An approximation algorithm for discrete minimum cost flows over time problem

Dynamic network models are widely employed for system analysis and performance evaluation of computer and communication systems. In dynamic networks each arc is weighted with a capacity and a transit time. The former is the maximum amount of flow that can travel through the arc per unit time, the later is the time period needed for flow to travel through the arc. In this article, an additional weight operation probability, is assigned to each arc to note the capability of the arc's successful transition. The performance of dynamic networks is defined by the probability that the maximum dynamic flow from source to sink within required time horizon is no less than specified threshold. To the best of our knowledge, no existing article had considered dynamic flow and network reliability simultaneously. Based on facts that there is always a maximum dynamic flow among the temporally repeated flows and the maximum temporally repeated flow can be obtained via an equivalent minimum cost maximum flow problem, we present a pioneering algorithm to compute performance of dynamic networks by solving minimum cost maximum flow and two-terminal capacity reliability at the same time.

A theoretical and experimental study of a new algorithm for minimum cost flow in dynamic graphs

In this paper, we present a new strongly polynomial time algorithm for the minimum cost flow problem, based on a refinement of the Edmonds-Karp scaling technique. Our algorithm solves the uncapacitated minimum cost flow problem as a sequence of O(n log n) shortest path problems on networks with n nodes and m arcs and runs in O(n log n(m + n log n)) time. Using a standard transformation, this approach yields an O(m log n(m + n log n)) algorithm for the capacitated minimum cost flow problem. This algorithm improves the best previous strongly polynomial time algorithm, due to Z. Galil and E. Tardos, by a factor of n2/m. Our algorithm for the capacitated minimum cost flow problem is even more efficient if the number of arcs with finite upper bounds, say m′, is much less than m. In this case, the running time of the algorithm is O((m′ + n) log n(m + n log n)).

<div class="htmlview paragraph">Recently, the control of traffic flow has been proposed using several types of criteria (e.g. minimum-time control, minimum fuel control and so on). Most recently, an environmental noise pollution problem caused by the road traffic is being aggravated more and more by the consolidation and expansion of roadway system particularly in urban areas. However, the objective of this paper is to control road traffic flow by regulating traffic noise propagation in an urban area in Cairo city. The results of traffic noise prediction obtained by trending of the experimental data collecting by systematic noise measurement and the evaluation of the traffic noise which is in close connection with physical parameters of traffic flow and noise propagation characteristics is presented. The analysis of road traffic flow noise control is based on the mixed integer non-linear programming technique, where the optimal control strategy is used. The results indicate that significant information gained for controlling road traffic in urban areas.</div>

Given a directed graph G = (N,A) with arc capacities u and a minimum cost flow problem defined on G, the capacity inverse minimum cost flow problem is to find a new capacity vector u' for the arc set A such that a given feasible flow x' is optimal with respect to the modified capacities. Among all capacity vectors u' satisfying this condition, we would like to find one with minimum ||u' - u|| value. We consider two distance measures for ||u' - u||, rectilinear and Chebyshev distances. By reduction from the feedback arc set problem we show that the capacity inverse minimum cost flow problem is NP-hard in the rectilinear case. On the other hand, it is polynomially solvable by a greedy algorithm for the Chebyshev norm. In the latter case we propose a heuristic for the bicriteria problem, where we minimize among all optimal solutions the number of affected arcs. We also present computational results for this heuristic.

The problem of high similarity in attack data leading to unsatisfactory detection results of air traffic control network security attack behavior is addressed. This article designs a new clustering detection method for air traffic control network security attack behavior. Set the characteristic state of air traffic control network security attack behavior, obtain the set of air traffic control network security attack behavior characteristics through recursive feature addition method, and extract the characteristics of air traffic control network security attack behavior by determining the degree of feature criticality. Calculate the expected information gain and entropy value of feature data, determine the information gain of feature data, and reduce the interference of similar feature data. Introduce an automatic encoder in artificial intelligence algorithms to encode and decode the characteristics of air traffic control network security attack behavior, and achieve dimensionality reduction processing of air traffic control network security attack behavior data. Based on the above processing, a Unsupervised learning algorithm for clustering detection of air traffic control network security attacks is designed. Firstly, determine the distance between clustering clusters of air traffic control network security attack behavior characteristics, calculate the clustering threshold, and construct the initial clustering center. Then, recalculate the new mean of all feature objects in each cluster as the new cluster center point. Secondly, traverse all objects in the clustering cluster of air traffic control network security attack behavior feature data. Finally, clustering detection of air traffic control network security attack behavior is completed through the calculation of the objective function. The experiment takes three sets of experimental attack behavior datasets as the test subjects, with detection rate, false detection rate, and recall rate as the test indicators, and selects three similar methods for comparative testing. The experimental results show that the detection rate of the proposed method remains around 98%, the false detection rate remains below 1%, and the recall rate is above 97%. It has been proven that the proposed method can improve the detection performance of air traffic control network security attack behavior.

An introduction to dynamic generative networks: Minimum cost flow

In this work, we contribute a parallel implementation of the network simplex algorithm that is used for the solution of minimum cost flow problem. In the network simplex algorithm, finding an entering arc requires searching through many arcs to decide which one should be included in the spanning tree solution on the next iteration. We propose finding the entering arc in parallel as it often takes the majority of the execution time. A usual strategy is to pick the arc violating the optimality the most out of all possible candidates. Scanning all arcs can take quite some time, so it is common to consider only a fixed number of arcs which is referred as the block search pivoting rule. Arc scans can easily be done in parallel to find the best candidate as the calculations are independent of each other. We used shared memory parallelism using OpenMP along with vectorization using AVX instructions. We also tried adjusting block sizes to increase the parallel portion of the algorithm. Our dataset consists of various natural and synthetic graphs with sizes up to a billion arc. Our experiments show speedups up to four are possible, though they are typically lower.

Developing a polynomial time primal network simplex algorithm for the minimum cost flow problem has been a long standing open problem. In this paper, we develop one such algorithm that runs in O(min(n 2m lognC, n 2m2 logn)) time, wheren is the number of nodes in the network,m is the number of arcs, andC denotes the maximum absolute arc costs if arc costs are integer and ∞ otherwise. We first introduce a pseudopolynomial variant of the network simplex algorithm called the “premultiplier algorithm”. We then develop a cost-scaling version of the premultiplier algorithm that solves the minimum cost flow problem in O(min(nm lognC, nm 2 logn)) pivots. With certain simple data structures, the average time per pivot can be shown to be O(n). We also show that the diameter of the network polytope is O(nm logn).

Decision support for truckload carriers in one-shot combinatorial auctions

The author describes a formulation of National Airspace System (NAS) traffic management problem as a multicommodity minimum cost flow problem over a network in space-time. It is a formulation of the multidestination delay minimization problem of managing traffic in the NAS. The model's potential for improving over present practice is described in terms of six assumptions of present practice. The space-time network model can address uncertainty in capacity values, restrictive airways capacities, and hubbing. The minimum cost flow formulation further assumes that attempted entries into the system are deterministic, not Poisson, and that actual entries are controllable. The formulation specifically allows dynamic capacities and possesses good potential for short execution time. >

It is known that minimum cost flow problems can be solved by successive augmentations along shortest paths. In this paper the issues of implementing shortest path algorithms in this context are examined. Of particular interest is the dynamic topology that the flow networks exhibit. We develop a network generator capable of emulating such topology. Strategies for exploiting the special structures in such networks are discussed. A set of 9000 test problems is offered, from which a particular strategy/algorithm combination is shown to consistently produce superior results when compared to the other combinations.

Physarum polycephalum (true slime mold) has recently emerged as a fascinating example of biological computation through morphogenesis. Despite being a single cell organism, experiments have observed that through its growth process, the Physarum is able to solve various minimum cost flow problems. This paper analyzes a mathematical model of the Physarum growth dynamics. We show how to encode general linear programming (LP) problems as instances of the Physarum. We prove that under the growth dynamics, the Physarum is guaranteed to converge to the optimal solution of the LP. We further derive an efficient discrete algorithm based on the Physarum model, and experimentally verify its performance on assignment problems.KeywordsAssignment ProblemLinear Program ProblemShort Path ProblemSlime MoldPhysarum PolycephalumThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We address the energy-efficient data redistribution problem in data intensive sensor networks (DISNs). The key question in sensor networks with large volumes of sensory data is how to redistribute the data efficiently under limited storage and energy constraints at the sensor nodes. The goal of the redistribution scheme is to minimize the energy consumption during the process, while guaranteeing full utilization of the distributed storage capacity in the DISNs. We formulate this problem as a minimum cost flow problem, which can be solved optimally. However, the optimal solution's centralized nature makes it unsuitable for large-scale distributed sensor networks. We thus design a distributed algorithm for the data redistribution problem which performs very close to the optimal, and compare its performance with various intuitive heuristics. Our proposed algorithm relies on potential function based computations, incurs limited message and computational overhead at both the sensor nodes and data generator nodes, and is easily implementable in a distributed manner. We analytically show the convergence of our algorithm, and demonstrate its near-optimal performance and scalability under various network scenarios considered. Finally, we implement our distributed algorithm in TinyOS and evaluate it using TOSSIM simulator, and show that it outperforms EnviroStore, the only existing scheme for data redistribution in sensor networks, in both solution quality and overhead messages.

A grid-based coverage approach for target tracking in hybrid sensor networks