https://ink.library.smu.edu.sg/cgi/viewcontent.cgi?article=4273&context=sis_research

Orienteering Problem: A survey of recent variants, solution approaches and applications

THE difficulty of reconciling line spectra with the kinetic theory of gases, has been referred to by Prof. Fitzgerald (NATURE, January 3, p. 221). The following considerations show that it is possible under certain suppositions to have a number of spectral rays with a very restricted number of degrees of freedom. Most of us, I believe, now accept a definite atomic charge of electricity, and if each charge is imagined to be capable of moving along the surface of an atom, it would represent two degrees of freedom. If a molecule is capable of sending out a homogeneous vibration, it means that there must be a definite position of equilibrium of the “electron.” If there are several such positions, the vibrations may take place in several periods. Any one molecule may perform for a certain time a simple periodic oscillation about one position of equilibrium, and owing to some impact the electron may be knocked over into a new position. The vibrations under these circumstances would not be quite homogeneous, but if the electron oscillates about any one position sufficiently long to perform a few thousand oscillations, we should hardly notice the want of homogeneity. Each electron at a given time would only send out vibrations which in our instruments would appear as homogeneous. Each molecule could thus successively give rise to a number of spectral rays, and at any one time the electron in the different molecules would, by the laws of probability, be distributed over all possible positions of equilibrium, so that we should always see all the vibrations which any one molecule of the gas is capable of sending out. The probability of an electron oscillating about one of its positions of equilibrium need not be the same in all cases. Hence a line may be weak not because the vibration has a smaller amplitude, but because fewer molecules give rise to it. The fact that the vibrations of a gas are not quite homogeneous, is borne out by experiment. If impacts become more frequent by increased pressure, we should expect from the above views that the time during which an electron performs a certain oscillation is shortened; hence the line should widen, which is the case. I have spoken, for the sake of simplicity, as if an electron vibrating about one position of equilibrium could only do so in one period. If the forces called into play, by a displacement, depend on the direction of the displacement, there would be two possible frequencies. If the surface is nearly symmetrical, we should have double lines.

/pdf/the-kinetic-theory-of-gases-13lklkm24y.pdf

The Kinetic Theory of Gases

A new definition of distance-based outlier and an algorithm, called HilOut, designed to efficiently detect the top n outliers of a large and high-dimensional data set are proposed. Given an integer k, the weight of a point is defined as the sum of the distances separating it from its k nearest-neighbors. Outlier are those points scoring the largest values of weight. The algorithm HilOut makes use of the notion of space-filling curve to linearize the data set, and it consists of two phases. The first phase provides an approximate solution, within a rough factor, after the execution of at most d + 1 sorts and scans of the data set, with temporal cost quadratic in d and linear in N and in k, where d is the number of dimensions of the data set and N is the number of points in the data set. During this phase, the algorithm isolates points candidate to be outliers and reduces this set at each iteration. If the size of this set becomes n, then the algorithm stops reporting the exact solution. The second phase calculates the exact solution with a final scan examining further the candidate outliers that remained after the first phase. Experimental results show that the algorithm always stops, reporting the exact solution, during the first phase after much less than d + 1 steps. We present both an in-memory and disk-based implementation of the HilOut algorithm and a thorough scaling analysis for real and synthetic data sets showing that the algorithm scales well in both cases.

http://wwwinfo.deis.unical.it/angiulli/papers/angiulli_tkde2005.pdf

Outlier mining in large high-dimensional data sets

Force-directed graph drawing algorithms are widely used for drawing general graphs. However, these methods do not guarantee a sub-quadratic running time in general. We present a new force-directed method that is based on a combination of an efficient multilevel scheme and a strategy for approximating the repulsive forces in the system by rapidly evaluating potential fields. Given a graph G=(V,E), the asymptotic worst case running time of this method is O(|V|log|V|+|E|) with linear memory requirements. In practice, the algorithm generates nice drawings of graphs containing 100000 nodes in less than 5 minutes. Furthermore, it clearly visualizes even the structures of those graphs that turned out to be challenging for some other methods.

/pdf/drawing-large-graphs-with-a-potential-field-based-multilevel-39ka7pn3lj.pdf

Drawing large graphs with a potential-field-based multilevel algorithm

Load-balancing algorithms in cloud computing

Summary: Knowledge of pathogen–host protein interactions is required to better understand infection mechanisms. The pathogen– host interaction search tool (PHISTO) is a web-accessible platform that provides relevant information about pathogen–host interactions (PHIs). It enables access to the most up-to-date PHI data for all pathogen types for which experimentally verified protein interactions with human are available. The platform also offers integrated tools for visualization of PHI networks, graph–theoretical analysis of targeted human proteins, BLAST search and text mining for detecting missing experimental methods. PHISTO will facilitate PHI studies that provide potential therapeutic targets for infectious diseases. Availability: http://www.phisto.org.

/pdf/phisto-pathogen-host-interaction-search-tool-3up70881od.pdf

PHISTO: pathogen–host interaction search tool

Partitioning techniques based on space filling curves have received much recent attention due to their low running time and good load balance characteristics. The basic idea underlying these methods is to order the multidimensional data according to a space filling curve and partition the resulting one dimensional order. However, space filling curves are defined for points that lie on a uniform grid of a particular resolution. It is typically assumed that the coordinates of the points are representable using a fixed number of bits, and the run times of the algorithms depend upon the number of bits used. We present a simple and efficient technique for ordering arbitrary and dynamic multidimensional data using space filling curves and its application to parallel domain decomposition and load balancing. Our technique is based on a comparison routine that determines the relative position of two points in the order induced by a space filling curve. The comparison routine could then be used in conjunction with any parallel sorting algorithm to effect parallel domain decomposition.

/pdf/parallel-domain-decomposition-and-load-balancing-using-space-31ujqd639y.pdf

Parallel domain decomposition and load balancing using space-filling curves

Hyperoctree is a popular data structure for organizing multidimensional point data. The main drawback ofthi s data structure is that its size and the run-time ofo perations supported by it are dependent upon the distribution of the points. Clarkson rectified the distribution-dependency in the size ofh yperoctrees by introducing compressed hyperoctrees. He presents an O(n log n) expected time randomized algorithm to construct a compressed hyperoctree. In this paper, we give three deterministic algorithms to construct a compressed hyperoctree in O(n log n) time, for any fixed dimension d. We present O(log n) algorithms for point and cubic region searches, point insertions and deletions. We propose a solution to the N-body problem in O(n) time, given the tree. Our algorithms also reduce the run-time dependency on the number of dimensions.

Dynamic Compressed Hypertoctrees with Application to the N-Body Problem

The N-body problem is to simulate the motion of N particles under the influence of mutual force fields based on an inverse square law. Greengards algorithm claims to compute the cumulative force on each particle in O(N) time for a fixed precision irrespective of the distribution of the particles. In this paper, we show that Greengards algorithm is distribution dependent and has a lower bound of ­(N log 2 N) in two dimensions and ­(N log 4 N) in three dimensions. We analyze the Greengard and Barnes-Hut algorithms and show that they are unbounded for arbitrary distributions. We also present a truly distribution independent algorithm for the N-body problem that runs in O(N log N) time for any fixed dimension.

Distribution-Independent Hierarchical Algorithmsfor the N-body Problem

The Fast Multipole Method (FMM) is a robust technique for the rapid evaluation of the combined effect of pairwise interactions of n data sources. Parallel computation of the FMM is considered a challenging problem due to the dependence of the computation on the distribution of the data sources, usually resulting in dynamic data decomposition and load balancing problems. In this paper, we present the first provably efficient and distribution-independent parallel algorithm for the FMM on distributed memory parallel computers. Our algorithm does not require any dynamic data decomposition or load balancing step. We present our algorithm in terms of a few basic and well understood primitive operations such as sorting and parallel prefix.

Fatih Erdogan Sevilgen

Papers

PHISTO: pathogen–host interaction search tool

Parallel domain decomposition and load balancing using space-filling curves

Dynamic Compressed Hypertoctrees with Application to the N-Body Problem

Distribution-Independent Hierarchical Algorithmsfor the N-body Problem

A provably optimal, distribution-independent parallel fast multipole method