Approximation Algorithms for Connected Maximum Cut and Related Problems

An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V, E) and the goal is to find a subset of vertices S $\subseteq$ V that maximizes the number of edges in the cut \delta(S) such that the induced graph G[S] is connected. We present the first non-trivial \Omega(1/log n) approximation algorithm for the connected maximum cut problem in general graphs using novel techniques. We then extend our algorithm to an edge weighted case and obtain a poly-logarithmic approximation algorithm. Interestingly, in stark contrast to the classical max-cut problem, we show that the connected maximum cut problem remains NP-hard even on unweighted, planar graphs. On the positive side, we obtain a polynomial time approximation scheme for the connected maximum cut problem on planar graphs and more generally on graphs with bounded genus.Comment: 17 pages, Conference version to appear in ESA 201

Fast Distributed Approximation for Max-Cut

Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their neighbors according to the underlying graph, known as the $\mathcal{LOCAL}$ or $\mathcal{CONGEST}$ models. We amend this by obtaining almost optimal algorithms for Max-Cut on a wide class of graphs in these models. In particular, for any $\epsilon > 0$, we develop randomized approximation algorithms achieving a ratio of $(1-\epsilon)$ to the optimum for Max-Cut on bipartite graphs in the $\mathcal{CONGEST}$ model, and on general graphs in the $\mathcal{LOCAL}$ model. We further present efficient deterministic algorithms, including a $1/3$-approximation for Max-Dicut in our models, thus improving the best known (randomized) ratio of $1/4$. Our algorithms make non-trivial use of the greedy approach of Buchbinder et al. (SIAM Journal on Computing, 2015) for maximizing an unconstrained (non-monotone) submodular function, which may be of independent interest

Vertex-Coloring with Star-Defects

Defective coloring is a variant of traditional vertex-coloring, according to which adjacent vertices are allowed to have the same color, as long as the monochromatic components induced by the corresponding edges have a certain structure. Due to its important applications, as for example in the bipartisation of graphs, this type of coloring has been extensively studied, mainly with respect to the size, degree, and acyclicity of the monochromatic components. In this paper we focus on defective colorings in which the monochromatic components are acyclic and have small diameter, namely, they form stars. For outerplanar graphs, we give a linear-time algorithm to decide if such a defective coloring exists with two colors and, in the positive case, to construct one. Also, we prove that an outerpath (i.e., an outerplanar graph whose weak-dual is a path) always admits such a two-coloring. Finally, we present NP-completeness results for non-planar and planar graphs of bounded degree for the cases of two and three colors

Ultrasound investigation of the fetal cerebral ventricles

Peer Reviewe

Analysis of factors influencing the ultrasonic fetal weight estimation

Objective: The aim of our study was the evaluation of sonographic fetal weight estimation taking into consideration 9 of the most important factors of influence on the precision of the estimation. Methods: We analyzed 820 singleton pregnancies from 22 to 42 weeks of gestational age. We evaluated 9 different factors that potentially influence the precision of sonographic weight estimation ( time interval between estimation and delivery, experts vs. less experienced investigator, fetal gender, gestational age, fetal weight, maternal BMI, amniotic fluid index, presentation of the fetus, location of the placenta). Finally, we compared the results of the fetal weight estimation of the fetuses with poor scanning conditions to those presenting good scanning conditions. Results: Of the 9 evaluated factors that may influence accuracy of fetal weight estimation, only a short interval between sonographic weight estimation and delivery (0-7 vs. 8-14 days) had a statistically significant impact. Conclusion: Of all known factors of influence, only a time interval of more than 7 days between estimation and delivery had a negative impact on the estimation

A Fixed-Parameter Algorithm for the Max-Cut Problem on Embedded 1-Planar Graphs

We propose a fixed-parameter tractable algorithm for the \textsc{Max-Cut} problem on embedded 1-planar graphs parameterized by the crossing number $k$ of the given embedding. A graph is called 1-planar if it can be drawn in the plane with at most one crossing per edge. Our algorithm recursively reduces a 1-planar graph to at most $3^k$ planar graphs, using edge removal and node contraction. The \textsc{Max-Cut} problem is then solved on the planar graphs using established polynomial-time algorithms. We show that a maximum cut in the given 1-planar graph can be derived from the solutions for the planar graphs. Our algorithm computes a maximum cut in an embedded 1-planar graph with $n$ nodes and $k$ edge crossings in time $\mathcal{O}(3^k \cdot n^{3/2} \log n)$.Comment: conference version from IWOCA 201

Bostonia: The Boston University Alumni Magazine. Volume 10

Founded in 1900, Bostonia magazine is Boston University's main alumni publication, which covers alumni and student life, as well as university activities, events, and programs

Mephedrone pharmacokinetics after intravenous and oral administration in rats: relation to pharmacodynamics

Fe d'errates disponible a: http://​dx.​doi.​org/​10.​1007/​s00213-013-3283-6Rationale Mephedrone (4-methylmethcathinone) is a still poorly known drug of abuse, alternative to ecstasy or cocaine. Objective The major aims were to investigate the pharmacokineticsa and locomotor activity of mephedrone in rats and provide a pharmacokinetic/pharmacodynamic model. Methods Mephedrone was administered to male Sprague-Dawley rats intravenously (10 mg/kg) and orally (30 and 60 mg/kg). Plasma concentrations and metabolites were characterized using LC/MS and LC-MS/MS fragmentation patterns. Locomotor activity was monitored for 180-240 min. Results Mephedrone plasma concentrations after i.v. administration fit a two-compartment model (α=10.23 h−1, β=1.86 h−1). After oral administration, peak mephedrone concentrations were achieved between 0.5 and 1 h and declined to undetectable levels at 9 h. The absolute bioavailability of mephedrone was about 10 % and the percentage of mephedrone protein binding was 21.59±3.67%. We have identified five phase I metabolites in rat blood after oral administration. The relationship between brain levels and free plasma concentration was 1.85±0.08. Mephedrone induced a dose-dependent increase in locomotor activity, which lasted up to 2 h. The pharmacokinetic-pharmacodynamic model successfully describes the relationship between mephedrone plasma concentrations and its psychostimulant effect. Conclusions We suggest a very important first-pass effect for mephedrone after oral administration and an easy access to the central nervous system. The model described might be useful in the estimation and prediction of the onset, magnitude,and time course of mephedrone pharmacodynamics as well as to design new animal models of mephedrone addiction and toxicity