Robust capacitated trees and networks with uniform demands

We are interested in the design of robust (or resilient) capacitated rooted Steiner networks in case of terminals with uniform demands. Formally, we are given a graph, capacity and cost functions on the edges, a root, a subset of nodes called terminals, and a bound k on the number of edge failures. We first study the problem where k = 1 and the network that we want to design must be a tree covering the root and the terminals: we give complexity results and propose models to optimize both the cost of the tree and the number of terminals disconnected from the root in the worst case of an edge failure, while respecting the capacity constraints on the edges. Second, we consider the problem of computing a minimum-cost survivable network, i.e., a network that covers the root and terminals even after the removal of any k edges, while still respecting the capacity constraints on the edges. We also consider the possibility of protecting a given number of edges. We propose three different formulations: a cut-set based formulation, a flow based one, and a bilevel one (with an attacker and a defender). We propose algorithms to solve each formulation and compare their efficiency

Multicut and integral multiflow : a survey.

We present a survey about the maximum integral multiflow and minimum multicut problems and their subproblems, such as the multiterminal cut and the unsplittable flow problems. We consider neither continuous multiflow nor minimum cost multiflow. Most of the results are very recent and some are new. We recall the dual relationship between both problems, give complexity results and algorithms, firstly in unrestricted graphs and secondly in several special graphs: trees, bipartite or planar graphs. A table summarizes the most important results

A greedy algorithm for multicut and integral multiflow in rooted trees

We present an O(min(Kn,n2)) algorithm to solve the maximum integral multiflow and minimum multicut problems in rooted trees, where K is the number of commodities and n is the number of vertices. These problems are NP-hard in undirected trees but polynomial in directed trees. In the algorithm we propose, we first use a greedy procedure to build the multiflow then we use duality properties to obtain the multicut and prove the optimality

On the use of graphs in discrete tomography

In this tutorial paper, we consider the basic image reconstruction problem which stems from discrete tomography. We derive a graph theoretical model and we explore some variations and extensions of this model. This allows us to establish connections with scheduling and timetabling applications. The complexity status of these problems is studied and we exhibit some polynomially solvable cases. We show how various classical techniques of operations research like matching, 2-SAT, network flows are applied to derive some of these result

d-extensibles de stables dans les graphes bipartis

International audienc

Effectiveness of Stuttering Modification Treatment in School-Age Children Who Stutter:A Randomized Clinical Trial

PURPOSE: This study investigated the effectiveness of the stuttering modification intervention Kinder Dürfen Stottern (KIDS) in school-age children who stutter. METHOD: Seventy-three children who stutter were included in this multicenter, two-group parallel, randomized, wait-list controlled trial with a follow-up of 12 months. Children aged 7-11 years were recruited from 34 centers for speech therapy and randomized to either the immediate-treatment group or the 3 months delayed-treatment group. KIDS was provided by 26 clinicians who followed a treatment manual. Although the primary outcome measure was the impact of stuttering (Overall Assessment of the Speaker's Experience of Stuttering-School-Age [OASES-S]), the secondary outcomes included objective and subjective data on stuttering severity. RESULTS: At 3 months postrandomization, the mean score changes of the OASES-S differed significantly between the experimental (n = 33) and control group (n = 29; p = .026). Furthermore, treatment outcomes up to 12 months were analyzed (n = 59), indicating large effects of time on the OASES-S score (p &lt; .001, partial η2= .324). This was paralleled by significant improvements in parental ratings and objective ratings (stuttering severity, frequency, and physical concomitants). CONCLUSIONS: The significant short-term treatment effects in the OASES-S are in line with the (initial) focus of KIDS on cognitive and affective aspects of stuttering. Over 12 months, these changes were maintained and accompanied by behavioral improvements. The results suggest that individual treatment with KIDS is an adequate treatment option for this age group. SUPPLEMENTAL MATERIAL: https://doi.org/10.23641/asha.24207864.</p

A tutorial on the use of graphs in discrete tomography

Starting from the basic image reconstruction problem in discrete tomography some graph theoretical models are proposed. This suggests the study of some variations and extensions of the basic problem. Applications in scheduling and timetabling are described. We exhibit polynomially solvable cases and we review the complexity status of some related problems

Bicolored Matchings in Some Classes of Graphs

We consider the problem of finding in a graph a set R of edges to be colored in red so that there are maximum matchings having some prescribed numbers of red edges. For regular bipartite graphs with n nodes on each side, we give sufficient conditions for the existence of a set R with |R| = n + 1 such that perfect matchings with k red edges exist for all k, 0 ≤ k ≤ n. Given two integers p < q we also determine the minimum cardinality of a set R of red edges such that there are perfect matchings with p red edges and with q red edges. For 3-regular bipartite graphs, we show that if p ≤ 4 there is a set R with |R| = p for which perfect matchingsMk exist with |Mk ∩R| ≤ k for all k ≤ p. For trees we design a linear time algorithm to determine a minimum set R of red edges such that there exist maximum matchings with k red edges for the largest possible number of values of k