Minimum Degree up to Local Complementation: Bounds, Parameterized Complexity, and Exact Algorithms

The local minimum degree of a graph is the minimum degree that can be reached by means of local complementation. For any n, there exist graphs of order n which have a local minimum degree at least 0.189n, or at least 0.110n when restricted to bipartite graphs. Regarding the upper bound, we show that for any graph of order n, its local minimum degree is at most 3n/8+o(n) and n/4+o(n) for bipartite graphs, improving the known n/2 upper bound. We also prove that the local minimum degree is smaller than half of the vertex cover number (up to a logarithmic term). The local minimum degree problem is NP-Complete and hard to approximate. We show that this problem, even when restricted to bipartite graphs, is in W[2] and FPT-equivalent to the EvenSet problem, which W[1]-hardness is a long standing open question. Finally, we show that the local minimum degree is computed by a O*(1.938^n)-algorithm, and a O*(1.466^n)-algorithm for the bipartite graphs

The Parameterized Complexity of Domination-type Problems and Application to Linear Codes

We study the parameterized complexity of domination-type problems. (sigma,rho)-domination is a general and unifying framework introduced by Telle: a set D of vertices of a graph G is (sigma,rho)-dominating if for any v in D, |N(v)\cap D| in sigma and for any $v\notin D, |N(v)\cap D| in rho. We mainly show that for any sigma and rho the problem of (sigma,rho)-domination is W[2] when parameterized by the size of the dominating set. This general statement is optimal in the sense that several particular instances of (sigma,rho)-domination are W[2]-complete (e.g. Dominating Set). We also prove that (sigma,rho)-domination is W[2] for the dual parameterization, i.e. when parameterized by the size of the dominated set. We extend this result to a class of domination-type problems which do not fall into the (sigma,rho)-domination framework, including Connected Dominating Set. We also consider problems of coding theory which are related to domination-type problems with parity constraints. In particular, we prove that the problem of the minimal distance of a linear code over Fq is W[2] for both standard and dual parameterizations, and W[1]-hard for the dual parameterization. To prove W[2]-membership of the domination-type problems we extend the Turing-way to parameterized complexity by introducing a new kind of non deterministic Turing machine with the ability to perform `blind' transitions, i.e. transitions which do not depend on the content of the tapes. We prove that the corresponding problem Short Blind Multi-Tape Non-Deterministic Turing Machine is W[2]-complete. We believe that this new machine can be used to prove W[2]-membership of other problems, not necessarily related to dominationComment: 19 pages, 2 figure

Déterminants de la structure spatio-temporelle de l’assemblage piscicole d’une grande rivière méditerranéenne régulée : stochasticité environnementale vs régulation du débit

International audienceSustainably managing water resources in Mediterranean regions is a major challenge for the coming years. The Durance River (south-eastern France) is a highly regulated river whose water serves for hydropower production, agricultural, recreational, industrial, and domestic purposes. Powerplant managers strive to mitigate the deleterious impacts of flow alterations by experimenting with different levels of minimum flow increases in by-passed sections, and monitoring relevant physical and biological parameters. Using fish data collected during 1991-2010 on control and regulated sites along the Medium-Durance, we investigated the relationships between changes in fish assemblage structure and key environmental variables (flow, temperature, and physical habitat) that are partly affected by the operation of hydropower plants. Analyses showed that assemblages through time were alternatively dominated by a subset of species, and that this structure mostly depended on ‘extreme’ events, such as major floods. Functional responses were consistent with expectations, with e.g., rheophilic and lithophilic species being favoured by high flows during the spawning season. Our multiple site and year approach helped us better understand the functioning of fish communities in a large regulated system.La gestion durable des ressources en eau en région méditerranéenne est un défi majeur pour les années à venir. La Durance est une rivière fortement régulée utilisée pour la production hydroélectrique, mais aussi pour des usages agricoles, récréatifs, industriels et domestiques. Les gestionnaires d’ouvrages hydroélectriques s’efforcent d’atténuer les impacts des altérations hydrologiques en expérimentant différents niveaux de débit réservé dans les sections court-circuitées, associés à des suivis d’indicateurs physiques et biologiques. Sur la base d’échantillonnages piscicoles réalisés entre 1991 et 2010 sur des sites témoin ainsi que sur des sites soumis à régulation, nous avons analysé les relations entre la variabilité de la structure de l’assemblage piscicole et des variables environnementales clés (débit, température, habitat physique) partiellement dépendantes du fonctionnement des ouvrages. Les analyses ont montré que l’assemblage était alternativement dominé par des sous-ensembles d’espèces, et que cette structure résultait principalement d’événements hydrologiques majeurs (crues). Les réponses fonctionnelles étaient pertinentes, avec par exemple une augmentation des proportions d’individus rhéophiles et lithophiles lorsque les débits sont élevés durant la période de reproduction. Cette approche multi-sites et pluriannuelle apporte un éclairage sur le fonctionnement de l’assemblage piscicole d’une grande rivière soumise à régulatio

Climate and land-use changes affecting river sediment and brown trout in alpine countries--a review

BACKGROUND, AIM, AND SCOPE: Catch decline of freshwater fish has been recorded in several countries. Among the possible causes, habitat change is discussed. This article focuses on potentially increased levels of fine sediments going to rivers and their effects on gravel-spawning brown trout. Indications of increased erosion rates are evident from land-use change in agriculture, changes in forest management practices, and from climate change. The latter induces an increase in air and river water temperatures, reduction in permafrost, changes in snow dynamics and an increase in heavy rain events. As a result, an increase in river sediment is likely. Suspended sediment may affect fish health and behaviour directly. Furthermore, sediment loads may clog gravel beds impeding fish such as brown trout from spawning and reducing recruitment rates. To assess the potential impact on fine sediments, knowledge of brown trout reproductive needs and the effects of sediment on brown trout health were evaluated. APPROACH: We critically reviewed the literature and included results from ongoing studies to answer the following questions, focusing on recent decades and rivers in alpine countries. Have climate change and land-use change increased erosion and sediment loads in rivers? Do we have indications of an increase in riverbed clogging? Are there indications of direct or indirect effects on brown trout from increased suspended sediment concentrations in rivers or from an increase in riverbed clogging? RESULTS: Rising air temperatures have led to more intensive precipitation in winter months, earlier snow melt in spring, and rising snow lines and hence to increased erosion. Intensification of land use has supported erosion in lowland and pre-alpine areas in the second half of the twentieth century. In the Alps, however, reforestation of abandoned land at high altitudes might reduce the erosion risk while intensification on the lower, more easily accessible slopes increases erosion risk. Data from laboratory experiments show that suspended sediments affect the health and behaviour of fish when available in high amounts. Point measurements in large rivers indicate no common lethal threat and suspended sediment is rarely measured continuously in small rivers. However, effects on fish can be expected under environmentally relevant conditions. River bed clogging impairs the reproductive performance of gravel-spawning fish. Discussion: Overall, higher erosion and increased levels of fine sediment going into rivers are expected in future. Additionally, sediment loads in rivers are suspected to have considerably impaired gravel bed structure and brown trout spawning is impeded. Timing of discharge is put forward and is now more likely to affect brown trout spawning than in previous decades. Conclusions: Reports on riverbed clogging from changes in erosion and fine sediment deposition patterns, caused by climate change and land-use change are rare. This review identifies both a risk of increases in climate erosive forces and fine sediment loads in rivers of alpine countries. Increased river discharge and sediment loads in winter and early spring could be especially harmful for brown trout reproduction and development of young life stages. Recently published studies indicate a decline in trout reproduction from riverbed clogging in many rivers in lowlands and alpine regions. However, the multitude of factors in natural complex ecosystems makes it difficult to address a single causative factor. Recommendations and perspectives: Further investigations into the consequences of climate change and land-use change on river systems are needed. Small rivers, of high importance for the recruitment of gravel-spawning fish, are often neglected. Studies on river bed clogging are rare and the few existing studies are not comparable. Thus, there is a strong need for the development of methods to assess sediment input and river bed clogging. As well, studies on the effects to fish from suspended sediments and consequences of gravel beds clogging under natural conditions are urgently needed

Contextuality in multipartie pseudo-telepathy graph games

International audienceAnalyzing pseudo-telepathy graph games, we propose a way to build contextuality scenarios exhibiting the quantum supremacy using graph states. We consider the combinatorial structures generating equivalent scenarios. We investigate which scenarios are more multipartite and show that there exist graphs generating scenarios with a linear multipartiteness width

Improved algorithms for k-domination and total k-domination in proper interval graphs

Given a positive integer k, a k-dominating set in a graph G is a set of vertices such that every vertex not in the set has at least k neighbors in the set. A total k-dominating set, also known as a k-tuple total dominating set, is a set of vertices such that every vertex of the graph has at least k neighbors in the set. The problems of finding the minimum size of a k-dominating, resp. total k-dominating set, in a given graph, are referred to as k-domination, resp. total k-domination. These generalizations of the classical domination and total domination problems are known to be NP-hard in the class of chordal graphs, and, more specifically, even in the classes of split graphs (both problems) and undirected path graphs (in the case of total k-domination). On the other hand, it follows from recent work by Kang et al. (2017) that these two families of problems are solvable in time O(|V(G)|6k+4) in the class of interval graphs. In this work, we develop faster algorithms for k-domination and total k-domination in the class of proper interval graphs. The algorithms run in time O(|V(G)|3k) for each fixed k≥1 and are also applicable to the weighted case.Fil: Chiarelli, Nina. University of Primorska; EsloveniaFil: Hartinger, Tatiana Romina. University of Primorska; EsloveniaFil: Leoni, Valeria Alejandra. Universidad Nacional de Rosario; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaFil: Lopez Pujato, María Inés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario; Argentina. Ministerio de Ciencia. Tecnología e Innovación Productiva. Agencia Nacional de Promoción Científica y Tecnológica; ArgentinaFil: Milanič, Martin. University of Primorska; Esloveni

Impacts of global changes and extreme hydroclimatic events on macroinvertebrate community structures in the French Rhône River

We assessed the temporal changes in and the relationships between the structures of the macroinvertebrate communities and the environmental conditions of the French Rhône River (the river from Lake Geneva to the Mediterranean Sea) over the last 20 years (1985–2004). Multisite environmental and biological datasets were analysed using multiple CO-inertia analysis (MCOA) and Procrustean analysis. Changes in environmental conditions were mainly marked by an improvement in water quality between 1985 and 1991 and by an increase in water temperature from 1985 onwards due to climate change. Improvement in water quality seemed to delay changes in community structures under global warming. We then observed trends in community structures coupled with high temperatures and a decrease in oxygen content. Interestingly, we observed both gradual changes and rapid switches in community states. These shifts seemed coupled to extreme hydroclimatic events (i.e. pulse disturbances). Floods and the 2003 heatwave enhanced the development of eurytolerant and invasive taxa which were probably able to take advantage of gradual warming environmental conditions. Despite various site-specific “press” constraints (e.g. hydropower schemes, nuclear power plants), similar changes in community structures were observed along the French Rhône River. Such consistency in temporal processes at large geographical scales underlined the strength of hydroclimatic constraints on community dynamics compared to specific local disturbances. Finally, community structures did not show any sign of recovery, and their relative sensitivities to extreme hydroclimatic events seemed to increase with time. Thus, our results suggest that global changes may reduce the resilience of current community states