Linear-Space Approximate Distance Oracles for Planar, Bounded-Genus, and Minor-Free Graphs

A (1 + eps)-approximate distance oracle for a graph is a data structure that supports approximate point-to-point shortest-path-distance queries. The most relevant measures for a distance-oracle construction are: space, query time, and preprocessing time. There are strong distance-oracle constructions known for planar graphs (Thorup, JACM'04) and, subsequently, minor-excluded graphs (Abraham and Gavoille, PODC'06). However, these require Omega(eps^{-1} n lg n) space for n-node graphs. We argue that a very low space requirement is essential. Since modern computer architectures involve hierarchical memory (caches, primary memory, secondary memory), a high memory requirement in effect may greatly increase the actual running time. Moreover, we would like data structures that can be deployed on small mobile devices, such as handhelds, which have relatively small primary memory. In this paper, for planar graphs, bounded-genus graphs, and minor-excluded graphs we give distance-oracle constructions that require only O(n) space. The big O hides only a fixed constant, independent of \epsilon and independent of genus or size of an excluded minor. The preprocessing times for our distance oracle are also faster than those for the previously known constructions. For planar graphs, the preprocessing time is O(n lg^2 n). However, our constructions have slower query times. For planar graphs, the query time is O(eps^{-2} lg^2 n). For our linear-space results, we can in fact ensure, for any delta > 0, that the space required is only 1 + delta times the space required just to represent the graph itself

Fast Dynamic Graph Algorithms for Parameterized Problems

Fully dynamic graph is a data structure that (1) supports edge insertions and deletions and (2) answers problem specific queries. The time complexity of (1) and (2) are referred to as the update time and the query time respectively. There are many researches on dynamic graphs whose update time and query time are $o(|G|)$, that is, sublinear in the graph size. However, almost all such researches are for problems in P. In this paper, we investigate dynamic graphs for NP-hard problems exploiting the notion of fixed parameter tractability (FPT). We give dynamic graphs for Vertex Cover and Cluster Vertex Deletion parameterized by the solution size $k$. These dynamic graphs achieve almost the best possible update time $O(\mathrm{poly}(k)\log n)$ and the query time $O(f(\mathrm{poly}(k),k))$, where $f(n,k)$ is the time complexity of any static graph algorithm for the problems. We obtain these results by dynamically maintaining an approximate solution which can be used to construct a small problem kernel. Exploiting the dynamic graph for Cluster Vertex Deletion, as a corollary, we obtain a quasilinear-time (polynomial) kernelization algorithm for Cluster Vertex Deletion. Until now, only quadratic time kernelization algorithms are known for this problem. We also give a dynamic graph for Chromatic Number parameterized by the solution size of Cluster Vertex Deletion, and a dynamic graph for bounded-degree Feedback Vertex Set parameterized by the solution size. Assuming the parameter is a constant, each dynamic graph can be updated in $O(\log n)$ time and can compute a solution in $O(1)$ time. These results are obtained by another approach.Comment: SWAT 2014 to appea

Development and critical evaluation of a generic 2-D agro-hydrological model (SMCR_N) for the responses of crop yield and nitrogen composition to nitrogen fertilizer

Models play an important role in optimizing fertilizer use in agriculture to maintain sustainable crop production and to minimize the risk to the environment. In this study, we present a new Simulation Model for Crop Response to Nitrogen fertilizer (SMCR_N). The SMCR_N model, based on the recently developed model EU-Rotate_N for the N-economies of a wide range of crops and cropping systems, includes new modules for the estimation of N in the roots and an associated treatment of the recovery of soil mineral N by crops, for the reduction of growth rates by excessive fertilizer-N, and for the N mineralization from soil organic matter. The validity of the model was tested against the results from 32 multi-level fertilizer experiments on 16 different crop species. For this exercise none of the coefficients or parameters in the model was adjusted to improve the agreement between measurement and simulation. Over the practical range of fertilizer-N levels model predictions were, with few exceptions, in good agreement with measurements of crop dry weight (excluding fibrous roots) and its %N. The model considered that the entire reduction of soil inorganic N during growth was due to the sum of nitrate leaching, retention of N in fibrous roots and N uptake by the rest of the plant. The good agreement between the measured and simulated uptakes suggests that in this arable soil, losses of N from other soil processes were small. At high levels of fertilizer-N yields were dominated by the negative osmotic effect of fertilizer-N and model predictions for some crops were poor. However, the predictions were significantly improved by using a different value for the coefficient defining the osmotic effect for saline sensitive crops. The developed model SMCR_N uses generally readily available inputs, and is more mechanistic than most agronomic models and thus has the potential to be used as a tool for optimizing fertilizer practice

Electric routing and concurrent flow cutting

We investigate an oblivious routing scheme, amenable to distributed computation and resilient to graph changes, based on electrical flow. Our main technical contribution is a new rounding method which we use to obtain a bound on the L1->L1 operator norm of the inverse graph Laplacian. We show how this norm reflects both latency and congestion of electric routing.Comment: 21 pages, 0 figures. To be published in Springer LNCS Book No. 5878, Proceedings of The 20th International Symposium on Algorithms and Computation (ISAAC'09

Catch Crops in Organic Farming Systems without Livestock Husbandry - Model Simulations

During the last years, an increasing number of stockless farms in Europe converted to organic farming practice without re-establishing a livestock. Due to the lack of animal manure as a nutrient input, the relocation and the external input of nutrients is limited in those organic cropping systems. The introduction of a one-year green manure fallow in a 4-year crop rotation, including clover-grass mixtures as a green manure crop is the classical strategy to solve at least some of the problems related to the missing livestock. The development of new crop rotations, including an extended use of catch crops and annual green manure (legumes) may be another possibility avoiding the economical loss during the fallow year. Modelling of the C and N turnover in the soil-plant-atmosphere system using the soil-plant-atmosphere model DAISY is one of the tools used for the development of new organic crop rotations. In this paper, we will present simulations based on a field experiment with incorporation of different catch crops. An important factor for the development of new crop rotations for stockless organic farming systems is the expected N mineralisation and immobilisation after incorporation of the plant materials. Therefore, special emphasise will be put on the simulation of N-mineralisation/-immobilisation and of soil microbial biomass N. Furthermore, particulate organic matter C and N as an indicator of remaining plant material under decomposition will be investigated

Sparse Fault-Tolerant BFS Trees

This paper addresses the problem of designing a sparse {\em fault-tolerant} BFS tree, or {\em FT-BFS tree} for short, namely, a sparse subgraph $T$ of the given network $G$ such that subsequent to the failure of a single edge or vertex, the surviving part $T'$ of $T$ still contains a BFS spanning tree for (the surviving part of) $G$. Our main results are as follows. We present an algorithm that for every $n$-vertex graph $G$ and source node $s$ constructs a (single edge failure) FT-BFS tree rooted at $s$ with O(n \cdot \min\{\Depth(s), \sqrt{n}\}) edges, where \Depth(s) is the depth of the BFS tree rooted at $s$. This result is complemented by a matching lower bound, showing that there exist $n$-vertex graphs with a source node $s$ for which any edge (or vertex) FT-BFS tree rooted at $s$ has $\Omega(n^{3/2})$ edges. We then consider {\em fault-tolerant multi-source BFS trees}, or {\em FT-MBFS trees} for short, aiming to provide (following a failure) a BFS tree rooted at each source $s\in S$ for some subset of sources $S\subseteq V$. Again, tight bounds are provided, showing that there exists a poly-time algorithm that for every $n$-vertex graph and source set $S \subseteq V$ of size $\sigma$ constructs a (single failure) FT-MBFS tree $T^*(S)$ from each source $s_i \in S$, with $O(\sqrt{\sigma} \cdot n^{3/2})$ edges, and on the other hand there exist $n$-vertex graphs with source sets $S \subseteq V$ of cardinality $\sigma$, on which any FT-MBFS tree from $S$ has $\Omega(\sqrt{\sigma}\cdot n^{3/2})$ edges. Finally, we propose an $O(\log n)$ approximation algorithm for constructing FT-BFS and FT-MBFS structures. The latter is complemented by a hardness result stating that there exists no $\Omega(\log n)$ approximation algorithm for these problems under standard complexity assumptions

Limitations to Frechet's Metric Embedding Method

Frechet's classical isometric embedding argument has evolved to become a major tool in the study of metric spaces. An important example of a Frechet embedding is Bourgain's embedding. The authors have recently shown that for every e>0 any n-point metric space contains a subset of size at least n^(1-e) which embeds into l_2 with distortion O(\log(2/e) /e). The embedding we used is non-Frechet, and the purpose of this note is to show that this is not coincidental. Specifically, for every e>0, we construct arbitrarily large n-point metric spaces, such that the distortion of any Frechet embedding into l_p on subsets of size at least n^{1/2 + e} is \Omega((\log n)^{1/p}).Comment: 10 pages, 1 figur

Migratory direction established in inexperienced bird migrants in the absence of magnetic field references in their pre-migratory period and during testing

Several studies have investigated the importance of different orientational cues that pre-migratory, naïve bird migrants might use to develop their appropriate migratory orientation. We tested the hypothesis that, without any interplay with the magnetic compass in the pre-migratory period, celestial rotation alone cannot lead to any migratory orientation that differs significantly from due south, i.e. celestial rotation is used as a reference only and it is set by the geomagnetic compass to the species-specific migration direction. In the present study, juvenile whitethroats, Sylvia communis, trapped in the field soon after fledging, developed appropriate migratory orientation when held in outdoor cages in full view of celestial cues, but in a strong, heterogeneous magnetic field without any meaningful, magnetic directional information and tested in a strong and approximately vertical magnetic field. The migratory orientation of these birds did not differ from that of birds held in an undisturbed magnetic field, and both differed significantly from south. Thus, the birds established a deviation from south (away from celestial rotation) in the absence of meaningful magnetic information in the pre-migratory phase. This indicates that magnetic information is not necessary for establishing the appropriate migratory direction when natural celestial cues are available in the pre-migratory period. key worDs: migration direction, orientation, animal behaviour, whitethroat, Sylvia communis

Intercropping effect on root growth and nitrogen uptake at different nitrogen levels

Aims Intercropping legumes and non-legumes may affect the root growth of both components in the mixture, and the non-legume is known to be strongly favored by increasing nitrogen (N) supply. The knowledge of how root systems affect the growth of the individual species is useful for understanding the interactions in intercrops as well as for planning cover cropping strategies. The aim of this work was (i) to determine if different levels of N in the topsoil influence root depth (RD) and intensity of barley and vetch as sole crops or as an intercropped mixture and (ii) to test if the choice of a mixture or the N availability in the topsoil will influence the N uptake by deep roots. Methods In this study, we combined rhizotron studies with root extraction and species identification by microscopy with studies of growth, N uptake and 15N uptake from deeper soil layers, for studying the root interactions of root growth and N foraging for barley (Hordeum vulgare L.) and vetch (Vicia sativa L.), frequently grown in mixtures as cover crops. N was added at 0 (N0), 50 (N1) and 150 (N2) kg N ha−1. The roots discrimination relying on the anatomical and morphological differences observed between dicots and monocots proved to be a reliable method providing valuable data for the analysis. Important Findings The intercrop and the barley attained slightly higher root intensity (RI) and RD than the vetch, with values around 150 crosses m−1 and 1.4 m, respectively, compared to 50 crosses m−1 and 0.9 m for the vetch. At deep soil layers, intercropping showed slightly larger RI values compared to the sole-cropped barley. The barley and the intercropping had larger root length density (RLD) values (200–600 m m−3) than the vetch (25–130) at 0.8–1.2 m depth. The topsoil N supply did not show a clear effect on the RI, RD or RLD; however, increasing topsoil N favored the proliferation of vetch roots in the intercropping at deep soil layers, with the barley:vetch root ratio ranging from 25 at N0 to 5 at N2. The N uptake of the barley was enhanced in the intercropping at the expense of the vetch (from ~100mg plant−1 to 200). The intercropped barley roots took up more labeled nitrogen (0.6mg 15N plant−1) than the sole-cropped barley roots (0.3mg 15N plant−1) from deep layers