Max flow vitality in general and stst-planar graphs

The \emph{vitality} of an arc/node of a graph with respect to the maximum flow between two fixed nodes $s$ and $t$ is defined as the reduction of the maximum flow caused by the removal of that arc/node. In this paper we address the issue of determining the vitality of arcs and/or nodes for the maximum flow problem. We show how to compute the vitality of all arcs in a general undirected graph by solving only $2(n-1)$ max flow instances and, In $st$-planar graphs (directed or undirected) we show how to compute the vitality of all arcs and all nodes in $O(n)$ worst-case time. Moreover, after determining the vitality of arcs and/or nodes, and given a planar embedding of the graph, we can determine the vitality of a `contiguous' set of arcs/nodes in time proportional to the size of the set.Comment: 12 pages, 3 figure

On-line algorithms for polynomially solvable satisfiability problems

AbstractGiven a propositional Horn formula, we show how to maintain on-line information about its satisfiability during the insertion of new clauses. A data structure is presented which answers each satisfiability question in O(1) time and inserts a new clause of length q in O(q) amortized time. This significantly outperforms previously known solutions of the same problem. This result is extended also to a particular class of non-Horn formulae already considered in the literature, for which the space bound is improved. Other operations are considered, such as testing whether a given hypothesis is consistent with a satisfying interpretation of the given formula and determining a truth assignment which satisfies a given formula. The on-line time and space complexity of these operations is also analyzed

Max-flow vitality in undirected unweighted planar graphs

We show a fast algorithm for determining the set of relevant edges in a planar undirected unweighted graph with respect to the maximum flow. This is a special case of the \emph{max flow vitality} problem, that has been efficiently solved for general undirected graphs and $st$-planar graphs. The \emph{vitality} of an edge of a graph with respect to the maximum flow between two fixed vertices $s$ and $t$ is defined as the reduction of the maximum flow caused by the removal of that edge. In this paper we show that the set of edges having vitality greater than zero in a planar undirected unweighted graph with $n$ vertices, can be found in $O(n \log n)$ worst-case time and $O(n)$ space.Comment: 9 pages, 4 figure

Identification of Soft Tissue-Mimicking Materials and Application in the Characterization of Sensors for Lung Sounds

Early diagnosis of pulmonary implications is fundamental for the treatment of several diseases, such as idiopathic pulmonary fibrosis, rheumatoid arthritis, connective tissue diseases and interstitial pneumonia secondary to COVID-19 among the many. Recent studies prove that a wide class of pulmonary diseases can be early detected by auscultation and suitably developed algorithms for the analysis of lung sounds. Indeed, the technical characteristics of sensors have an impact on the quality of the acquired lung sounds. The availability of a fair and quantitative approach to sensors’ comparison is a prerequisite for the development of new diagnostic tools. In this work the problem of a fair comparison between sensors for lung sounds is decoupled into two steps. The first part of this study is devoted to the identification of a synthetic material capable of mimicking the acoustic behavior of human soft tissues; this material is then adopted as a reference. In the second part, the standard skin is exploited to quantitatively compare several types of sensors in terms of noise floor and sensitivity. The proposed methodology leads to reproducible results and allows to consider sensors of different nature, e.g. laryngophone, electret microphone, digital MEMS microphone, mechanical phonendoscope and electronic phonendoscope. Finally, the experimental results are interpreted under the new perspective of equivalent sensitivity and some important guidelines for the design of new sensors are provided. These guidelines could represent the starting point for improving the devices for acquisition of lung sounds

Simple Programs on Strings and Their Decision Problems

Classes of simple programs operating on srings are considered. Their power as acceptors and their power as generation devices are compared and consequences on upper bounds and lower bounds for several decision problems are derived. It is shown that even for such a small class of programs some problems are undecidable

Reductions that preserve approximability

We present in this paper a tour d'horizon of the most important approximation-preserving reductions that have strongly influenced research about structure in approximability classes.ou