Efficient Fault-Tolerant Topology Reconfiguration Using a Maximum Flow Algorithm

Augmenting path algorithms, first introduced by Ford and Fulkerson (Ford, L. R., D. R. Fulkerson. 1962. Flows in Networks. Princeton University Press, Princeton, N.J.), are widely used in optimization. Examples include Schönsleben's polymatroid intersection algorithm (Schönsleben, P. 1980. Ganzzahlige polymatroid-intersection-algorithmen. Ph.D. thesis, Eidgenössischen Technischen Hochschule, Zürich.), the maximum polymatroidal network flow algorithm of Lawler and Martel (Lawler, E. L., C. U. Martel. 1982. Computing maximal polymatroidal network flows. Math. Oper. Res. 7 334–347.), Frank's algorithm for the Edmonds–Giles polyhedron (Frank, A. 1984. Finding feasible vectors of Edmonds-Giles polyhedra. J. Combin. Theory Ser. B 36 221-239.) and Cunningham's algorithm for testing membership in matroid polyhedra (Cunningham, H. W. 1984. Testing membership in matroid polyhedra. J. Combin. Theory Ser. B 36 161–188.). Here we give an order of magnitude improvement for the above algorithms by using an approach analogous to that of Dinits’ maximum flow algorithm (Dinits, E. A. 1970. Algorithm for solution of a problem of maximum flow in a network with power estimation. Soviet Math. Dokl. 11 1277–1280.).

The bulk power system is one of the largest man-made networks and its size makes control an extremely difficult task. This paper presents a method to control a power network using UPFCs set to levels determined by a maximum flow (max-flow) algorithm. The graph-theory-based max-flow is applied to the power system for UPFC placement and scheduling. A distributed version of max-flow is described to coordinate the actions of the UPFCs distributed in a power network. Two sample power systems were tested using max-flow for UPFC placement and settings. The resulting system characteristics are examined over all single-line contingencies and the appropriateness of the maximum flow algorithm for power flow control is discussed.

The aerial show of 1,218 drones in the Pyeongchang Winter Olympics was realized by animators drawing up the show with 3D design software in advance and by a central computer determining and assigning onsite which drone will play the role of which pixel in the animation. Manual creation of an animation in which a thousand drones move in harmony without collision is an expensive and difficult task. Thus, we propose a drone simulator to automate this process: given initial and final images, the system samples a given number of initial and final locations of drones, computes collision-free drone paths automatically (each starting from an initial location and arriving at a final location), and visualizes the results as a video. The set of drone paths is optimal in terms of the last arrival time, which is a desirable feature for drone paths.BR We propose two methods of computing the paths: a two-phase algorithm with a collision-removal modification and a single-phase algorithm for cost optimization. The former obtains paths by running a maximum flow algorithm and modifies them to be collision-free.BROn the other hand, the latter computes collision-free paths directly by running a minimum cost maximum flow algorithm with a carefully designed cost assignment. Both sets of output paths have a minimum last arrival time. The single-phase method needs more time than the two-phase method but gives much better values of stretch factor (the ratio of path length to the Euclidean distance between the initial and final locations). This trade-off between computation time and stretch factor is revealed empirically in the performance comparison of the two methods.

Due to the ever-increasing density and complexity of integrated circuits, FPGA prototyping has become a necessary part of the design process. To enhance observability into these devices, designers commonly insert trace-buffers to record and expose the values on a small subset of internal signals during live operation to help root-cause errors. For dense designs, routing congestion will restrict the number of signals that can be connected to these trace-buffers. In this work, we apply optimal network flow graph algorithms, a well studied technique, to the problem of transporting circuit signals to embedded trace-buffers for observation. Specifically, we apply a minimum cost maximum flow algorithm to gain maximum signal observability with minimum total wirelength. We showcase our techniques on both theoretical FPGA architectures using VPR, and with a Xilinx Virtex6 device, finding that for the latter, over 99.6% of all spare RAM inputs can be reclaimed for tracing across four large benchmarks.

A new maximal flow algorithm for solving optimization problems with linguistic capacities and flows

A fault tolerant massively parallel processing architecture

In this paper, we focus on the dynamic traffic assignment (DTA) problem on large-scale expressway networks especially under the condition of traffic events (such as severe weather, large traffic accidents etc.). We formulate the expressway network DTA problem as a nonconvex optimization problem. Considering the difficulty of solving the problem, we put forward an approximate solution algorithm based on the network flow theory with high computational efficiency and strong applicability. Specifically, a machine learning approach and a series of customization strategies of network flow model (including multi-origin and multidestination split, flow discretization and parallel edges addition methods) are proposed to transform the DTA problem into a resoluble network flow problem. After that, in order to improve the operational efficiency of an expressway network after traffic events occurring, the proposed network flow based two-layer DTA model (NTDM) is separated into two parts-traffic flow limitation model based on maximum flow algorithm and traffic assignment model based on minimum cost flow algorithm. Experiments on real expressway network data in some provinces of China show that our method can make a significant 26.03% reduction in saturation rate in a particular scenario. In efficiency test, the NTDM is at least 600 times faster than the traditional analytic method in a network with thousands of nodes.

We present an algorithm that computes exact maximum flows and minimum-cost flows on directed graphs with m edges and polynomially bounded integral demands, costs, and capacities in m 1+ o (1) time. Our algorithm builds the flow through a sequence of m 1+ o (1) approximate undirected minimum-ratio cycles, each of which is computed and processed in amortized m o (1) time using a new dynamic graph data structure. Our framework extends to algorithms running in m 1+ o (1) time for computing flows that minimize general edge-separable convex functions to high accuracy. This gives almost-linear time algorithms for several problems including entropy-regularized optimal transport, matrix scaling, p -norm flows, and p -norm isotonic regression on arbitrary directed acyclic graphs.

Predictive business process monitoring aims at providing the predictions about running instances by analyzing logs of completed cases of a business process. Recently, a lot of research focuses on increasing productivity and efficiency in a business process by forecasting potential problems during its executions. However, most of the studies lack suggesting concrete actions to improve the process. They leave it up to the subjective judgment of a user. In this paper, we propose a novel method to connect the results from predictive business process monitoring to actual business process improvements. More in detail, we optimize the resource allocation in a non-clairvoyant online environment, where we have limited information required for scheduling, by exploiting the predictions. The proposed method integrates offline prediction model construction that predicts the processing time and the next activity of an ongoing instance using LSTM with online resource allocation that is extended from the minimum cost and maximum flow algorithm. To validate the proposed method, we performed experiments using an artificial event log and a real-life event log from a global financial organization.

<p>In this paper, we solve this problem of finding maximum flow in extended mixed network by Revised preflow-push methods of Goldberg This algorithm completely different algorithm postflow-pull in [15]. However, we share some common theory with [15].</p>

We study the class of preflow push algorithms recently introduced by Goldberg and Tarjan for solving the maximum network flow problem on a weighted digraph G(V,E). We improve Goldberg and Tarjanis O(n3) time bound for the maximum distance preflow push algorithm to O(n2√m) and show that this bound is tight by constructing a parametrized worst case network. We then develop the maximal excess preflow push algorithm and show that it achieves a bound of O(n2√m) pushes. Based on this we develop a maximum network flow algorithm for the synchronous distributed model of computation that uses at most O(n2√m) messages and O(n2) time, thereby improving upon the best previously known algorithms for this model.

In this paper, A comparative study is made on the determination of maximum flow in a network by Maximal Flow Algorithm and Bounded Variable Simplex Method. We have introduced a technique to find the route of a flow in any iteration of the bounded variable simplex algorithm. Dhaka Univ. J. Sci. 61(1): 19-26, 2013 (January) DOI: http://dx.doi.org/10.3329/dujs.v61i1.15091

We provide a comprehensive study on network flow problems with arc reversal capabilities. The problem is to identify the arcs to be reversed in order to achieve a maximum flow from source(s) to sink(s). The problem finds its applications in emergency transportation management, where the lanes of a road network could be reversed to enable flow in the opposite direction. We study several network flow problems with the arc reversal capability and discuss their complexity. More specifically, we discuss the polynomial time algorithms for the maximum dynamic flow problem with arc reversal capability having a single source and a single sink, and for the maximum (static) flow problem. The presented algorithms are based on graph transformations and reductions to polynomially solvable flow problems. In addition, we show that the quickest transshipment problem with arc reversal capability and the problem of minimizing the total cost resulting from arc switching costs are \(\mathcal{NP}\) -hard.

A fast algorithm for maximum integral two-commodity flow in planar graphs

Massive spatiotemporal data scheduling in a cloud environment play a significant role in real-time visualization. Existing methods focus on preloading, prefetching, multithread processing and multilevel cache collaboration, which waste hardware resources and cannot fully meet the different scheduling requirements of diversified tasks. This paper proposes an optimized spatiotemporal data scheduling method based on maximum flow for multilevel visualization tasks. First, the spatiotemporal data scheduling framework is designed based on the analysis of three levels of visualization tasks. Second, the maximum flow model is introduced to construct the spatiotemporal data scheduling topological network, and the calculation algorithm of the maximum data flow is presented in detail. Third, according to the change in the data access hotspot, the adaptive caching algorithm and maximum flow model parameter switching strategy are devised to achieve task-driven spatiotemporal data optimization scheduling. Compared with two typical methods of first come first serve (FCFS) and priority scheduling algorithm (PSA) by simulating visualization tasks at three levels, the proposed maximum flow scheduling (MFS) method has been proven to be more flexible and efficient in adjusting each spatiotemporal data flow type as needed, and the method realizes spatiotemporal data flow global optimization under limited hardware resources in the cloud environment.