We provide first-time fixed-parameter tractability results for the NPhard problems Maximum Full-Degree Spanning Tree and MinimumVertex Feedback Edge Set. These problems are dual to each other: In Maximum Full-Degree Spanning Tree, the task is to find a spanning tree for a given graph that maximizes the number of vertices that preserve their degree. For Minimum-Vertex Feedback Edge Set, the task...

purpose: having a clinical information system is a good solution for monitoring medical problems. this system is designed to improve the speed and accuracy of data management. the goal is to replace medical records with a clinical information system to support storing, processing and distributing data in all the sections of a healthcare center. the purpose of this research was to determine the ...

We show that the geodetic number of proper interval graphs can be computed in polynomial time. This problem is NP-hard on chordal graphs and on bipartite weakly chordal graphs. Only an upper bound on the geodetic number of proper interval graphs has been known prior to

In the Tree Augmentation Problem (TAP) the goal is to augment a tree T by a minimum size edge set F from a given edge set E such that T ∪F is 2-edge-connected. The best approximation ratio known for TAP is 1.5. In the more general Weighted TAP problem, F should be of minimum weight. Weighted TAP admits several 2-approximation algorithms w.r.t. to the standard cut LP-relaxation, but for all of t...

The Hop-constrained Minimum Spanning Tree Problem (HMST) is defined as follows: given a graph G = (V,E) with node set V = {0, 1, . . . , n} and edge set E as well as a cost ce associated with each edge e of E and a natural number H , we wish to find a spanning tree T of the graph with minimum total cost and such that the unique path from a specified root node, node 0, to any other node has no m...

We consider the following problem: from a given set of gene families trees on a set of genomes, find a first speciation, that splits these genomes into two subsets, that minimizes the number of gene duplications that happened before this speciation. We call this problem the Minimum Duplication Bipartition Problem. Using a generalization of the Minimum Edge-Cut Problem, known as Submodular Funct...

We analyze the simple greedy algorithm that iteratively removes the endpoints of a maximum-degree edge in a graph, where the degree of an edge is the sum of the degrees of its endpoints. This algorithm provides a 2-approximation to the minimum edge dominating set and minimum maximal matching problems. We refine its analysis and give an expression of the approximation ratio that is strictly less...

Let G = (V, E) be a connected graph. Let G = (V, E) be a connected graph. An edge set F ⊂ E is said to be a k-restricted edge cut, if G− F is disconnected and every component of G− F has at least k vertices. The k-restricted edge connectivity of G, denoted by λk(G), is the cardinality of a minimum k-restricted edge cut of G. A graph G is λk-connected, if G contains a k-restricted edge cut. A λk...

Edge monitoring is a simple and effective mechanism for the security of wireless sensor networks. The idea is to award specific roles (monitors) to some sensor nodes of the network. A node v monitors an edge e if both extremities together with v form a triangle in the graph. Given an edge colored graph G = (V,E, c), the color c(e) is a positive integer representing the number of monitors needed...