Computing All Small Cuts in an Undirected Network

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.).

With an increasing number of processing elements (PEs) integrated on a single chip, fault-tolerant techniques are critical to ensure the reliability of such complex systems. In current reconfigurable architectures, redundant PEs are utilized for fault tolerance. In the presence of faulty PEs, the physical topologies of various chips may be different, so the concept of virtual topology from network embedding problem has been used to alleviate the burden for the operating systems. With limited hardware resources, how to reconfigure a system into the most effective virtual topology such that the maximum repair rate can be reached presents a significant challenge. In this article, a new approach using a maximum flow (MF) algorithm is proposed for an efficient topology reconfiguration in reconfigurable architectures. In this approach, topology reconfiguration is converted into a network flow problem by constructing a directed graph; the solution is then found by using the MF algorithm. This approach optimizes the use of spare PEs with minimal impacts on area, throughput, and delay, and thus it significantly improves the repair rate of faulty PEs. In addition, it achieves a polynomial reconfiguration time. Experimental results show that compared to previous methods, the MF approach increases the probability to repair faulty PEs by up to 50% using the same redundant resources. Compared to a fault-free system, the throughput only decreases by less than 2.5% and latency increases by less than 4%. To consider various types of PEs in a practical application, a cost factor is introduced into the MF algorithm. An enhanced approach using a minimum-cost MF algorithm is further shown to be efficient in the fault-tolerant reconfiguration of heterogeneous reconfigurable architectures.

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.

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

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.

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.

<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>

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.

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

Gomory and Hu proved that the [Formula: see text] maxflow problems in an undirected network have at most n − 1 distinct solution values. We generalize their theorems in several ways. An interesting special case is that the O(n4) 2-commodity maxflow problems on an undirected network have at most [Formula: see text] distinct solution values. These results follow from general theorems on the number of distinct solution values to sets of optimization problems. We then show how the solutions can be compactly represented by a basis of the solution matrix A, where aij = 1 if solution j is feasible for problem i, and aij = 0 otherwise. For the special case of the 2-cut problem we also show how to construct such a representation efficiently.

With the development of social economy, China’s foreign trade gradually develops into a green and low-carbon development, based on this situation, this paper studies the transformation and upgrading of China’s foreign trade from the perspective of logistics and transportation. This article analyzes various factors that affect the efficiency of foreign trade logistics distribution and the widely used methods of logistics distribution, and gives a logistics and distribution reference model suitable for the current situation of e-commerce in our country, proposes a reference model of e-commerce logistics distribution system based on Internet environment and designs a suitable transportation route selection model and algorithm for distribution center. After testing, the algorithm in this paper is suitable for practical work, and the algorithm has important reference value for designing and improving the logistics and distribution system and improving the delivery efficiency.

Fingerprint matching is the most important part in the field of fingerprint recognition. In this paper, a novel fingerprint matching algorithm based on the probabilistic graphical model and 3-tree model is proposed. First, minutiae matching problems are considered as a special point-set matching. Fingerprint minutiae are viewed as random variables. Each minutia pairs have some probability to be matched. Second, an algorithm is proposed to generate the graphical model and choose "signal points", which dynamically have corresponding points in other point set. We choose three base minutiae pairs as signal pairs. Third, the model is converted into a Junction Tree. A 3-tree model is built and the potentials of other minutiae pairs are calculated through Junction Tree (J.T.) algorithm. Then we translate the matching problem into the best matching problem of a weighted bipartite graph. Finally, the number of common matching pairs can be got through maximum flow algorithm. The similarity of two fingerprints is evaluated using the number of common matching pairs and the maximal posteriori probability. In order to deal with part-matching problems, we use the smallest convex hull which contains all the matched minutiae. Experiments evaluated on FVC 2004 show both effectiveness and efficiency of our methods.

In this paper, we first describe a constraint generation scheme for probabilistic mixed integer programming problems. Next, we present a decomposition approach to the peak capacity expansion planning of interconnected hydrothermal generating systems, with bounds on the transmission capacity between the regions. The objective is to minimize investments in generating units and interconnection links, subject to constraints on supply reliability. The problem is formulated as a stochastic integer program. The constraint generation scheme, which is similar to Benders decomposition, is applied in the solution of the peak capacity expansion problem. The master problem in this decomposition scheme is an integer program, solved by implicit enumeration. The operating subproblem corresponds to a stochastic network flow problem, and is solved by a maximum flow algorithm and Monte Carlo simulation. The approach is illustrated through a case study involving the expansion of the system of the Brazilian Southeastern region.

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.

This paper focuses on the use of different memory strategies to improve multistart methods. A network design problem in which the costs are given by discrete stepwise increasing cost functions of the capacities installed in the edges is used to illustrate the contributions of adaptive memory and vocabulary building strategies. Heuristics based on shortest path and maximum flow algorithms are combined with adaptive memory in order to obtain an approximate solution to the problem in the framework of a multistart algorithm. Furthermore, a vocabulary building intensification mechanism supported by the resolution of a linear program is also explored. Numerical experiments have shown that the proposed algorithm obtained the best known solutions for some instances in the literature. These results show the contribution of each memory component and the effectiveness of their combination.