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

Almost 2-SAT is Fixed-Parameter Tractable

We consider the following problem. Given a 2-CNF formula, is it possible to remove at most $k$ clauses so that the resulting 2-CNF formula is satisfiable? This problem is known to different research communities in Theoretical Computer Science under the names 'Almost 2-SAT', 'All-but-$k$ 2-SAT', '2-CNF deletion', '2-SAT deletion'. The status of fixed-parameter tractability of this problem is a long-standing open question in the area of Parameterized Complexity. We resolve this open question by proposing an algorithm which solves this problem in $O(15^k*k*m^3)$ and thus we show that this problem is fixed-parameter tractable.Comment: This new version fixes the bug found by Somnath Sikdar in the proof of Claim 8. In the repaired version the modification of the Almost 2-SAT problem called 2-SLASAT is no longer needed and only the modification called 2-ASLASAT remains relevant. Hence the whole manuscript is updated so that the 2-SLASAT problem is not mentioned there anymor

Evaluation of ILP-based approaches for partitioning into colorful components

The NP-hard Colorful Components problem is a graph partitioning problem on vertex-colored graphs. We identify a new application of Colorful Components in the correction of Wikipedia interlanguage links, and describe and compare three exact and two heuristic approaches. In particular, we devise two ILP formulations, one based on Hitting Set and one based on Clique Partition. Furthermore, we use the recently proposed implicit hitting set framework [Karp, JCSS 2011; Chandrasekaran et al., SODA 2011] to solve Colorful Components. Finally, we study a move-based and a merge-based heuristic for Colorful Components. We can optimally solve Colorful Components for Wikipedia link correction data; while the Clique Partition-based ILP outperforms the other two exact approaches, the implicit hitting set is a simple and competitive alternative. The merge-based heuristic is very accurate and outperforms the move-based one. The above results for Wikipedia data are confirmed by experiments with synthetic instances

Ação de agroquímicos no controle de mofo branco em soja

Soybean is one of the most important crops in the world. However, several times the yield is reduced due to diseases as the stem rot (white mold) caused by Sclerotinia sclerotiorum, which is a several fungal, mainly in areas with low temperatures and high moisture. The disease control, including the use of fungicides, is difficult. Thus, the objective of this study was to verify the effect of herbicides and foliar fertilizers with potassium phosphite on control of white mold soybean, determining the action of this agrochemicals about the phytoalexin, superoxide dismutase and peroxidase synthesis, and the direct action on the pathogen. For this, the in vitro effect of agrochemicals on the pathogen was evaluated. Also, the induction was tested in the laboratory by evaluation of phytoalexin synthesis in soybean cotyledons, and POX and SOD enzymes, subjected to the same treatment field. The field trials were conducted in Coronel Domingos Soares – PR, evaluations were made in 2012/2013 crop. A randomized-complete blocks design with 6 treatments and 4 replicates was used. The treatments were: lactofen (0,6 L ha-1 applied in V4), bentazon (1,5 L ha-1 in V4), fluazinam (1 L ha-1 in R1) and two foliar fertilizers called fosfito A (30 p/p % de P2O5 and 20 p/p % de K2O) (3 L ha-1 in V4 + R1) and fosfito B (26 p/p % de P2O5 and 19 p/p % de K2O) (2 L ha-1 in V4 + R1). . The fungicide was the only product that completely inhibited fungal growth in vitro. In the laboratory, the bentazon reached the highest levels of phytoalexin production, but the foliar fertilizers did not induce the production of the same. Both herbicides and phosphite A had the potential to elicit the production of peroxidase enzyme. In field experiments the herbicides bentazon and lactofen stood out in the control of white mold, being 60.5% and 52.3% respectively, and treatment with the fosfito A provided a control of 37.9%, being superior to the treatment with fungicide. Regarding the grain fields compounds had increase using the herbicides, but did not differed from the control by Duncan test at 5%.A soja é uma das principais commodities produzidas no mundo. Entretanto, tem sua produtividade reduzida, significativamente, devido às doenças, dentre estas o mofo branco, causado pelo fungo Sclerotinia sclerotiorum, com expressiva severidade em regiões de clima ameno e úmido. O controle da doença, incluindo o uso de fungicidas, é pouco eficiente. Assim, o trabalho teve por objetivo avaliar a eficiência de herbicidas e adubos foliares à base de fosfito de potássio no manejo do mofo branco em soja, bem como a ação dos produtos, indução da síntese de fitoalexinas e das enzimas peroxidases e superóxido dismutase, assim como a ação direta dos agroquímicos sobre o patógeno. Para isso, avaliou-se a ação in vitro dos produtos químicos sobre o crescimento micelial do fungo e germinação de escleródios. A indução foi testada em laboratório por meio da avaliação da síntese de fitoalexinas em cotilédones de soja, e das enzimas POX e SOD, submetidas aos mesmos tratamentos de campo. O experimento de campo foi implantado em Coronel Domingos Soares - PR, safra 2012/2013, em área com infestação natural do fitopatógeno. O delineamento experimental foi de blocos ao acaso, com 4 repetições e 6 tratamentos: testemunha, lactofen (0,6 L ha-1 em V4), bentazon (1,5 L ha-1 em V4), fluazinam (1 L ha-1 em R1) e dois adubos foliares denominados fosfito A (30 p/p % de P2O5 e 20 p/p % de K2O) (3 L ha-1 em V4 + R1) e fosfito B (26 p/p % de P2O5 e 19 p/p % de K2O) (2 L ha-1 em V4 + R1). O fungicida foi o único produto que inibiu totalmente o desenvolvimento do fungo in vitro. Em laboratório, o bentazon alcançou os maiores índices de produção de fitoalexinas, enquanto os adubos foliares não as induziram. Ambos os herbicidas e o fosfito A tiveram potencial para aumentar a atividade da enzima POX. No experimento de campo os herbicidas bentazon e lactofen destacaram-se no controle do mofo branco, sendo de 60,5% e 52,3%, respectivamente, e o tratamento com fosfito A com um controle de 37,9%, superiores ao tratamento com fungicida. Em relação aos componentes de rendimento houve incrementos utilizando os herbicidas, entretanto, não diferiram estatisticamente da testemunha pelo teste de Duncan a 5%

Exploiting bounded signal flow for graph orientation based on cause-effect pairs

Background: We consider the following problem: Given an undirected network and a set of sender–receiver pairs, direct all edges such that the maximum number of “signal flows ” defined by the pairs can be routed respecting edge directions. This problem has applications in understanding protein interaction based cell regulation mechanisms. Since this problem is NP-hard, research so far concentrated on polynomial-time approximation algorithms and tractable special cases. Results: We take the viewpoint of parameterized algorithmics and examine several parameters related to the maximum signal flow over vertices or edges. We provide several fixed-parameter tractability results, and in one case a sharp complexity dichotomy between a linear-time solvable case and a slightly more general NP-hard case. We examine the value of these parameters for several real-world network instances. Conclusions: Several biologically relevant special cases of the NP-hard problem can be solved to optimality. In this way, parameterized analysis yields both deeper insight into the computational complexity and practical solving strategies. Background Current technologies [1] like two-hybrid screening ca

Balanced Interval Coloring

We consider the discrepancy problem of coloring $n$ intervals with $k$ colors such that at each point on the line, the maximal difference between the number of intervals of any two colors is minimal. Somewhat surprisingly, a coloring with maximal difference at most one always exists. Furthermore, we give an algorithm with running time $O(n \log n + kn \log k)$ for its construction. This is in particular interesting because many known results for discrepancy problems are non-constructive. This problem naturally models a load balancing scenario, where $n$ tasks with given start- and endtimes have to be distributed among $k$ servers. Our results imply that this can be done ideally balanced. When generalizing to $d$-dimensional boxes (instead of intervals), a solution with difference at most one is not always possible. We show that for any $d \ge 2$ and any $k \ge 2$ it is NP-complete to decide if such a solution exists, which implies also NP-hardness of the respective minimization problem. In an online scenario, where intervals arrive over time and the color has to be decided upon arrival, the maximal difference in the size of color classes can become arbitrarily high for any online algorithm.Comment: Accepted at STACS 201

Fast branching algorithm for Cluster Vertex Deletion

In the family of clustering problems, we are given a set of objects (vertices of the graph), together with some observed pairwise similarities (edges). The goal is to identify clusters of similar objects by slightly modifying the graph to obtain a cluster graph (disjoint union of cliques). Hueffner et al. [Theory Comput. Syst. 2010] initiated the parameterized study of Cluster Vertex Deletion, where the allowed modification is vertex deletion, and presented an elegant O(2^k * k^9 + n * m)-time fixed-parameter algorithm, parameterized by the solution size. In our work, we pick up this line of research and present an O(1.9102^k * (n + m))-time branching algorithm

Orientation-dependent C60 electronic structures revealed by photoemission

We observe, with angle-resolved photoemission, a dramatic change in the electronic structure of two C60 monolayers, deposited respectively on Ag (111) and (100) substrates, and similarly doped with potassium to half-filling of the C60 lowest unoccupied molecular orbital. The Fermi surface symmetry, the bandwidth, and the curvature of the dispersion at Gamma point are different. Orientations of the C60 molecules on the two substrates are known to be the main structural difference between the two monolayers, and we present new band-structure calculations for some of these orientations. We conclude that orientations play a key role in the electronic structure of fullerides.Comment: 4 pages, 4 figure

The Parameterized Complexity of Centrality Improvement in Networks

The centrality of a vertex v in a network intuitively captures how important v is for communication in the network. The task of improving the centrality of a vertex has many applications, as a higher centrality often implies a larger impact on the network or less transportation or administration cost. In this work we study the parameterized complexity of the NP-complete problems Closeness Improvement and Betweenness Improvement in which we ask to improve a given vertex' closeness or betweenness centrality by a given amount through adding a given number of edges to the network. Herein, the closeness of a vertex v sums the multiplicative inverses of distances of other vertices to v and the betweenness sums for each pair of vertices the fraction of shortest paths going through v. Unfortunately, for the natural parameter "number of edges to add" we obtain hardness results, even in rather restricted cases. On the positive side, we also give an island of tractability for the parameter measuring the vertex deletion distance to cluster graphs

The effect of negative feedback loops on the dynamics of Boolean networks

Feedback loops in a dynamic network play an important role in determining the dynamics of that network. Through a computational study, in this paper we show that networks with fewer independent negative feedback loops tend to exhibit more regular behavior than those with more negative loops. To be precise, we study the relationship between the number of independent feedback loops and the number and length of the limit cycles in the phase space of dynamic Boolean networks. We show that, as the number of independent negative feedback loops increases, the number (length) of limit cycles tends to decrease (increase). These conclusions are consistent with the fact, for certain natural biological networks, that they on the one hand exhibit generally regular behavior and on the other hand show less negative feedback loops than randomized networks with the same numbers of nodes and connectivity