The one-round Voronoi game replayed

We consider the one-round Voronoi game, where player one (``White'', called ``Wilma'') places a set of n points in a rectangular area of aspect ratio r <=1, followed by the second player (``Black'', called ``Barney''), who places the same number of points. Each player wins the fraction of the board closest to one of his points, and the goal is to win more than half of the total area. This problem has been studied by Cheong et al., who showed that for large enough $n$ and r=1, Barney has a strategy that guarantees a fraction of 1/2+a, for some small fixed a. We resolve a number of open problems raised by that paper. In particular, we give a precise characterization of the outcome of the game for optimal play: We show that Barney has a winning strategy for n>2 and r>sqrt{2}/n, and for n=2 and r>sqrt{3}/2. Wilma wins in all remaining cases, i.e., for n>=3 and r<=sqrt{2}/n, for n=2 and r<=sqrt{3}/2, and for n=1. We also discuss complexity aspects of the game on more general boards, by proving that for a polygon with holes, it is NP-hard to maximize the area Barney can win against a given set of points by Wilma.Comment: 14 pages, 6 figures, Latex; revised for journal version, to appear in Computational Geometry: Theory and Applications. Extended abstract version appeared in Workshop on Algorithms and Data Structures, Springer Lecture Notes in Computer Science, vol.2748, 2003, pp. 150-16

Bryophyte extracts with activity against plant pathogenic fungi

The effects of extracts from 17 different bryophyte species were investigated against economically important plant pathogenic fungi. In vitro experiments showed that ethanol extracts of bryophytes inhibited mycelial growth of Botrytis cinerea and Alternaria solani. Extracts from Bazzania trilobata, Diplophyllum albicans, Sphagnum quinquefarium, Dicranodontium denudatum, and Hylocomium splendens inhibited fungal development by over 50%. Green pepper plants sprayed with the extracts from 17 bryophytes (at 1% mv-1), with the fungicide dichlofluanide (50 ppm), and untreated plants were compared. Treatments were applied 4 hours prior to inoculation with conidial suspension of the grey mould (B. cinerea). Significant variations between treatments were detected. Extract treatments reduced the grey mould severity ranging from 15 to 23%, whereas dichlofluanide showed efficacy up to 92%. Three dose levels of five candidate extracts sprayed at three pre-infectional time intervals were compared under low and high inoculum pressures of the late blight, Phytophthora infestans, of tomatoes and powdery mildew, Blumeria graminis, of wheat. In general, extracts from B. trilobata and D. albicans showed better efficient disease protection than that of S. quinquefarium, D. denudatum, and H. splendens. The direct mode-of-action of treatments on the surface of leaves gave inefficient disease protection, evidenced on treated plants at 4 hours before the inoculation. However, plants treated by the same extracts at least 2 days before inoculation exhibited less than 90% disease severity. Therefore, products of bryophytes deserved to be reliable sources as biocontrol agents and may play significant roles for future practical applications in a socially and ecologically healthy crop management system. Key words/phrases: Alternaria solani, Blumeria graminis, Botrytis cinerea, Bryophyte extracts, Phytophthora infestans SINET: Ethiop. J. Sci Vol.26(1) 2003: 55-6

Arbuscular Mycorrhizal Symbiosis Limits Foliar Transcriptional Responses to Viral Infection and Favors Long-Term Virus Accumulation

Tomato (Solanum lycopersicum) can establish symbiotic interactions with arbuscular mycorrhizal (AM) fungi, and can be infected by several pathogenic viruses. Here, we investigated the impact of mycorrhization by the fungus Glomus mosseae on the Tomato spotted wilt virus (TSWV) infection of tomato plants by transcriptomic and hormones level analyses. In TSWV-infected mycorrhizal plants, the AM fungus root colonization limited virus-induced changes in gene expression in the aerial parts. The virus-responsive upregulated genes, no longer induced in infected mycorrhizal plants, were mainly involved in defense responses and hormone signaling, while the virus-responsive downregulated genes, no longer repressed in mycorrhizal plants, were involved in primary metabolism. The presence of the AM fungus limits, in a salicylic acid-independent manner, the accumulation of abscissic acid observed in response to viral infection. At the time of the molecular analysis, no differences in virus concentration or symptom severity were detected between mycorrhizal and nonmycorrhizal plants. However, in a longer period, increase in virus titer and delay in the appearance of recovery were observed in mycorrhizal plants, thus indicating that the plant's reaction to TSWV infection is attenuated by mycorrhization. </jats:p

Algorithms for Stable Matching and Clustering in a Grid

We study a discrete version of a geometric stable marriage problem originally proposed in a continuous setting by Hoffman, Holroyd, and Peres, in which points in the plane are stably matched to cluster centers, as prioritized by their distances, so that each cluster center is apportioned a set of points of equal area. We show that, for a discretization of the problem to an $n\times n$ grid of pixels with $k$ centers, the problem can be solved in time $O(n^2 \log^5 n)$, and we experiment with two slower but more practical algorithms and a hybrid method that switches from one of these algorithms to the other to gain greater efficiency than either algorithm alone. We also show how to combine geometric stable matchings with a $k$-means clustering algorithm, so as to provide a geometric political-districting algorithm that views distance in economic terms, and we experiment with weighted versions of stable $k$-means in order to improve the connectivity of the resulting clusters.Comment: 23 pages, 12 figures. To appear (without the appendices) at the 18th International Workshop on Combinatorial Image Analysis, June 19-21, 2017, Plovdiv, Bulgari

Polynomial kernels for 3-leaf power graph modification problems

A graph G=(V,E) is a 3-leaf power iff there exists a tree T whose leaves are V and such that (u,v) is an edge iff u and v are at distance at most 3 in T. The 3-leaf power graph edge modification problems, i.e. edition (also known as the closest 3-leaf power), completion and edge-deletion, are FTP when parameterized by the size of the edge set modification. However polynomial kernel was known for none of these three problems. For each of them, we provide cubic kernels that can be computed in linear time for each of these problems. We thereby answer an open problem first mentioned by Dom, Guo, Huffner and Niedermeier (2005).Comment: Submitte

A distributed tree data structure for real-time OLAP on cloud architectures

In contrast to queries for on-line transaction processing (OLTP) systems that typically access only a small portion of a database, OLAP queries may need to aggregate large portions of a database which often leads to performance issues. In this paper we introduce CR-OLAP, a Cloud based Real-time OLAP system based on a new distributed index structure for OLAP, the distributed PDCR tree, that utilizes a cloud infrastructure consisting of (m + 1) multi-core processors. With increasing database size, CR-OLAP dynamically increases m to maintain performance. Our distributed PDCR tree data structure supports multiple dimension hierarchies and efficient query processing on the elaborate dimension hierarchies which are so central to OLAP systems. It is particularly efficient for complex OLAP queries that need to aggregate large portions of the data warehouse, such as 'report the total sales in all stores located in California and New York during the months February-May of all years'. We evaluated CR-OLAP on the Amazon EC2 cloud, using the TPC-DS benchmark data set. The tests demonstrate that CR-OLAP scales well with increasing number of processors, even for complex queries. For example, on an Amazon EC2 cloud instance with eight processors, for a TPC-DS OLAP query stream on a data warehouse with 80 million tuples where every OLAP query aggregates more than 50% of the database, CR-OLAP achieved a query latency of 0.3 seconds which can be considered a real time response