Tree 3-spanners in 2-sep chordal graphs: Characterization and algorithms

A spanning tree T of a graph G is said to be a tree t-spanner if the distance between any two vertices in T is at most t times their distance in G. A graph that has a tree t-spanner is called a tree t-spanner admissible graph. The problem of deciding whether a graph is tree t-spanner admissible is NP-complete for any fixed t >= 4 and is linearly solvable for t <= 2. The case t = 3 still remains open. A chordal graph is called a 2-sep chordal graph if all of its minimal a - b vertex separators for every pair of non-adjacent vertices a and b are of size two. It is known that not all 2-sep chordal graphs admit tree 3-spanners This paper presents a structural characterization and a linear time recognition algorithm of tree 3-spanner admissible 2-sep chordal graphs. Finally, a linear time algorithm to construct a tree 3-spanner of a tree 3-spanner admissible 2-sep chordal graph is proposed. (C) 2010 Elsevier B.V. All rights reserved.

A review of hybrid rockets: present status and future potential

This paper discusses the potential of the hybrid rocket engine as a viable and attractive mode of propulsion for both space vehicles and missiles. Research and development work on this engine in other countries is presented and evaluated. The various advantages of a hybrid engine over solid and liquid engines and its problems are highlighted. It has been argued that because of the low technology needed in the development of the hybrid system, it constitutes a cost-and-time-effective propulsion system for several applications in space programmes as well as weapon systems. In support of this conclusion, experience on the developmental studies of a variable thrust 100 kg engine is presented. Some future possibilities for hybrid propulsion systems are cited.

Nonlinear Transport in Hybrid Polypyrrole-Gold Nanostructures

We have studied charge transport in nanometer scale films of polypyrrole (PPy) that were grown electrochemically onto discontinuous ultrathin films of gold. The gold films consisted of 100 nm size islands, separated from each other by nanometer-size gaps. The thickness of PPy can be varied from 30 to 200 nm. The I-V characteristics of these hybrid PPy-Au nanostructures show strong non-linearity at low temperatures, and in particular for the more insulating samples. The hopping transport is further verified from the log / versus V-1/4 plots. Furthermore, the I-V data follow an empirical relation dlog//dV(1/4) similar to T-1/2.

Photocatalytic treatment of municipal wastewater using modified neodymium doped TiO2 hybrid nanoparticles

Photocatalytic degradation of municipal wastewater was investigated using reagent grade TiO2 and modified neodymium doped TiO2 hybrid nanoparticles. For the first time, surface modification of Nd3+ doped TiO2 hybrid nanoparticles were carried out with n-butylamine as surface modifier under mild hydrothermal conditions. The modified nanoparticles obtained were characterized by Powder XRD, FTIR, DLS, TEM, BET surface area, zeta potential and UV-Vis Spectroscopy. The characterization results indicated better morphology, particle size distribution and low agglomeration of the nanoparticles synthesized. It was found that photodegradation of wastewater using surface modified neodymium doped TiO2 nanoparticles was more compared to pure TiO2, which can be attributed to the doping and modification with n-butylamine.

Distributed algorithms for edge dominating sets

An edge dominating set for a graph G is a set D of edges such that each edge of G is in D or adjacent to at least one edge in D. This work studies deterministic distributed approximation algorithms for finding minimum-size edge dominating sets. The focus is on anonymous port-numbered networks: there are no unique identifiers, but a node of degree d can refer to its neighbours by integers 1, 2, ..., d. The present work shows that in the port-numbering model, edge dominating sets can be approximated as follows: in d-regular graphs, to within 4 − 6/(d + 1) for an odd d and to within 4 − 2/d for an even d; and in graphs with maximum degree Δ, to within 4 − 2/(Δ − 1) for an odd Δ and to within 4 − 2/Δ for an even Δ. These approximation ratios are tight for all values of d and Δ: there are matching lower bounds.

Fast distributed approximation algorithms for vertex cover and set cover in anonymous networks

We present a distributed algorithm that finds a maximal edge packing in O(Δ + log* W) synchronous communication rounds in a weighted graph, independent of the number of nodes in the network; here Δ is the maximum degree of the graph and W is the maximum weight. As a direct application, we have a distributed 2-approximation algorithm for minimum-weight vertex cover, with the same running time. We also show how to find an f-approximation of minimum-weight set cover in O(f2k2 + fk log* W) rounds; here k is the maximum size of a subset in the set cover instance, f is the maximum frequency of an element, and W is the maximum weight of a subset. The algorithms are deterministic, and they can be applied in anonymous networks.

Analysing local algorithms in location-aware quasi-unit-disk graphs

A local algorithm with local horizon r is a distributed algorithm that runs in r synchronous communication rounds; here r is a constant that does not depend on the size of the network. As a consequence, the output of a node in a local algorithm only depends on the input within r hops from the node. We give tight bounds on the local horizon for a class of local algorithms for combinatorial problems on unit-disk graphs (UDGs). Most of our bounds are due to a refined analysis of existing approaches, while others are obtained by suggesting new algorithms. The algorithms we consider are based on network decompositions guided by a rectangular tiling of the plane. The algorithms are applied to matching, independent set, graph colouring, vertex cover, and dominating set. We also study local algorithms on quasi-UDGs, which are a popular generalisation of UDGs, aimed at more realistic modelling of communication between the network nodes. Analysing the local algorithms on quasi-UDGs allows one to assume that the nodes know their coordinates only approximately, up to an additive error. Despite the localisation error, the quality of the solution to problems on quasi-UDGs remains the same as for the case of UDGs with perfect location awareness. We analyse the increase in the local horizon that comes along with moving from UDGs to quasi-UDGs.

A heuristic clustering algorithm using union of overlapping pattern-cells

Relative geometric arrangements of the sample points, with reference to the structure of the imbedding space, produce clusters. Hence, if each sample point is imagined to acquire a volume of a small M-cube (called pattern-cell), depending on the ranges of its (M) features and number (N) of samples; then overlapping pattern-cells would indicate naturally closer sample-points. A chain or blob of such overlapping cells would mean a cluster and separate clusters would not share a common pattern-cell between them. The conditions and an analytic method to find such an overlap are developed. A simple, intuitive, nonparametric clustering procedure, based on such overlapping pattern-cells is presented. It may be classified as an agglomerative, hierarchical, linkage-type clustering procedure. The algorithm is fast, requires low storage and can identify irregular clusters. Two extensions of the algorithm, to separate overlapping clusters and to estimate the nature of pattern distributions in the sample space, are also indicated.

Hybrid Solar Cooking

In the existing traditional solar cookers, the cooking is performed near the collector which may be at an inconvenient location for cooking purposes. This paper proposes a hybrid solar cooking system where the solar energy is brought to the kitchen. The energy source is a combination of the solar thermal energy and the Liquefied Petroleum Gas (LPG) that is very common in kitchens. The solar thermal energy is transferred to the kitchen by means of a circulating fluid like oil. The transfer of solar heat is a two fold process wherein the energy from the collector is transferred first to an intermediate energy storage tank and then the energy is subsequently transferred from the tank to the cooking load. There are three parameters that are controlled in order to maximize the energy transfer from the collector to the load viz. the fluid flow rate from collector to tank, fluid flow rate from tank to load and the diameter of the pipes. The entire system is modeled using the bond graph approach. This paper discusses the implementation of such a system.

Turbulent flow computations on a hybrid cartesian point distribution using meshless solver LSFD-U

This paper may be considered as a sequel to one of our earlier works pertaining to the development of an upwind algorithm for meshless solvers. While the earlier work dealt with the development of an inviscid solution procedure, the present work focuses on its extension to viscous flows. A robust viscous discretization strategy is chosen based on positivity of a discrete Laplacian. This work projects meshless solver as a viable cartesian grid methodology. The point distribution required for the meshless solver is obtained from a hybrid cartesian gridding strategy. Particularly considering the importance of an hybrid cartesian mesh for RANS computations, the difficulties encountered in a conventional least squares based discretization strategy are highlighted. In this context, importance of discretization strategies which exploit the local structure in the grid is presented, along with a suitable point sorting strategy. Of particular interest is the proposed discretization strategies (both inviscid and viscous) within the structured grid block; a rotated update for the inviscid part and a Green-Gauss procedure based positive update for the viscous part. Both these procedures conveniently avoid the ill-conditioning associated with a conventional least squares procedure in the critical region of structured grid block. The robustness and accuracy of such a strategy is demonstrated on a number of standard test cases including a case of a multi-element airfoil. The computational efficiency of the proposed meshless solver is also demonstrated. (C) 2010 Elsevier Ltd. All rights reserved.

Algorithms for Exact Structure Discovery in Bayesian Networks

Bayesian networks are compact, flexible, and interpretable representations of a joint distribution. When the network structure is unknown but there are observational data at hand, one can try to learn the network structure. This is called structure discovery. This thesis contributes to two areas of structure discovery in Bayesian networks: space--time tradeoffs and learning ancestor relations. The fastest exact algorithms for structure discovery in Bayesian networks are based on dynamic programming and use excessive amounts of space. Motivated by the space usage, several schemes for trading space against time are presented. These schemes are presented in a general setting for a class of computational problems called permutation problems; structure discovery in Bayesian networks is seen as a challenging variant of the permutation problems. The main contribution in the area of the space--time tradeoffs is the partial order approach, in which the standard dynamic programming algorithm is extended to run over partial orders. In particular, a certain family of partial orders called parallel bucket orders is considered. A partial order scheme that provably yields an optimal space--time tradeoff within parallel bucket orders is presented. Also practical issues concerning parallel bucket orders are discussed. Learning ancestor relations, that is, directed paths between nodes, is motivated by the need for robust summaries of the network structures when there are unobserved nodes at work. Ancestor relations are nonmodular features and hence learning them is more difficult than modular features. A dynamic programming algorithm is presented for computing posterior probabilities of ancestor relations exactly. Empirical tests suggest that ancestor relations can be learned from observational data almost as accurately as arcs even in the presence of unobserved nodes.