The Matching Problem in General Graphs is in Quasi-NC

We show that the perfect matching problem in general graphs is in Quasi-NC. That is, we give a deterministic parallel algorithm which runs in $O(\log^3 n)$ time on $n^{O(\log^2 n)}$ processors. The result is obtained by a derandomization of the Isolation Lemma for perfect matchings, which was introduced in the classic paper by Mulmuley, Vazirani and Vazirani [1987] to obtain a Randomized NC algorithm. Our proof extends the framework of Fenner, Gurjar and Thierauf [2016], who proved the analogous result in the special case of bipartite graphs. Compared to that setting, several new ingredients are needed due to the significantly more complex structure of perfect matchings in general graphs. In particular, our proof heavily relies on the laminar structure of the faces of the perfect matching polytope.Comment: Accepted to FOCS 2017 (58th Annual IEEE Symposium on Foundations of Computer Science

Fast Generation of Random Spanning Trees and the Effective Resistance Metric

We present a new algorithm for generating a uniformly random spanning tree in an undirected graph. Our algorithm samples such a tree in expected $\tilde{O}(m^{4/3})$ time. This improves over the best previously known bound of $\min(\tilde{O}(m\sqrt{n}),O(n^{\omega}))$ -- that follows from the work of Kelner and M\k{a}dry [FOCS'09] and of Colbourn et al. [J. Algorithms'96] -- whenever the input graph is sufficiently sparse. At a high level, our result stems from carefully exploiting the interplay of random spanning trees, random walks, and the notion of effective resistance, as well as from devising a way to algorithmically relate these concepts to the combinatorial structure of the graph. This involves, in particular, establishing a new connection between the effective resistance metric and the cut structure of the underlying graph

Streaming Robust Submodular Maximization: A Partitioned Thresholding Approach

We study the classical problem of maximizing a monotone submodular function subject to a cardinality constraint k, with two additional twists: (i) elements arrive in a streaming fashion, and (ii) m items from the algorithm's memory are removed after the stream is finished. We develop a robust submodular algorithm STAR-T. It is based on a novel partitioning structure and an exponentially decreasing thresholding rule. STAR-T makes one pass over the data and retains a short but robust summary. We show that after the removal of any m elements from the obtained summary, a simple greedy algorithm STAR-T-GREEDY that runs on the remaining elements achieves a constant-factor approximation guarantee. In two different data summarization tasks, we demonstrate that it matches or outperforms existing greedy and streaming methods, even if they are allowed the benefit of knowing the removed subset in advance.Comment: To appear in NIPS 201

Heuristic Algorithms for Optimization of Task Allocation and Result Distribution in Peer-to-Peer Computing Systems

Recently, distributed computing system have been gaining much attention due to a growing demand for various kinds of effective computations in both industry and academia. In this paper, we focus on Peer-to-Peer (P2P) computing systems, also called public-resource computing systems or global computing systems. P2P computing systems, contrary to grids, use personal computers and other relatively simple electronic equipment (e.g., the PlayStation console) to process sophisticated computational projects. A significant example of the P2P computing idea is the BOINC (Berkeley Open Infrastructure for Network Computing) project. To improve the performance of the computing system, we propose to use the P2P approach to distribute results of computational projects, i.e., results are transmitted in the system like in P2P file sharing systems (e.g., BitTorrent). In this work, we concentrate on offline optimization of the P2P computing system including two elements: scheduling of computations and data distribution. The objective is to minimize the system OPEX cost related to data processing and data transmission. We formulate an Integer Linear Problem (ILP) to model the system and apply this formulation to obtain optimal results using the CPLEX solver. Next, we propose two heuristic algorithms that provide results very close to an optimum and can be used for larger problem instances than those solvable by CPLEX or other ILP solvers

From Environmental Sequences to Morphology: Observation and Characterisation of a Paulinellid Testate Amoeba (<i>Micropyxidiella edaphonis gen. nov. sp. nov. </i> Euglyphida, Paulinellidae) from Soil using Fluorescent in situ Hybridization

High microbial diversity is revealed by environmental DNA surveys. However, nothing is known about the morphology and function of these potentially new organisms. In the course of an environmental soil diversity study, we found for the first time environmental sequences that reveal the presence of Paulinellidae (a mostly marine and marginally freshwater family of euglyphid testate amoebae) in samples of forest litter from different geographic origins. The new sequences form a basal, robust clade in the family. We used fluorescent in situ hybridization (FISH) to detect the organisms from which these sequences derived. We isolated the cells and documented them with light and scanning electron microscopy. Based on these observations, we described these organisms as Micropyxidiella edaphonis gen. nov. sp. nov. The organisms were very small testate amoebae (generally less than 10 μm) with an irregular proteinaceous test. This suggests an unknown diversity in testate amoebae, and calls for extending this type of investigations to other protist groups which are known only as environmental DNA sequences

Verwey transition in Fe3_{3}O4_{4} at high pressure: quantum critical behavior at the onset of metallization

We provide evidence for the existence of a {\em quantum critical point} at the metallization of magnetite Fe$_{3}$O$_{4}$ at an applied pressure of $p_{c} \approx 8$ GPa. We show that the present ac magnetic susceptibility data support earlier resistivity data. The Verwey temperature scales with pressure $T_{V}\sim (1-p/p_{c})^{\nu}$, with $\nu\sim 1/3$. The resistivity data shows a temperature dependence $\rho(T)=\rho_{0}+AT^{n}$, with $n\simeq 3$ above and 2.5 at the critical pressure, respectively. This difference in $n$ with pressure is a sign of critical behavior at $p_{c}$. The magnetic susceptibility is smooth near the critical pressure, both at the Verwey transition and near the ferroelectric anomaly. A comparison with the critical behavior observed in the Mott-Hubbard and related systems is made.Comment: 5 pages, 5 figure

Frequency and Diversity of Nitrate Reductase Genes among Nitrate-Dissimilating Pseudomonas in the Rhizosphere of Perennial Grasses Grown in Field Conditions

A total of 1246 Pseudomonas strains were isolated from the rhizosphere of two perennial grasses (Lolium perenne and Molinia coerulea) with different nitrogen requirements. The plants were grown in their native soil under ambient and elevated atmospheric CO2 content (pCO2) at the Swiss FACE (Free Air CO2 Enrichment) facility. Root-, rhizosphere-, and non-rhizospheric soil-associated strains were characterized in terms of their ability to reduce nitrate during an in vitro assay and with respect to the genes encoding the membrane-bound (named NAR) and periplasmic (NAP) nitrate reductases so far described in the genus Pseudomonas. The diversity of corresponding genes was assessed by PCR-RFLP on narG and napA genes, which encode the catalytic subunit of nitrate reductases. The frequency of nitrate-dissimilating strains decreased with root proximity for both plants and was enhanced under elevated pCO2 in the rhizosphere of L. perenne. NAR (54% of strains) as well as NAP (49%) forms were present in nitrate-reducing strains, 15.5% of the 439 strains tested harbouring both genes. The relative proportions of narG and napA detected in Pseudomonas strains were different according to root proximity and for both pCO2 treatments: the NAR form was more abundant close to the root surface and for plants grown under elevated pCO2. Putative denitrifiers harbored mainly the membrane-bound (NAR) form of nitrate reductase. Finally, both narG and napA sequences displayed a high level of diversity. Anyway, this diversity was correlated neither with the root proximity nor with the pCO2 treatmen

Extension of soil thermal conductivity models to frozen meats with low and high fat content

Thermal conductivity models of frozen soils were analyzed and compared with similar models developed for frozen foods. In total, eight thermal conductivity models and 54 model versions were tested against experimental data of 13 meat products in the temperature range from 0 toK40 8C. The model by deVries, with waterCice (wi) as the continuous phase, showed overall the best predictions. The use of wi leads generally to improved predictions in comparison to ice; water as the continuous phase is beneficial only to deVries model, mostly from K1 to K20 8C; fat is advantageous only to meats with high fat content. The results of this work suggest that the more sophisticated way of estimating the thermal conductivity for a disperse phase in the deVries model might be more appropriate than the use of basic multi-phase models (geometric mean, parallel, and series). Overall, relatively small differences in predictions were observed between the best model versions by deVries, Levy, Mascheroni, Maxwell or Gori as applied to frozen meats with low content of fat. These differences could also be generated by uncertainty in meat composition, temperature dependence of thermal conductivity of ice, measurement errors, and limitation of predictive models