Exact Algorithms for B-Bandwidth Problem with Restricted B

The B-BANDWIDTH problem is a decision problem whether the bandwidth of a given graph is smaller than B, and it is NP-complete even if the graph is a small graph class of trees. Cygan and Pilipczuk proposed exponential time and space algorithms for B-BANDWIDTH with n/3 ≤ B where n is the number of vertices. In this paper, we propose two algorithms for the B-BANDWIDTH problem with n/4 ≤ B < n/3. These algorithms are extension of Cygan and Pilipczuk algorithms with restricted B. One of the algorithms takes O∗(4.5n) time and O∗(1.5n) space when n/4 ≤ B < n / 2 log2 1.5, and the other takes O∗(4.77n) time and O∗(1.59n) space when n / 2 log2 1.5 ≤ B < n/3. Our algorithms are fastest O∗(2n) space algorithms for n/4 ≤B < n/3.The 17th Korea-Japan Joint Workshop on Algorithms and Computation, July 13-15, 2014, Okinawa, Japa

3-D Microwave Imaging for Breast Cancer

We introduce a novel microwave imaging technique for breast cancer detection. Our approach provides a one-pass inverse image solution, which is completely new and unprecedented, unrelated to tomography or radar-based algorithms, and unburdened by the optimization toil which lies at the heart of numerical schemes. It operates effectively at a single frequency, without requiring the bandwidth of radar techniques. Underlying this new method is our unique Field Mapping Algorithm (FMA), which transforms electromagnetic fields acquired upon one surface, be it through outright measurement or some auxiliary computation, into those upon another in an exact sense

Reproducibility, accuracy and performance of the Feltor code and library on parallel computer architectures

Feltor is a modular and free scientific software package. It allows developing platform independent code that runs on a variety of parallel computer architectures ranging from laptop CPUs to multi-GPU distributed memory systems. Feltor consists of both a numerical library and a collection of application codes built on top of the library. Its main target are two- and three-dimensional drift- and gyro-fluid simulations with discontinuous Galerkin methods as the main numerical discretization technique. We observe that numerical simulations of a recently developed gyro-fluid model produce non-deterministic results in parallel computations. First, we show how we restore accuracy and bitwise reproducibility algorithmically and programmatically. In particular, we adopt an implementation of the exactly rounded dot product based on long accumulators, which avoids accuracy losses especially in parallel applications. However, reproducibility and accuracy alone fail to indicate correct simulation behaviour. In fact, in the physical model slightly different initial conditions lead to vastly different end states. This behaviour translates to its numerical representation. Pointwise convergence, even in principle, becomes impossible for long simulation times. In a second part, we explore important performance tuning considerations. We identify latency and memory bandwidth as the main performance indicators of our routines. Based on these, we propose a parallel performance model that predicts the execution time of algorithms implemented in Feltor and test our model on a selection of parallel hardware architectures. We are able to predict the execution time with a relative error of less than 25% for problem sizes between 0.1 and 1000 MB. Finally, we find that the product of latency and bandwidth gives a minimum array size per compute node to achieve a scaling efficiency above 50% (both strong and weak)

Multi-capacity bin packing with dependent items and its application to the packing of brokered workloads in virtualized environments

Providing resource allocation with performance predictability guarantees is increasingly important in cloud platforms, especially for data-intensive applications, in which performance depends greatly on the available rates of data transfer between the various computing/storage hosts underlying the virtualized resources assigned to the application. Existing resource allocation solutions either assume that applications manage their data transfer between their virtualized resources, or that cloud providers manage their internal networking resources. With the increased prevalence of brokerage services in cloud platforms, there is a need for resource allocation solutions that provides predictability guarantees in settings, in which neither application scheduling nor cloud provider resources can be managed/controlled by the broker. This paper addresses this problem, as we define the Network-Constrained Packing (NCP) problem of finding the optimal mapping of brokered resources to applications with guaranteed performance predictability. We prove that NCP is NP-hard, and we define two special instances of the problem, for which exact solutions can be found efficiently. We develop a greedy heuristic to solve the general instance of the NCP problem , and we evaluate its efficiency using simulations on various application workloads, and network models.This work was done while author was at Boston University. It was partially supported by NSF CISE awards #1430145, #1414119, #1239021 and #1012798. (1430145 - NSF CISE; 1414119 - NSF CISE; 1239021 - NSF CISE; 1012798 - NSF CISE

Distributed top-k aggregation queries at large

Top-k query processing is a fundamental building block for efficient ranking in a large number of applications. Efficiency is a central issue, especially for distributed settings, when the data is spread across different nodes in a network. This paper introduces novel optimization methods for top-k aggregation queries in such distributed environments. The optimizations can be applied to all algorithms that fall into the frameworks of the prior TPUT and KLEE methods. The optimizations address three degrees of freedom: 1) hierarchically grouping input lists into top-k operator trees and optimizing the tree structure, 2) computing data-adaptive scan depths for different input sources, and 3) data-adaptive sampling of a small subset of input sources in scenarios with hundreds or thousands of query-relevant network nodes. All optimizations are based on a statistical cost model that utilizes local synopses, e.g., in the form of histograms, efficiently computed convolutions, and estimators based on order statistics. The paper presents comprehensive experiments, with three different real-life datasets and using the ns-2 network simulator for a packet-level simulation of a large Internet-style network