We consider the problem of augmenting a graph with n vertices embedded in a metric space, by inserting one additional edge in order to minimize the diameter of the resulting graph. We present an exact algorithm for the cases when the input graph is a path that runs in O(n log n) time. We also present an algorithm that computes a (1 + ε)approximation in O(n+1/ε) time for paths in R, where d is a...

In the Intervalizing Colored Graphs problem, one must decide for a given graph G = (V,E) with a proper vertex coloring of G whether G is the subgraph of a properly colored interval graph. For the case that the number of colors k is xed, we give an exact algorithm that uses O∗(2n/log (n)) time for all > 0. We also give an O∗(2n) algorithm for the case that the number of colors k is not xed.

this text carries out some ideas about exact and p− exact sequences of transformationsemigroups. some theorems like the short five lemma (lemma 1.3 and lemma 2.3) are valid here as inexact sequences of r − modules.

In the last lecture, two terms Average Delay and RMS Delay Spread were defined as below () () ∫ ∫ ∞ ∞ Φ Φ = 0 0 τ τ τ τ τ µ τ d d (1) () () () ∫ ∫ ∞ ∞ Φ Φ − = 0 0 2 τ τ τ τ µ τ σ τ τ d d c c (2) If the power density is discrete like Figure 1, the Average Delay and RMS Delay Spread for the multipath profile could be written in the following way: () () ∑ ∑ = k k k k k p p τ τ τ τ (3) () 2 2 τ τ σ...

BACKGROUND Shotgun wound classification systems attempt to predict the need for surgical intervention based on the size of wounds, pellet spread, or distance from the weapon rather than clinical findings. METHODS A 5-year retrospective review of patients sustaining a thoracoabdominal shotgun wound was performed. Factors believed to be associated with the need for surgical intervention were ex...

Evaluating the Schoeffler criterion for Sallen-Key filters leads to expressions having two degrees of freedom and prohibitive complexity. Such expressions are normally solved only after making approximations. We show, using the lowpass filter as an example, how the two degrees of freedom can be separated by a simple non-linear coordinate transform. Exact design equations for the minimum-sensiti...

BACKGROUND If the epidural spread of contrast medium can be well correlated with the spread of local anesthetics, epidurography can predict the dermatomal distribution of the anesthetic block. The authors evaluated the relation between radiographic and analgesic spread. METHODS An epidural catheter was inserted in 90 patients, and predicted catheter tip position was recorded. The analgesic ar...

Hypersensitive response (HR)-conferred resistance to viral infection restricts the virus spread and is accompanied by the induction of cell death, manifested as the formation of necrotic lesions. While it is known that salicylic acid is the key component in the orchestration of the events restricting viral spread in HR, the exact function of the cell death in resistance is still unknown. We sho...

Let G be an unweighted graph on n vertices. We show that an embedding of the shortest path metric of G into the line with minimum distortion can be found in time 5. This is the first algorithm breaking the trivial n!-barrier.

Realization of efficient Universal Logic Modules (ULMs) is a challenging topic in circuit design. The goal is to find a representation that allows to realize as many Boolean functions as possible by permutation of inputs or phase assignment. In this paper an exact algorithm for finding a minimal circuit for a ULM is presented. The approach is parametrisized in several ways, e.g. the user can de...