary Tree Minimizing Total Path Length

2009 ◽  
Author(s):  
Kiyoshi Sawada ◽  
Sio-Iong Ao ◽  
Alan Hoi-Shou Chan ◽  
Hideki Katagiri ◽  
Osca Castillo ◽  
...  
Keyword(s):  
Binary Tree ◽  
Path Length ◽  
Complete Binary Tree ◽  
Total Path Length

scholarly journals Permutation Steganography for Polygonal Meshes Based on Coding Tree

2010 ◽  
Vol 9 (4) ◽  
pp. 55-60 ◽  
Author(s):  
Shihchun Tu ◽  
Hungwei Hsu ◽  
Wenkai Tai
Keyword(s):  
Binary Tree ◽  
Experimental Results ◽  
Affine Transformations ◽  
Complete Binary Tree ◽  
Polygonal Meshes ◽  
Maximal Capacity

We propose a coding tree for permutation steganography in polygonal meshes. Instead of conceptually building a complete binary tree for remaining embedding/extracting primitives to encode/decode bitstream, our method lengthens bitstream by exploiting the coding tree of the primitives, a binary tree which is a little bit skewed. The coding tree has higher levels than the complete binary tree so that as experimental results show, the average capacity of our approach is more about 0.39 bit/vertex than that of Bogomjakov et al. [5], and the improvement of the maximal capacity comes up to 40% of Bogomjakov et al. [5]. Still, our method has the minimal capacity same with Bogomjakov et al. [5], and is simple and easy to implement as well. This ordering is obtained based on the mesh connectivity [14], making our method robust to geometric affine transformations. Also, the primitive rearrangement does not distort the cover media and cause suspicion of the hidden message

Sign in / Sign up

Export Citation Format

Share Document