Oblivious buy-at-bulk network design algorithms

Large-scale networks such as the Internet has emerged as arguably the most complex distributed communication network system. The mere size of such networks and all the various applications that run on it brings a large variety of challenging problems. Similar problems lie in any network - transportation, logistics, oil/gas pipeline etc where efficient paths are needed to route the flow of demands. This dissertation studies the computation of efficient paths from the demand sources to their respective destination(s). We consider the buy-at-bulk network design problem in which we wish to compute efficient paths for carrying demands from a set of source nodes to a set of destination nodes. In designing networks, it is important to realize economies of scale. This is can be achieved by aggregating the flow of demands. We want the routing to be oblivious: no matter how many source nodes are there and no matter where they are in the network, the demands from the sources has to be routed in a near-optimal fashion. Moreover, we want the aggregation function f to be unknown, assuming that it is a concave function of the total flow on the edge. The total cost of a solution is determined by the amount of demand routed through each edge. We address questions such as how we can (obliviously) route flows and get competitive algorithms for this problem. We study the approximability of the resulting buy-at-bulk network design problem. Our aim is to _x000C_find minimum-cost paths for all the demands to the sink(s) under two assumptions: (1) The demand set is unknown, that is, the number of source nodes that has demand to send is unknown. (2) The aggregation cost function at intermediate edges is also unknown. We consider di_x000B_fferent types of graphs (doubling-dimension, planar and minor-free) and provide approximate solutions for each of them. For the case of doubling graphs and minor-free graphs, we construct a single spanning tree for the single-source buy-at-bulk network design problem. For the case of planar graphs, we have built a set of paths with an asymptotically tight competitive ratio

Split and join: strong partitions and Universal Steiner trees for graphs

We study the problem of constructing universal Steiner trees for undirected graphs. Given a graph G and a root node r, we seek a single spanning tree T of minimum stretch, where the stretch of T is defined to be the maximum ratio, over all subsets of terminals X, of the ratio of the cost of the sub-tree TX that connects r to X to the cost of an optimal Steiner tree connecting X to r. Universal Steiner trees (USTs) are important for data aggregation problems where computing the Steiner tree from scratch for every input instance of terminals is costly, as for example in low energy sensor network applications. We provide a polynomial time UST construction for general graphs with 2O(√log n)-stretch. We also give a polynomial time polylogarithmic-stretch construction for minor-free graphs. One basic building block in our algorithm is a hierarchy of graph partitions, each of which guarantees small strong cluster diameter and bounded local neighbourhood intersections. Our partition hierarchy for minor-free graphs is based on the solution to a cluster aggregation problem that may be of independent interest. To our knowledge, this is the first sub-linear UST result for general graphs, and the first polylogarithmic construction for minor-free graphs

Diagnosing Schizophrenia: A Deep Learning Approach

This paper presents a new method for diagnosing schizophrenia using deep learning. This experiment used a secondary dataset supplied by the National Institute of Health. The experiment analyzes the dataset and identifies schizophrenia using traditional machine learning methods such as logistic regression, support vector machines, and random forest. Finally, a deep neural network with three hidden layers is applied to the dataset. The results show that the neural network model yielded the highest accuracy, suggesting that deep learning may be a feasible method for diagnosing schizophrenia

Identification of low-level point radiation sources using a sensor network

Abstract—Identification of a low-level point radiation source amidst background radiation is achieved by a network of radiation sensors using a two-step approach. Based on measurements from three sensors, the geometric difference triangulation method is used to estimate the location and strength of the source. Then a sequential probability ratio test based on current measurements and estimated parameters is employed to finally decide: (1) the presence of a source with the estimated parameters, or (2) the absence of the source, or (3) the insufficiency of measurements to make a decision. This method achieves specified levels of false alarm and missed detection probabilities, while ensuring a close-to-minimal number of measurements for reaching a decision. This method minimizes the ghost-source problem of current estimation methods, and achieves a lower false alarm rate compared with current detection methods. This method is tested and demonstrated using: (1) simulations, and (2) a test-bed that utilizes the scaling properties of point radiation sources to emulate high intensity ones that cannot be easily and safely handled in laboratory experiments. Index Terms—Point radiation source, detection and localization, sequential probability ratio test. I