Minimum Cost Flow Research Articles

PTTS: Zero-knowledge proof-based private token transfer system on Ethereum blockchain and its network flow based balance range privacy attack analysis

Blockchains are decentralized and immutable databases that are shared among the nodes of the network. Although blockchains have attracted a great scale of attention in the recent years by disrupting the traditional financial systems, the transaction privacy is still a challenging issue that needs to be addressed and analysed. We propose a Private Token Transfer System (PTTS) for the Ethereum public blockchain in the first part of this paper. For the proposed framework, zero-knowledge based protocol has been designed using Zokrates and integrated into our private token smart contract. With the help of web user interface designed, the end users can interact with the smart contract without any third-party setup. In the second part of the paper, we provide security and privacy analysis including the replay attack and the balance range privacy attack which has been modeled as a network flow problem. It is shown that in case some balance ranges are deliberately leaked out to particular organizations or adversarial entities, it is possible to extract meaningful information about the user balances by employing minimum cost flow network algorithms that have polynomial complexity. The experimental study reports the Ethereum gas consumption and proof generation times for the proposed framework. It also reports network solution times and goodness rates for a subset of addresses under the balance range privacy attack with respect to number of addresses, number of transactions and ratio of leaked transfer transaction amounts.

Intra-Frame Graph Structure and Inter-Frame Bipartite Graph Matching with ReID-Based Occlusion Resilience for Point Cloud Multi-Object Tracking

Three-dimensional multi-object tracking (MOT) using lidar point cloud data is crucial for applications in autonomous driving, smart cities, and robotic navigation. It involves identifying objects in point cloud sequence data and consistently assigning unique identities to them throughout the sequence. Occlusions can lead to missed detections, resulting in incorrect data associations and ID switches. To address these challenges, we propose a novel point cloud multi-object tracker called GBRTracker. Our method integrates an intra-frame graph structure into the backbone to extract and aggregate spatial neighborhood node features, significantly reducing detection misses. We construct an inter-frame bipartite graph for data association and design a sophisticated cost matrix based on the center, box size, velocity, and heading angle. Using a minimum-cost flow algorithm to achieve globally optimal matching, thereby reducing ID switches. For unmatched detections, we design a motion-based re-identification (ReID) feature embedding module, which uses velocity and the heading angle to calculate similarity and association probability, reconnecting them with their corresponding trajectory IDs or initializing new tracks. Our method maintains high accuracy and reliability, significantly reducing ID switches and trajectory fragmentation, even in challenging scenarios. We validate the effectiveness of GBRTracker through comparative and ablation experiments on the NuScenes and Waymo Open Datasets, demonstrating its superiority over state-of-the-art methods.

Combinatorial algorithms for restricted inverse optimal value problems on minimum spanning tree under weighted [formula omitted] norm

We study the restricted inverse optimal value problem on minimum spanning tree under weighted l1 norm. In a connected edge-weighted network G(V,E,w), we are given a spanning tree T0, a cost vector c and a value K. We aim to obtain a new weight vector w̄ satisfying the bounded constraint such that T0 is a minimum spanning tree under w̄ whose weight is just K. We focus on minimizing the modification cost under weighted l1 norm. We first convert its mathematical model into a linear programming problem (P). Then we solve its dual problem (D) by a sub-problem (Dz∗) corresponding to the critical value z∗ which can be calculated by a binary search method. Impressively the sub-problem Dz for z∈R can be transformed into a minimum cost flow problem on an auxiliary network. Finally, we propose an O(|E|2|V|2log|V|log(|V|cmax)) algorithm, where cmax is the maximum cost of the vector c.

Real-time adaptive scheduling optimization for inter-satellite contact window resources in dynamic satellite networks

Real-time scheduling of contact window resources is a fundamental technology for the future construction of Space–Terrestrial Integrated Networks (STIN). The spatio-temporal dynamics of satellite networks result in continuous variations in satellite relative positions and inter-satellite visibility window resource status. Furthermore, frequent changes in task priority make real-time resource scheduling extremely challenging. Centralized online scheduling methods often lead to a significant amount of waiting time, while distributed online scheduling methods struggle to adapt to the high dynamics of satellite networks. Therefore, the real-time scheduling technology for contact window resources in satellite networks is still in the exploration phase. We propose an inter-satellite online resource allocation method to solve the latency issue caused by the seizure of contact window resources. First, we determine the shortest and maximum flow paths set in the satellite network according to task requirements and construct them as the core network. Then, we comprehensively analyze the supply and demand situation of the task and the core network at a specific moment and verify the reliability of our minimum cost flow-solving method based on the core network. Moreover, we consider factors such as changes in task priority and edge modifications and validate the correctness of our method to update the minimum cost flow at the next moment based on local network changes. Finally, through extensive comparative simulations, we evaluate the absolute advantage of our inter-satellite online scheduling method and validate a significant improvement in task scheduling timeliness.

Optimizing pathfinding for goal legibility and recognition in cooperative partially observable environments

In this paper, we perform a joint design of goal legibility and recognition in a cooperative, multi-agent pathfinding setting with partial observability. More specifically, we consider a set of identical agents (the actors) that move in an environment only partially observable to an observer in the loop. The actors are tasked with reaching a set of locations that need to be serviced in a timely fashion. The observer monitors the actors' behavior from a distance and needs to identify each actor's destination based on the actor's observable movements. Our approach generates legible paths for the actors; namely, it constructs one path from the origin to each destination so that these paths overlap as little as possible while satisfying budget constraints. It also equips the observer with a goal-recognition mapping between unique sequences of observations and destinations, ensuring that the observer can infer an actor's destination by making the minimum number of observations (legibility delay). Our method substantially extends previous work, which is limited to an observer with full observability, showing that optimizing pathfinding for goal legibility and recognition can be performed via a reformulation into a classical minimum cost flow problem in the partially observable case when the algorithms for the fully observable case are appropriately modified. Our empirical evaluation shows that our techniques are as effective in partially observable settings as in fully observable ones.

Robust reverse 1-center problems on trees with interval costs

This paper concerns the problem of reducing the edge lengths of a tree in a minimum cost way such that the 1-center function at a predetermined vertex is at most a given threshold value. Moreover, it is assumed that the costs of reducing edge lengths are not exactly determined, but they are estimated within intervals and their total deviation is limited within a given bound. This problem is called the robust reverse 1-center problem on trees with interval costs. We first reformulate the problem as a Stackelberg game and translate it into a univariate optimization problem. Based on the special properties of the feasible set, we can state the corresponding problem as a parameterized minimum cost flow problem. Then we develop an algorithm that solves the problem in O ( n 2 log ⁡ n ) time due to the convexity of the univariate objective function. We finally discuss the problem of improving the international transportation network in Iran as a real-life application.

Кількісне оцінювання функціональної ефективності мережевих структур за аналізом чутливості оптимізаційної моделі до зовнішніх впливів

The real network organizational structure is constantly under the influence of external influences, which can cause unexpected consequences due to the cascading spread of relevant disturbances directed at critically important parameters. Parametric sensitivity analysis is the latest computational procedure, the results of which provide the researcher with an idea and quantitative assessment of the appropriate response of the structure in the form of an analytical platform as a composition and interaction of scenario analysis, cascade process development and optimization modeling technology. The main task is timely adaptation to expected changes in business analytics, oriented to optimal resources distribution. The generalized minimum cost problem is a typical example of widespread problems of optimal distribution and use of limited, in particular, energy resources, of any nature and purpose, using the scientific management and analysis of decisions, in its network model attention is paid to the potentials of nodes. The maximum flow problem is an example of the active and effective application of methods and models of flows optimization, where the processes and objects used a network organization, the energy systems and complexes investigated, where arc parameters are critical in its model. In the article, for these classic optimization problems, mathematical and spreadsheet models were built on concrete examples. Direct and dual mathematical programming problems were solved, the following stages were carried out - the organization of a computer experiment and the construction of an analytical platform for evaluating the behavior of the network structure under the influence of external influences and disturbances as their consequences. To take into account the specific conditions of real objects with a network structure at the stage of modification, the model supplemented with appropriate restrictions and correction of input data sets. The obtained results should be useful for planning and management personnel and top-management for discussion and decision-making regarding, for example, the optimal placement of energy equipment, the weighted distribution of energy flows in the "source-sink" system or the appointment of executors for work, automated project management using project networks, etc. Keywords: optimization modeling, maximum network flow, minimum cost flows, network organizational structures, decision making, spreadsheet modeling and analytics.

Sufficient control of complex networks

In this paper, we propose to study sufficient control of complex networks, which is to control a sufficiently large portion of the network, where only the quantity of controllable nodes matters. To the best of our knowledge, this is the first time that such a problem is investigated. We prove that the sufficient controllability problem can be converted into a minimum-cost flow problem, for which an algorithm with polynomial complexity can be devised. Further, we study the problem of minimum-cost sufficient control, which is to drive a sufficiently large subset of the network nodes to any predefined state with the minimum cost using a given number of controllers. The problem is NP-hard. We propose an “extended L0-norm-constraint-based Projected Gradient Method” (eLPGM) algorithm, which achieves suboptimal solutions for the problems at small or medium sizes. To tackle the large-scale problems, we propose to convert the control problem into a graph problem and devise an efficient low-complexity “Evenly Divided Control Paths” (EDCP) algorithm to tackle the graph problem. Simulation results on both synthetic and real-life networks are provided, demonstrating the satisfactory performance of the proposed methods.

A Novel Skip Orthogonal List for Dynamic Optimal Transport Problem

Optimal transport is a fundamental topic that has attracted a great amount of attention from the optimization community in the past decades. In this paper, we consider an interesting discrete dynamic optimal transport problem: can we efficiently update the optimal transport plan when the weights or the locations of the data points change? This problem is naturally motivated by several applications in machine learning. For example, we often need to compute the optimal transport cost between two different data sets; if some changes happen to a few data points, should we re-compute the high complexity cost function or update the cost by some efficient dynamic data structure? We are aware that several dynamic maximum flow algorithms have been proposed before, however, the research on dynamic minimum cost flow problem is still quite limited, to the best of our knowledge. We propose a novel 2D Skip Orthogonal List together with some dynamic tree techniques. Although our algorithm is based on the conventional simplex method, it can efficiently find the variable to pivot within expected O(1) time, and complete each pivoting operation within expected O(|V|) time where V is the set of all supply and demand nodes. Since dynamic modifications typically do not introduce significant changes, our algorithm requires only a few simplex iterations in practice. So our algorithm is more efficient than re-computing the optimal transport cost that needs at least one traversal over all |E|=O(|V|^2) variables, where |E| denotes the number of edges in the network. Our experiments demonstrate that our algorithm significantly outperforms existing algorithms in the dynamic scenarios.

Accurate prediction of RNA secondary structure including pseudoknots through solving minimum-cost flow with learned potentials

Pseudoknots are key structure motifs of RNA and pseudoknotted RNAs play important roles in a variety of biological processes. Here, we present KnotFold, an accurate approach to the prediction of RNA secondary structure including pseudoknots. The key elements of KnotFold include a learned potential function and a minimum-cost flow algorithm to find the secondary structure with the lowest potential. KnotFold learns the potential from the RNAs with known structures using an attention-based neural network, thus avoiding the inaccuracy of hand-crafted energy functions. The specially designed minimum-cost flow algorithm used by KnotFold considers all possible combinations of base pairs and selects from them the optimal combination. The algorithm breaks the restriction of nested base pairs required by the widely used dynamic programming algorithms, thus enabling the identification of pseudoknots. Using 1,009 pseudoknotted RNAs as representatives, we demonstrate the successful application of KnotFold in predicting RNA secondary structures including pseudoknots with accuracy higher than the state-of-the-art approaches. We anticipate that KnotFold, with its superior accuracy, will greatly facilitate the understanding of RNA structures and functionalities.

Minimum cost flow problems in generalized fuzzy environments. Credibilistic CVaR minimization approach

The paper focuses on the problems of linear programming (LP) with generalized fuzzy numbers (GFNs) as coefficients of the objective function. It is necessary to characterize consistent arithmetic operations to lower the error and information loss compared to the minimum operator usage and normalization in cases where experts are not completely certain of their subjective opinions. The uncertainty is eliminated using the total cost as a loss function and credibilistic conditional value at risk (CVaR) minimization. To crispify and generate a GFN, we utilize a ranking function that allows us to consider risky realizations. By solving many deterministic problems with LP solvers, projections of the error in the objective function can be presented. To describe and implement our methodology, we mainly focus on network optimization problems, especially generalized fuzzy transportation, assignment, and shortest path problems.

Interactive fuzzy goal programming approach for solving possibilistic multi-objective minimum cost flow problems

Interactive fuzzy goal programming approach for solving possibilistic multi-objective minimum cost flow problems

Interactive Fuzzy Goal Programming Approach for Solving Possibilistic Multi-Objective Minimum Cost Flow Problems

Interactive Fuzzy Goal Programming Approach for Solving Possibilistic Multi-Objective Minimum Cost Flow Problems

Data-Driven Distributionally Robust Optimization for Railway Timetabling Problem

Unpredictable disturbances that occur when the train is running often make the actual timetable deviate from the planned timetable and deteriorate service quality for passengers. To provide a robust planned timetable that is reliable in operation, this paper presents a two-stage distributionally robust railway timetabling (DRRT) model, where the decisions in the first and second stages are the planned and actual timetables, respectively. To deal with the uncertain travel time, the proposed DRRT model assumes the true distribution belongs to a Wasserstein ambiguity set centered at the empirical distribution constructed from finite samples and aims to minimize the sum of the total idle time, travel time, and worst-case expected delay over the ambiguity set. To solve this model, we design a decomposition algorithm with provable convergence, which iteratively solves a master problem and a set of subproblems. To enhance the algorithm efficiency, a blend of two popular decomposition methods is proposed to integrate their advantages, and the solution of the subproblems is accelerated by using an uncapacitated minimum-cost flow interpretation of the second-stage optimization problem. Experiments on real-world instances demonstrate the effectiveness of these enhancements. The results also show that our model prominently outperforms the sample average approximation model in terms of the out-of-sample performance, especially when only a small sample set is available. Moreover, at the expense of equal traffic efficiency, our model is more robust than those models that do not utilize distribution information. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper was motivated by the problem of using finite historical data to provide a robust planned railway timetable, aiming at minimizing the traffic efficiency losses and expected delays under the worst-case distribution. Existing studies on dealing with the uncertain travel time usually assumed that the distribution is exactly known, or the distribution is completely unknown but the travel time belongs to an uncertainty set. However, in practice, the exact distribution is hard to know but can only be coarsely estimated from data. This paper proposes a data-driven two-stage model by assuming that the true distribution belongs to a 1-Wasserstein ball centered at the empirical distribution with a bounded support set, which is a middle ground between the above two distribution assumptions. To solve this problem efficiently, we propose a customized algorithm with provable convergence and then enhance it by exploiting problem-specific properties. This distributionally robust model can be easily shifted to other timetabling problems, and the algorithm enhancement techniques can also be applied to efficiently solve other two-stage recourse models with similar properties.

Modeling and solving a corporate vehicle-sharing problem combined with other modes of transport

We consider a car-sharing problem in a company during business hours. The employees, located at one or several offices, have to travel to one or more appointments each with a fixed location and fixed start and end times and return to one of the offices afterwards. Each employee trip can be carried out with one out of several alternative modes of transport. The considered modes of transport are a company car from the company car pool, walking, public transport, bike, and taxi. The aim is to assign modes of transport to employee trips such that the total costs of covering the trips is minimized.We first consider that the company is operating a shared fleet of a single type of vehicle and then that the fleet consists of different vehicle types. By relying on minimizing the savings when using a vehicle compared to the cheapest alternative available mode of transport (which is used if no vehicle is assigned to a trip), we do not need to model the alternative modes explicitly. For the case where the vehicle fleet consists of a single type of vehicle, we model the vehicle-sharing problem as a minimum-cost flow problem. Secondly, if multiple types of vehicles are available the problem can be formulated as a multi-commodity flow problem. Since very efficient solution methods are available for these formulations, they are applicable in daily operations.We provide a comprehensive computational study for both cases on instances based on demographic, spatial, and economic data of Vienna. We show that our formulations for the problem solve these instances in a few seconds, which makes them usable in an online booking system. In the analysis, we discuss different potential settings. We study different sizes and compositions of the shared fleet, restricted sets of modes of transport, and variations of the objective function.

Optimal Task Allocation for Battery-Assisted and Price-Aware Mobile Edge Computing

In this paper, we propose a battery-assisted approach to improve energy efficiency for mobile edge computing (MEC) networks by utilizing the space-time-varying characteristics of electricity price. We formulate a price-aware task allocation problem (PATA) that jointly considers the cost for task computation, the cost of task offloading, and the cost of battery degradation. PATA is seemingly a mixed integer non-linear programming problem. By a graph-based reformulation, solving PATA is mapped to finding minimum cost flows or convex cost flows in the graph. This discovery reveals that the global optimum of PATA is obtained in polynomial time. Performance evaluation manifests that the proposed approach significantly outperforms other approaches.

Almost-Linear-Time Algorithms for Maximum Flow and Minimum-Cost Flow

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.

Minimum Cost Flow-Based Integrated Model for Electric Vehicle and Crew Scheduling

Vehicle and crew scheduling is vital in public transit planning. Conventionally, the issues are handled sequentially as the vehicle scheduling problem (VSP) and crew scheduling problem (CSP). However, integrating these planning steps offers additional flexibility, resulting in improved efficiency compared with sequential planning. Given the ever-growing market share of electric buses, this paper introduces a new model for integrated electric VSP and CSP, called EVCSPM. This model employs the minimum cost flow formulations for electric VSP, set partitioning for CSP, and linking constraints. Due to the nonlinear integer property of EVCSPM, we propose a method that hybrids a matching-based heuristic and integer linear programming solver, GUROBI. The numerical results demonstrate the efficiency of our methodology, and the integrated model outperforms the sequential model in real-life scenarios.

Truthful and Optimal Data Preservation in Base Station-less Sensor Networks: An Integrated Game Theory and Network Flow Approach

We aim to preserve a large amount of data generated inside base station-less sensor networks (BSNs) while considering that sensor nodes are selfish. BSNs refer to emerging sensing applications deployed in challenging and inhospitable environments (e.g., underwater exploration); as such, there do not exist data-collecting base stations in the BSN to collect the data. Consequently, the generated data has to be stored inside the BSN before uploading opportunities become available. Our goal is to preserve the data inside the BSN with minimum energy cost by incentivizing the storage- and energy-constrained sensor nodes to participate in the data preservation process. We refer to the problem as DPP: d ata p reservation p roblem in the BSN. Previous research assumes that all the sensor nodes are cooperative and that sensors have infinite battery power and design a minimum-cost flow-based data preservation solution. However, in a distributed setting and under different control, the resource-constrained sensor nodes could behave selfishly only to conserve their resources and maximize their benefit. In this article, we first solve DPP by designing an integer linear programming (ILP)-based optimal solution without considering selfishness. We then establish a game-theoretical framework that achieves provably truthful and optimal data preservation in BSNs. For a special case of DPP wherein nodes are not energy-constrained, referred to as DPP-W, we design a data preservation game DPG-1 that integrates algorithmic mechanism design (AMD) and a more efficient minimum cost flow-based data preservation solution. We show that DPG-1 yields dominant strategies for sensor nodes and delivers truthful and optimal data preservation. For the general case of DPP (wherein nodes are energy-constrained), however, DPG-1 fails to achieve truthful and optimal data preservation. Utilizing packet-level flow observation of sensor node behaviors computed by minimum cost flow and ILP, we uncover the cause of the failure of the DPG-1. It is due to the packet dropping by the selfish nodes that manipulate the AMD technique. We then design a data preservation game DPG-2 for DPP that traces and punishes manipulative nodes in the BSN. We show that DPG-2 delivers dominant strategies for truth-telling nodes and achieves provably optimal data preservation with cheat-proof guarantees. Via extensive simulations under different network parameters and dynamics, we show that our games achieve system-wide data preservation solutions with optimal energy cost while enforcing truth-telling of sensor nodes about their private cost types. One salient feature of our work is its integrated game theory and network flows approach. With the observation of flow level sensor node behaviors provided by the network flows, our proposed games can synthesize “microscopic” (i.e., selfish and local) behaviors of sensor nodes and yield targeted “macroscopic” (i.e., optimal and global) network performance of data preservation in the BSN.

The single robot line coverage problem: Theory, algorithms, and experiments

AbstractLine coverage is the task of servicing a given set of one‐dimensional features in an environment. It is important for the inspection of linear infrastructure such as road networks, power lines, and oil and gas pipelines. This paper addresses the single robot line coverage problem for aerial and ground robots by modeling it as an optimization problem on a graph. The problem belongs to the broad class of arc routing problems and is closely related to the rural postman problem (RPP) on asymmetric graphs. The paper presents an integer linear programming formulation with proofs of correctness. Using the minimum cost flow problem, we develop approximation algorithms with guarantees on the solution quality. These guarantees also improve the existing results for the asymmetric RPP. The main algorithm partitions the problem into three cases based on the structure of the required graph, that is, the graph induced by the features that require servicing. We evaluate our algorithms on road networks from the 50 most populous cities in the world, consisting of up to 730 road segments. The algorithms, augmented with improvement heuristics, run within 3 s and generate solutions that are within 10% of the optimum. We experimentally demonstrate our algorithms with commercial UAVs on the UNC Charlotte campus road network.