A fast and simple algorithm for the maximum flow problem

Includes bibliographical references (p. 31-33)

Maximum Flow on Highly Dynamic Graphs

Recent advances in dynamic graph processing have enabled the analysis of highly dynamic graphs with change at rates as high as millions of edge changes per second. Solutions in this domain, however, have been demonstrated only for relatively simple algorithms like PageRank, breadth-first search, and connected components. Expanding beyond this, we explore the maximum flow problem, a fundamental, yet more complex problem, in graph analytics. We propose a novel, distributed algorithm for max-flow on dynamic graphs, and implement it on top of an asynchronous vertex-centric abstraction. We show that our algorithm can process both additions and deletions of vertices and edges efficiently at scale on fast-evolving graphs, and provide a comprehensive analysis by evaluating, in addition to throughput, two criteria that are important when applied to real-world problems: result latency and solution stability

Airfilm cooling through laser drilled holes

One of the major problems in enhancing the specific work output and efficiency in gas turbines is the maximum possible value of the turbine inlet temperature due to blade material properties. To increase this maximum, turbine blades need to be cooled (internal or external), which is usually done by compressor air. Based on its high cooling efficiency, film cooling is one of the major cooling techniques used, especially for the hottest blades. In film cooling cold air is injected into the boundary layer through small nozzles in the blade surface. Impingement of the jets into the (laminar) boundary layer flow is essentially three-dimensional. The collision of the laminar jet with the boundary layer flow produces a local turbulent shear layer and changes the local heat transfer to the blade (when poorly constructed it may even increase the local heat transfer). In this project we have studied local grid refinement methods and their application to flow problems in general and to air film cooling in particular. Local defect correction (LDC) is an iterative method for solving pure boundary value or initial-boundary value problems on composite grids. It is based on using simple data structures and simple discretization stencils on uniform or tensor-product grids. Fast solution techniques exist for solving the system of equations resulting from discretization on a structured grid. We have combined the standard LDC method with high order finite differences by using a new strategy of defect calculation. Numerical results prove high accuracy and fast convergence of the proposed method. We made a review of boundary conditions for compressible flows. Since we would like to use local grid refinement for such flow problems, we studied the spreading of an acoustic pulse. For this model problem we introduced local grid refinement and made a series of tests in order to see if the artificial boundary conditions introduced for the local fine grid cause any reflections of the acoustic waves. The numerical techniques developed have been used to study film cooling. Because this problem concerns the interaction between a main flow and a jet, we also propose a domain decomposition algorithm in order to supply proper boundary conditions for the cooling jet. This domain decomposition combines a structured DNS flow solver for the problem of interest with an unstructured solver for the flow in the cooling nozzle. Additionally we implemented local grid refinement for the flow problem to save computational costs

Alternate path routing algorithm for traffic engineering in the Internet

Data flowing through the internet continues to grow every year. Increase in traffic demands increase in bandwidth. But bandwidth1 does not grow as fast as the traffic. This leads to congestion in the network and performance degradation. One way to avoid this problem is to use efficient routing algorithm that efficiently maps the flow of data onto the network; The most often used routing algorithm in the internet is the shortest path algorithm (Dijkstra\u27s algorithm). This algorithm is simple and easy to implement. But this algorithm leads to over-utilization of part of the network, while the other part remains under-utilized. In this study, a new algorithm to route traffic efficiently is proposed. This algorithm is as simple as the Dijkstra\u27s algorithm, but routes traffic more efficiently and reduces the discrepancy in the network utilization; The proposed algorithm identifies the critical links in the network that are responsible for congestion and finds additional routes in a network which do not contain critical links. The traffic in the network is routed via paths that have no or least number of critical links. This avoids congestion in the critical links and increases the performance of the network. The performance of the algorithm is compared with the shortest path (Dijkstra\u27s) algorithm. The simulation is done using myNetSim which was developed for this thesis; 1Bandwidth of a link is defined as the maximum traffic that the link can accommodate at any given time. In other words it is the capacity of the link

Combinatorial Continuous Maximal Flows

Maximum flow (and minimum cut) algorithms have had a strong impact on computer vision. In particular, graph cuts algorithms provide a mechanism for the discrete optimization of an energy functional which has been used in a variety of applications such as image segmentation, stereo, image stitching and texture synthesis. Algorithms based on the classical formulation of max-flow defined on a graph are known to exhibit metrication artefacts in the solution. Therefore, a recent trend has been to instead employ a spatially continuous maximum flow (or the dual min-cut problem) in these same applications to produce solutions with no metrication errors. However, known fast continuous max-flow algorithms have no stopping criteria or have not been proved to converge. In this work, we revisit the continuous max-flow problem and show that the analogous discrete formulation is different from the classical max-flow problem. We then apply an appropriate combinatorial optimization technique to this combinatorial continuous max-flow CCMF problem to find a null-divergence solution that exhibits no metrication artefacts and may be solved exactly by a fast, efficient algorithm with provable convergence. Finally, by exhibiting the dual problem of our CCMF formulation, we clarify the fact, already proved by Nozawa in the continuous setting, that the max-flow and the total variation problems are not always equivalent.Comment: 26 page

Competent genetic-evolutionary optimization of water distribution systems

A genetic algorithm has been applied to the optimal design and rehabilitation of a water distribution system. Many of the previous applications have been limited to small water distribution systems, where the computer time used for solving the problem has been relatively small. In order to apply genetic and evolutionary optimization technique to a large-scale water distribution system, this paper employs one of competent genetic-evolutionary algorithms - a messy genetic algorithm to enhance the efficiency of an optimization procedure. A maximum flexibility is ensured by the formulation of a string and solution representation scheme, a fitness definition, and the integration of a well-developed hydraulic network solver that facilitate the application of a genetic algorithm to the optimization of a water distribution system. Two benchmark problems of water pipeline design and a real water distribution system are presented to demonstrate the application of the improved technique. The results obtained show that the number of the design trials required by the messy genetic algorithm is consistently fewer than the other genetic algorithms