Minimum Cost Flow Research Articles

Self-Supervised Association of Wi-Fi Probe Requests Under MAC Address Randomization

Wi-Fi-on devices such as smartphones search for network availability by periodically broadcasting probe requests which encapsulate MAC addresses as device identifiers. To protect identity privacy, modern devices embed random MAC addresses in probe frames, the so-called MAC address randomization. Such randomization disrupts the frame association, inadvertently frustrating identity-oblivious statistical analytic efforts such as people counting and trajectory inference. To address that, we propose <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Cappuccino</b> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> , a novel privacy-preserving approach that captures the association of probe requests under MAC address randomization. Cappuccino first estimates pairwise frame correlation and then associates frames over time. For frame correlation, it employs a self-supervised estimator that jointly considers multiple modalities, i.e., information elements, sequence number, and received signal strength. For multiple frame association, Cappuccino formulates frames as a minimum-cost flow optimization. To the best of our knowledge, this is the first piece of work that leverages self-supervised learning to estimate frame correlation based on multiple modalities and formulates the probe request association problem as the network flow optimization. We have conducted extensive experiments in a leading and crowded shopping mall for more than three months. Cappuccino achieves remarkable performance in terms of V-measure scores ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$&gt;0.85$</tex-math></inline-formula> ).

Robust minimum cost flow problem under consistent flow constraints

The robust minimum cost flow problem under consistent flow constraints (RobMCFequiv ) is a new extension of the minimum cost flow (MCF) problem. In the RobMCFequiv problem, we consider demand and supply that are subject to uncertainty. For all demand realizations, however, we require that the flow value on an arc needs to be equal if it is included in the predetermined arc set given. The objective is to find feasible flows that satisfy the equal flow requirements while minimizing the maximum occurring cost among all demand realizations. In the case of a finite discrete set of scenarios, we derive structural results which point out the differences with the polynomial time solvable MCF problem in networks with integral demands, supplies, and capacities. In particular, the Integral Flow Theorem of Dantzig and Fulkerson does not hold. For this reason, we require integral flows in the entire paper. We show that the RobMCFequiv problem is strongly mathcal {NP}-hard on acyclic digraphs by a reduction from the (3, B2)-Sat problem. Further, we demonstrate that the RobMCFequiv problem is weakly mathcal {NP}-hard on series-parallel digraphs by providing a reduction from Partition. If in addition the number of scenarios is constant, we propose a pseudo-polynomial algorithm based on dynamic programming. Finally, we present a special case on series-parallel digraphs for which we can solve the RobMCFequiv problem in polynomial time.

A Network-Flows-Based Satellite Handover Strategy for LEO Satellite Networks

This letter proposes a satellite handover strategy for the huge low earth orbit (LEO) satellite constellation. As the increasing of the constellation scale and the number of user terminals (UTs), the satellite handover becomes more complicated. Thus, we formulate the network-flows model of the satellite handover, and the handover UTs can access the satellites according to the flow matrix. In the proposed network-flows model, the weighted edges are determined by the requests of UTs and the quality of satellite services. The multiple matching between the satellites and UTs can be determined by calculating the minimum cost and maximum flow of the network-flows. Besides, we propose a modified handover strategy based on network-flows (HSNF) algorithm to enhance the algorithm performance by preventing infinite loop. Finally, the simulations show the effectiveness and superiority of the proposed strategy.

Column generation and rounding heuristics for minimizing the total weighted completion time on a single batching machine

This paper deals with the single-machine, parallel batching, total weighted completion time scheduling problem. A new graph-based formulation of the problem is proposed, where such graph has an exponential number of nodes and arcs. The problem is modeled as an integer linear program on this graph, combining features of a minimum cost flow problem and features of a set-partition problem as well. The continuous relaxation of this integer problem is solved via column generation, providing a very tight lower bound. Two different flavors of column generation are tested, leading to two models with identical performances in terms of bound tightness but in practice very different in terms of running time. A simple and effective rounding strategy applied to the faster model allows to generate heuristic solutions with values within a few percentage points from the optimum. Two different variants of the heuristic rounding procedure are tested; one allows to certify the optimality gap, while the other trades the ability to certify the gap with a greater computational speed.

A Novel Phase Unwrapping Method Used for Monitoring the Land Subsidence in Coal Mining Area Based on U-Net Convolutional Neural Network

Large-scale and high-intensity mining underground coal has resulted in serious land subsidence. It has caused a lot of ecological environment problems and has a serious impact on the sustainable development of economy. Land subsidence cannot be accurately monitored by InSAR (interferometric synthetic aperture radar) due to the low coherence in the mining area, excessive deformation gradient, and the atmospheric effect. In order to solve this problem, a novel phase unwrapping method based on U-Net convolutional neural network was constructed. Firstly, the U-Net convolutional neural network is used to extract edge to automatically obtain the boundary information of the interferometric fringes in the region of subsidence basin. Secondly, an edge-linking algorithm is constructed based on edge growth and predictive search. The interrupted interferometric fringes are connected automatically. The whole and continuous edges of interferometric fringes are obtained. Finally, the correct phase unwrapping results are obtained according to the principle of phase unwrapping and the wrap-count (integer jump of 2π) at each pixel by edge detection. The Huaibei Coalfield in China was taken as the study area. The real interferograms from D-InSAR (differential interferometric synthetic aperture radar) processing used Sentinel-1A data which were used to verify the performance of the new method. Subsidence basins with clear interferometric fringes, interrupted interferometric fringes, and confused interferometric fringes are selected for experiments. The results were compared with the other methods, such as MCF (minimum cost flow) method. The tests showed that the new method based on U-Net convolutional neural network can resolve the problem that is difficult to obtain the correct unwrapping phase due to interrupted or partially confused interferometric fringes caused by low coherence or other reasons in the coal mining area. Hence, the new method can help to accurately monitor the subsidence in mining areas under different conditions using InSAR technology.

Matching One Sample According to Two Criteria in Observational Studies

Multivariate matching has two goals (i) to construct treated and control groups that have similar distributions of observed covariates, and (ii) to produce matched pairs or sets that are homogeneous in a few key covariates. When there are only a few binary covariates, both goals may be achieved by matching exactly for these few covariates. Commonly, however, there are many covariates, so goals (i) and (ii) come apart, and must be achieved by different means. As is also true in a randomized experiment, similar distributions can be achieved for a high-dimensional covariate, but close pairs can be achieved for only a few covariates. We introduce a new polynomial-time method for achieving both goals that substantially generalizes several existing methods; in particular, it can minimize the earthmover distance between two marginal distributions. The method involves minimum cost flow optimization in a network built around a tripartite graph, unlike the usual network built around a bipartite graph. In the tripartite graph, treated subjects appear twice, on the far left and the far right, with controls sandwiched between them, and efforts to balance covariates are represented on the right, while efforts to find close individual pairs are represented on the left. In this way, the two efforts may be pursued simultaneously without conflict. The method is applied to our on-going study in the Medicare population of the relationship between superior nursing and sepsis mortality. The match2C package in R implements the method. Supplementary materials for this article are available online.

Reverse 1-centre problem on trees under convex piecewise-linear cost function

ABSTRACT Given a network as well as a prescribed vertex s in which a facility is located, the aim of solving reverse 1-centre problems is to decrease edge lengths under a budget constraint in a way that the maximum distance between s and the other vertices is minimized. This paper considers the reverse 1-centre problem on general tree networks with weights associated to vertices under a convex piecewise-linear cost function. It is shown that the problem can be transformed into a parametric minimum cost flow problem. A polynomial time approximation scheme (PTAS) is first developed using the bisection method. Then, the problem on unweighted trees is investigated. Using sensitivity analysis, a pseudo-polynomial time algorithm is designed. Finally, a hybrid algorithm is developed to obtain an exact solution in polynomial time.

Optimization of Multimodal Discrete Network Design Problems Based on Super Networks

In this paper, we investigate the multimodal discrete network design problem that simultaneously optimizes the car, bus, and rail transit network, in which inter-modal transfers are achieved by slow traffic modes including walking and bike-sharing. Specifically, a super network topology is presented to signify the modal interactions. Then, the generalized cost formulas of each type of links in the super network are defined. And based on the above formulas a bi-objective programming model is proposed to minimize the network operation cost and construction cost with traffic flow equilibrium constraints, investment constraints and expansion constraints. Moreover, a hybrid heuristic algorithm that combines the minimum cost flow algorithm and simulated annealing algorithm is presented to solve the proposed model. Finally, the effectiveness of the proposed model and algorithm is evaluated through two numerical tests: a simple test network and an actual multimodal transport network.

Parallel network simplex algorithm for the minimum cost flow problem

AbstractIn 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.

A solution approach to minimal average cost flow problem with lower and upper bounds on flows

As a variant of minimal cost flow problem, the minimal average cost flow problem with lower and upper bounds on flows (MACFLUB) is to search the feasible flow with minimal average cost in network with lower and upper arc capacities and fixed network cost. Only three methods are available in the literature to solve the special cases of MACFLUB, and they cannot be applied to the general case. This paper reduces the MACFLUB to the minimization of a function with U-shaped curve, and develops an algorithm named MACFLUB-MCMFA as more generalized solution approach based on minimal cost maximal flow algorithm. Computational study validates that the MACFLUB-MCMFA algorithm is a robust and efficient approach to solving the MACFLUB.

Optimizing time–cost trade-off decisions in an interval transportation problem with multiple shipment options

This article makes an attempt to build on the extant literature on time–cost trade-off in a transportation problem. The idea is to agglomerate the world of multiple shipment options along with the uncertainty in demand/supply requirements to the traditional set-up. The article introduces a bi-objective transportation model with multi-choice cost and time coefficients along with interval demand and supply constraints. Such a transportation framework is more generalized and provides a much broader view to a decision-maker. The research proposes an efficient iterative algorithm for generating the Pareto frontier that solves a minimum cost flow problem at each iteration. The special structure of this network flow problem is exploited to obtain computationally efficient results. The proposed method is applied to a real-world case study of UPS Express Critical in the United States. The analysis suggests that significant savings in cost and time objectives can be achieved over the traditional set-ups.

DAVINCI: online and Dynamic Adaptation of eVolvable vIrtual Network services over Cloud Infrastructures

Service function chains, or more generally, virtual network services, evolve throughout their life-cycle due to traffic fluctuations, resource usage, and the stringent requirements of the SLO (Service Level Objective) that must be fulfilled. Network operators resort to elasticity mechanisms (e.g., vertical and horizontal scaling) and migration procedures to adapt the service function chains dynamically to meet their requirements constantly. However, most state-of-the-art solutions do not evaluate the overall impact of such mechanisms on the service function chains or the resulting penalty costs (e.g., migration downtime and SLO violation). To bridge this gap, we propose DAVINCI, a decision-making tool with different adaptation policies that allows the network operator to adapt the service function chains to minimize network changes (e.g., reallocating paths and VNFs) while keeping penalty costs at their lowest level. Moreover, DAVINCI allows for the adaptations (e.g., migration, vertical and horizontal scaling) to be expressed as a set of decisions and leverages the Min Cost Flow problem to estimate migration downtime. The analytical evaluation shows that DAVINCI outperforms the existing state-of-the-art solution (NFV-PEAR) in terms of migration, traffic costs, and the overhead induced by the migration and elasticity mechanisms while significantly reducing penalty costs.

Parametric Computation of Minimum-Cost Flows with Piecewise Quadratic Costs

We develop algorithms solving parametric flow problems with separable, continuous, piecewise quadratic, and strictly convex cost functions. The parameter to be considered is a common multiplier on the demand of all nodes. Our algorithms compute a family of flows that are each feasible for the respective demand and minimize the costs among the feasible flows for that demand. For single commodity networks with homogenous cost functions, our algorithm requires one matrix multiplication for the initialization, a rank 1 update for each nondegenerate step and the solution of a convex quadratic program for each degenerate step. For nonhomogeneous cost functions, the initialization requires the solution of a convex quadratic program instead. For multi-commodity networks, both the initialization and every step of the algorithm require the solution of a convex program. As each step is mirrored by a breakpoint in the output this yields output-polynomial algorithms in every case.

A branch-and-price algorithm for solving the single-hub feeder network design problem

In liner shipping, containers are generally transshipped in major hub ports in each region, between larger inter-region vessels and smaller feeder vessels. In this paper, we study the problem of designing the feeder vessel network, transporting containers between a regional hub and the surrounding feeder ports. The problem, as modelled, has many similarities with the split delivery vehicle routing problem, but with additional characteristics such as simultaneous pickups and deliveries and weekly departures. The problem also includes fleet sizing with a heterogeneous fleet and allows demand rejection at a penalty cost. We present a branch-and-price framework to solve the problem, where the subproblem is solved by enumerating vessel routes and subsequently assigning commodities by solving a min-cost flow problem for each commodity. The algorithm is tested on instances with up to 12 ports, which are all solved to optimality. Since the problem is similar to the liner shipping network design problem but without transshipments, we further study selected instances from the LINER-LIB instance suite. The Baltic instance is solved to proven optimality and we find the best known solution to the West Africa instance, significantly improving on what can be found in the literature.

A high-performance VLSI array reconfiguration scheme based on network flow under row and column rerouting

The reconfiguration algorithms have been extensively investigated to ensure the reliability and stability for the processor arrays with faults. It is important to reduce the power consumption, capacitance and communication costs in the processors by reducing the interconnection length of the VLSI array. This paper discusses the reconfiguration problem of the high-performance VLSI processor array under the row and column rerouting constraints. A novel method, making use the idea of network flow, is proposed in this paper. Firstly, a network flow model of the VLSI processor array is constructed, such that the high-performance VLSI target array can be obtained by utilizing the minimal cost flow algorithm. Secondly, we propose a new strategy for bottleneck row selection in the logical array using the minimum cut technique, which can find a more suitable bottleneck row. Finally, we conducted reliable experiments to clearly reveal the efficiency of the new rerouting scheme and algorithm in reducing the number of long interconnects. The experimental results show that, for a host array with size of 256×256, the number of long interconnects in the subarray can be reduced by up to 79.22% and 55.88% without performance penalty for random faults with density of 1% and 25% respectively, when compared with state-of-the-art. In addition, the proposed scheme improves existing algorithm in terms of subarray size. On a 256×256 host array with 25% faulty density, the average improvement in subarray size is up to 3.77% compared with state-of-the-art.

An Analysis of the Stability of Hinterland Container Transport Cooperation

We study cooperation among hinterland container transport operators that may share transport capacity and demand in corridors between inland and sea ports. We model this transportation problem as a minimum cost flow problem and assume that operators share the total cost based on a bargaining outcome, which has been proven equivalent to the Shapley value. To examine the stability of such cooperation, we perform a sensitivity analysis of the membership of the Shapley value (the bargaining outcome) to the core (the set of stable outcomes) by leveraging a novel concept of parametric cooperative games. We obtain closed-form solutions for identical players that explicitly characterize the impact of overcapacity on the stability of cooperation. For more general cases, we develop a computational approach based on parametric optimization techniques. The numerical results indicate that our primary analytical result, that is, that overcapacity undermines stability, is generally valid, and that overcapacitated networks may permit stable cooperation in only a limited range of settings.

The Transformation of College Students’ Ideological and Political Education and Learning Analysis of Education System by Streaming Media Technology

The development of social economy and the continuous advancement of science and technology have opened the historical prelude of the information age. Streaming media technology, with its wide audience, diverse forms, and strong guiding technology, has infinitely narrowed the time and space distances of people in different regions of the world. The difficulty of political work has very important practical significance. Therefore, this paper focuses on the theme of the reform of the teaching method system of the ideological and political theory course in colleges and universities and the analysis of the education system. From the perspective of streaming media technology, we learn the opportunities and challenges faced by college students in the transformation of ideological education and the reform of education system and explain the strategies and measures for the transformation of ideological education and the reform of education system in college students. We hope that this study can provide some theoretical support for the ideological education and teaching of college students. The problem of data scheduling for ideological and political education in the P2P system is analyzed, the data scheduling problem is formalized, and the form of optimal data scheduling is analyzed. Through theoretical analysis, the optimal scheduling problem is transformed into an equivalent minimum cost flow problem that can be calculated in binomial time. It is proved by reasoning that the consistency of the optimal data scheduling problem and the minimum cost flow problem is verified, and the correctness and feasibility of the viewpoint are verified.

A Node-Charge Graph-Based Online Carshare Rebalancing Policy with Capacitated Electric Charging

Viability of electric car-sharing operations depends on rebalancing algorithms. Earlier methods in the literature suggest a trend toward nonmyopic algorithms using queueing principles. We propose a new rebalancing policy using cost function approximation. The cost function is modeled as a p-median relocation problem with minimum cost flow conservation and path-based charging station capacities on a static node-charge graph structure. The cost function is NP complete, so a heuristic is proposed that ensures feasible solutions that can be solved in an online system. The algorithm is validated in a case study of electric carshare in Brooklyn, New York, with demand data shared from BMW ReachNow operations in September 2017 (262 vehicle fleet, 231 pickups per day, and 303 traffic analysis zones) and charging station location data (18 charging stations with four-port capacities). The proposed nonmyopic rebalancing heuristic reduces the cost increase compared with myopic rebalancing by 38%. Other managerial insights are further discussed.

Adaptation of Random Binomial Graphs for Testing Network Flow Problems Algorithms

Algorithms for network flow problems, such as maximum flow, minimum cost flow, and multi-commodity flow problems, are continuously developed and improved, and so, random network generators become indispensable to simulate the functionality and to test the correctness and the execution speed of these algorithms. For this purpose, in this paper, the well-known Erdős–Rényi model is adapted to generate random flow (transportation) networks. The developed algorithm is fast and based on the natural property of the flow that can be decomposed into directed elementary s-t paths and cycles. So, the proposed algorithm can be used to quickly build a vast number of networks as well as large-scale networks especially designed for s-t flows.

Maximal concurrent minimal cost flow problems on extended multi-cost multi-commodity networks

The graph is a great mathematical tool, which has been effectively applied to many fields such as economy, informatics, communication, transportation, etc. It can be seen that in an ordinary graph the weights of edges and vertexes are taken into account independently where the length of a path is the sum of weights of the edges and the vertexes on this path. Nevertheless, in many practical problems, weights at vertexes are not equal for all paths going through these vertexes, but are depending on coming and leaving edges. Moreover, on a network, the capacities of edges and vertexes are shared by many goods with different costs. Therefore, it is necessary to study networks with multiple weights. Models of extended multi-cost multi-commodity networks can be applied to modelize many practical problems more exactly and effectively. The presented article studies the maximal concurrent minimal cost flow problems on multi-cost and multi-commodity networks, which are modelized as optimization problems. On the base of the algorithm to find maximal concurrent flow and the algorithm to find maximal concurrent limited cost flow, an effective polynomial approximate procedure is developed to find a good solution.