For a non-negative integer $$\ell $$ , the -leaf power of tree T is simple graph G on leaves such that two vertices are adjacent in if and only their distance at most . We provide polynomial kernel for problem deciding whether we can delete k to make an input 3-leaf some tree. More specifically, present polynomial-time algorithm instance (G, k) output equivalent $$(G',k')$$ $$k'\leqslant k$$ $$...

We study in this paper the problem of finding in a graph a subset of k edges whose deletion causes the largest increase in the weight of a minimum spanning tree. We propose for this problem an explicit enumeration algorithm whose complexity, when compared to the current best algorithm, is better for general k but very slightly worse for fixed k. More interestingly, unlike in the previous algori...

In this paper we study embeddings of complete ternary trees in a 2-D lattice. Suppose we are given an n-node complete ternary tree Tn with height h. We can construct an embedding of Th on a 2-D lattice L so that every node in Th corresponds to a vertex in L, and every edge in Th corresponds to a horizontal or vertical path in the lattice. We provide a better upper bound on the area requirement ...

A degree sequence for a graph is a list of positive integers, one for every vertex, where each integer corresponds to the number of neighbors of that vertex. It is possible to create sequences that have no corresponding graphs, as well as sequences that correspond to multiple distinct (i.e., non-isomorphic) graphs. A graph that corresponds to a given degree sequence is called a realization of t...

Let X 0 be a nonnegative integer-valued random variable and let an independent copy of X 0 be assigned to each leaf of a binary tree of depth k. If X 0 and X0′ are adjacent leaves let X 1 = (X 0 − 1 ) + + (X0′ − 1 ) + be assigned to the parent node. In general, if X j and Xj′ , are assigned to adjacent nodes at level j = 0 , ... , k − 1, then X j and Xj′ are, in turn, independent and the value ...

A competence set is a collection of skills used to solve a problem. Based on deduction graph concepts, this paper proposes a method of finding an optimal process so as to expand a decision maker’s competence set to enable him to solve his problem confidently. Using the concept of minimum spanning tree, Yu and Zhang addressed the problem of the optimal expansion of competence sets. In contrast, ...

This is the ongoing BibT E X bibliography. Unlike the original publication 63], additions do not have annotations. They are located at the beginning of the bib le, and the most recent additions were References 1] J. Acevedo and E.N. Pistikopoulos. A hybrid parametric/stochastic programming approach for mixed-integer linear problems under uncertainty. The problem is to nd a minimum cost spanning...

When dealing with infinite-state systems, Regular Tree Model Checking approaches may have some difficulties to represent infinite sets of data. We propose Lattice Tree Automata, an extended version of tree automata to represent complex data domains and their related operations in an efficient manner. Moreover, we introduce a new completionbased algorithm for computing the possibly infinite set ...

Multiple constant multiplication scheme is the most effective common sub expression sharing technique which is used for implementing the transposed FIR filters. Ripple carry operation allows adder tree to minimize hardware cost, unfortunately it detriment timing and gives low speed operation. To outperform this high speed adder is proposed and analyzed for real time speech signal applications. ...