Maximum Number of Minimum Dominating and Minimum Total Dominating Sets

Given a connected graph with domination (or total domination) number \gamma>=2, we ask for the maximum number m_\gamma and m_{\gamma,T} of dominating and total dominating sets of size \gamma. An exact answer is provided for \gamma=2and lower bounds are given for \gamma>=3.Comment: 6 page

Minimum Entropy Orientations

We study graph orientations that minimize the entropy of the in-degree sequence. The problem of finding such an orientation is an interesting special case of the minimum entropy set cover problem previously studied by Halperin and Karp [Theoret. Comput. Sci., 2005] and by the current authors [Algorithmica, to appear]. We prove that the minimum entropy orientation problem is NP-hard even if the graph is planar, and that there exists a simple linear-time algorithm that returns an approximate solution with an additive error guarantee of 1 bit. This improves on the only previously known algorithm which has an additive error guarantee of log_2 e bits (approx. 1.4427 bits).Comment: Referees' comments incorporate

Minimum maximum reconfiguration cost problem

This paper discusses the problem of minimizing the reconfiguration cost of some types of reconfigurable systems. A formal definition of the problem and a proof of its NP-completeness are provided. In addition, an Integer Linear Programming formulation is proposed. The proposed problem has been used for optimizing a design stage of Finite Virtual State Machines

Minimum Tillage Corn Trial

Minimum tillage practices have significant potential to reduce expenses and the potential negative environmental effects caused by intensive tillage operations. Conventional tillage practices require heavy machinery to work and groom the soil surface in preparation for the planter. The immediate advantage of reduced tillage for the farm operator is less fuel expense, equipment, time, and labor required. It’s also clear that intensive tillage potentially increases nutrient and soil losses to our surface waterways. By turning the soil and burying surface residue, more soil particles are likely to detach from the soil surface and increase the potential for run off from agricultural fields. Reducing the amount and intensity of tillage can help build soil structure and reduce soil erosion

Minimum Density Hyperplanes

Associating distinct groups of objects (clusters) with contiguous regions of high probability density (high-density clusters), is central to many statistical and machine learning approaches to the classification of unlabelled data. We propose a novel hyperplane classifier for clustering and semi-supervised classification which is motivated by this objective. The proposed minimum density hyperplane minimises the integral of the empirical probability density function along it, thereby avoiding intersection with high density clusters. We show that the minimum density and the maximum margin hyperplanes are asymptotically equivalent, thus linking this approach to maximum margin clustering and semi-supervised support vector classifiers. We propose a projection pursuit formulation of the associated optimisation problem which allows us to find minimum density hyperplanes efficiently in practice, and evaluate its performance on a range of benchmark datasets. The proposed approach is found to be very competitive with state of the art methods for clustering and semi-supervised classification

Distributed Minimum Cut Approximation

We study the problem of computing approximate minimum edge cuts by distributed algorithms. We use a standard synchronous message passing model where in each round, $O(\log n)$ bits can be transmitted over each edge (a.k.a. the CONGEST model). We present a distributed algorithm that, for any weighted graph and any $\epsilon \in (0, 1)$, with high probability finds a cut of size at most $O(\epsilon^{-1}\lambda)$ in $O(D) + \tilde{O}(n^{1/2 + \epsilon})$ rounds, where $\lambda$ is the size of the minimum cut. This algorithm is based on a simple approach for analyzing random edge sampling, which we call the random layering technique. In addition, we also present another distributed algorithm, which is based on a centralized algorithm due to Matula [SODA '93], that with high probability computes a cut of size at most $(2+\epsilon)\lambda$ in $\tilde{O}((D+\sqrt{n})/\epsilon^5)$ rounds for any $\epsilon>0$. The time complexities of both of these algorithms almost match the $\tilde{\Omega}(D + \sqrt{n})$ lower bound of Das Sarma et al. [STOC '11], thus leading to an answer to an open question raised by Elkin [SIGACT-News '04] and Das Sarma et al. [STOC '11]. Furthermore, we also strengthen the lower bound of Das Sarma et al. by extending it to unweighted graphs. We show that the same lower bound also holds for unweighted multigraphs (or equivalently for weighted graphs in which $O(w\log n)$ bits can be transmitted in each round over an edge of weight $w$), even if the diameter is $D=O(\log n)$. For unweighted simple graphs, we show that even for networks of diameter $\tilde{O}(\frac{1}{\lambda}\cdot \sqrt{\frac{n}{\alpha\lambda}})$, finding an $\alpha$-approximate minimum cut in networks of edge connectivity $\lambda$ or computing an $\alpha$-approximation of the edge connectivity requires $\tilde{\Omega}(D + \sqrt{\frac{n}{\alpha\lambda}})$ rounds

Minimum Tillage Corn Trial

Minimum tillage practices have tremendous potential to reduce expenses and potential negative environmental effects caused by intensive cropping operations. Conventional tillage practices require heavy machinery to work and groom the soil surface in preparation for the planter. The immediate advantage of reduced tillage for the farm operator is less fuel expense, equipment, time, and labor required. It’s also clear that intensive tillage potentially increases nutrient and soil losses to our surface waterways. By turning the soil and burying surface residue, more soil particles are likely to detach from the soil surface and run off from agricultural fields. Reducing the amount and intensity of tillage can help build soil structure and reduce soil erosion

Minimum Magnetizability Principle

A new electronic structure principle, viz. the minimum magnetizability principle (MMP) has been proposed and also has been verified through ab initio calculations, to extend the domain of applicability of the conceptual density functional theory (DFT) in explaining the magnetic interactions and magnetochemistry. This principle may be stated as, "A stable configuration/conformation of a molecule or a favorable chemical process is associated with a minimum value of the magnetizability". It has also been shown that a soft molecule is easily polarizable and magnetizable than a hard one.Comment: 2 Pages, 3 Figure