منابع مشابه
Edge separators for quasi-binary trees
One wishes to remove k − 1 edges of a vertex-weighted tree T such that the weights of the k induced connected components are approximately the same. How well can one do it ? In this paper, we investigate such k-separator for quasi-binary trees. We show that, under certain conditions on the total weight of the tree, a particular k-separator can be constructed such that the smallest (respectively...
متن کاملWell-Quasi-Orderings on Binary Trees
We provide a set of “natural” requirements for quasi-orderings of finite and infinite binary trees. We show that any ordering satisfying these requirements must be well-ordered and that there is a unique minimal such ordering. The checker has to verify that the process comes to an end. Here again he should be assisted by the programmer giving a further definite assertion to be verified. This ma...
متن کاملGeneralized Huffman Coding for Binary Trees with Choosable Edge Lengths
In this paper we study binary trees with choosable edge lengths, in particular rooted binary trees with the property that the two edges leading from every non-leaf to its two children are assigned integral lengths l1 and l2 with l1 + l2 = k for a constant k ∈ N. The depth of a leaf is the total length of the edges of the unique root-leaf-path. We present a generalization of the Huffman Coding t...
متن کاملLabeled binary planar trees and quasi-Lie algebras
Let H be a finitely-generated free abelian group and L(H) the graded free Lie algebra on H . There is a natural homomorphism H ⊗ L(H)→ L(H) defined by bracketing, whose kernel is denoted D(H). If H supports a non-singular symplectic form, eg H = H1(Σ), where Σ is a closed orientable surface, with symplectic basis {xi, yi}, then D(H) is, in fact, a Lie algebra. It can be identified with the Lie ...
متن کاملEdge separators for graphs of bounded genus with applications
Many divide-and-conquer algorithms on graphs are based on finding a small set of vertices or edges whose removal divides the graph roughly in half. Applications include VLSI layouts [14], Gaussian elimination Cl.51 and graph embeddings [17]. Formally, a class of graphs hasf’(n) vertex (edge) separator if every n-vertex graph in the class has a vertex (edge) cutset of sizef(n) that divides the g...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2016
ISSN: 0166-218X
DOI: 10.1016/j.dam.2014.12.004