Courcelle's Theorem - A Game-Theoretic Approach

Courcelle's Theorem states that every problem definable in Monadic Second-Order logic can be solved in linear time on structures of bounded treewidth, for example, by constructing a tree automaton that recognizes or rejects a tree decomposition of the structure. Existing, optimized software like the MONA tool can be used to build the corresponding tree automata, which for bounded treewidth are of constant size. Unfortunately, the constants involved can become extremely large - every quantifier alternation requires a power set construction for the automaton. Here, the required space can become a problem in practical applications. In this paper, we present a novel, direct approach based on model checking games, which avoids the expensive power set construction. Experiments with an implementation are promising, and we can solve problems on graphs where the automata-theoretic approach fails in practice.Comment: submitte

Analysis and simulation of nutrient retention and management for a lowland river-lake system

International audienceIn the context of the European Water Framework Directive, we studied the possible impact of reduced emissions on phosphorus and nitrogen concentrations in a lowland river-lake system (Havel River, Germany). As a prerequisite, we quantified the retention of nutrients in the river from mass balances and deduced its seasonal variation. We detected that about 30% of the total nitrogen input is retained within the surveyed river section. In contrast, phosphorus release from sediments was shown to cause a considerable increase in present P concentrations. Average net phosphorus release rates of about 20 mg P m?2 d?1 in late summer were estimated for the Havel Lakes. Based on the observed patterns of N retention and P release we parametrized a newly developed water quality simulation program (TRAM), which allows alternative model approaches of different complexity to be implemented and tested. To account for the future trend of internal P loading, the phosphorus excess in lake sediments was estimated from core samples and included in the model as a state variable. For analyzing scenarios of reduced nutrient emissisions, the water quality simulation program was linked to mesoscale hydrological catchment models for the first time. From scenario simulations we conclude that internal P loading is likely to counteract efforts of emission control for decades. Even by significant reductions in external P loads, a persistent phosphorus limitation of primary production can hardly be established in the analyzed time frame of 13 years. Though in the short run a continued reduction in nitrogen loads appears to be the more promising approach of eutrophication management, we recommend enhanced efforts to diminish both N and P emissions

Model-based analysis of nutrient retention and management for a lowland river

International audienceIn the context of the European Water Framework Directive options for improving the water quality of the lowland river Havel (Germany) were assessed. The lower section of this river is actually a polytrophic river-lake system suffering from high external nutrient loading and exhibiting significant in-river turnover. In order to gain a better understanding of present conditions and to allow integrated scenarios of nutrient management to be evaluated the catchment models SWIM and ArcEGMO-Urban were coupled with a simple, newly developed nutrient TRAnsport Model (TraM). Using the TraM model, the retention of nitrogen and phosphorus in a 55 km reach of the Lower Havel River was quantified and its temporal variation was analyzed. It was examined that about 30% of the external nitrogen input to the Lower Havel is retained within the surveyed river section. A comparison of simulation results generated with and without consideration of phosphorus retention/release revealed that summer TP concentrations are currently increased by 100?200% due to internal loading. Net phosphorus release rates of about 20 mg P m?2 d-1 in late summer were estimated for the Havel lakes. Scenario simulations with lowered external nutrient inputs revealed that persistent phosphorus limitation of primary production cannot be established within the next decade. It was shown that a further reduction in nitrogen concentrations requires emissions to be reduced in all inflows. Though the TraM model needs further extension it proved to be appropriate for conducting integrated catchment and river modeling

A high-throughput approach to the culture-based estimation of plasmid transfer rates

Horizontal gene transfer is an essential component of bacterial evolution. Quantitative information on transfer rates is particularly useful to better understand and possibly predict the spread of antimicrobial resistance. A variety of methods has been proposed to estimate the rates of plasmid-mediated gene transfer all of which require substantial labor input or financial resources. A cheap but reliable method with high-throughput capabilities is yet to be developed in order to better capture the variability of plasmid transfer rates, e.g. among strains or in response to environmental cues. We explored a new approach to the culture-based estimation of plasmid transfer rates in liquid media allowing for a large number of parallel experiments. It deviates from established approaches in the fact that it exploits data on the absence/presence of transconjugant cells in the wells of a well plate observed over time. Specifically, the binary observations are compared to the probability of transconjugant detection as predicted by a dynamic model. The bulk transfer rate is found as the best-fit value of a designated model parameter. The feasibility of the approach is demonstrated on mating experiments where the RP4 plasmid is transfered from Serratia marcescens to several Escherichia coil recipients. The methods uncertainty is explored via split sampling and virtual experiments.Peer reviewe

Approximation hardness of deadline-TSP reoptimization

AbstractGiven an instance of an optimization problem together with an optimal solution, we consider the scenario in which this instance is modified locally. In graph problems, e.g., a singular edge might be removed or added, or an edge weight might be varied, etc. For a problem U and such a local modification operation, let lm-U (local-modification-U) denote the resulting problem. The question is whether it is possible to exploit the additional knowledge of an optimal solution to the original instance or not, i.e.,whether lm-U is computationally more tractable than U. While positive examples are known e.g. for metric TSP, we give some negative examples here: Metric TSP with deadlines (time windows), if a single deadline or the cost of a single edge is modified, exhibits the same lower bounds on the approximability in these local-modification versions as those currently known for the original problem

Finding the Minimum-Weight k-Path

Given a weighted $n$-vertex graph $G$ with integer edge-weights taken from a range $[-M,M]$, we show that the minimum-weight simple path visiting $k$ vertices can be found in time \tilde{O}(2^k \poly(k) M n^\omega) = O^*(2^k M). If the weights are reals in $[1,M]$, we provide a $(1+\varepsilon)$-approximation which has a running time of \tilde{O}(2^k \poly(k) n^\omega(\log\log M + 1/\varepsilon)). For the more general problem of $k$-tree, in which we wish to find a minimum-weight copy of a $k$-node tree $T$ in a given weighted graph $G$, under the same restrictions on edge weights respectively, we give an exact solution of running time \tilde{O}(2^k \poly(k) M n^3) and a $(1+\varepsilon)$-approximate solution of running time \tilde{O}(2^k \poly(k) n^3(\log\log M + 1/\varepsilon)). All of the above algorithms are randomized with a polynomially-small error probability.Comment: To appear at WADS 201