Directed Flow Network Research Articles

Flow Allocation Games

We study a game-theoretic variant of the maximum circulation problem. In a flow allocation game, we are given a directed flow network. Each node is a rational agent and can strategically allocate any incoming flow to the outgoing edges. Given the strategy choices of all agents, a maximal circulation that adheres to the chosen allocation strategies evolves in the network. Each agent wants to maximize the amount of flow through his or her node. Flow allocation games can be used to express strategic incentives of clearing in financial networks. We provide a cumulative set of results on the existence and computational complexity of pure Nash and strong equilibria as well as tight bounds on the (strong) prices of anarchy and stability. Our results show an interesting dichotomy. Ranking strategies over individual flow units allows us to obtain optimal strong equilibria for many objective functions. In contrast, more intuitive ranking strategies over edges can give rise to unfavorable incentive properties. Funding: This work was supported by Deutsche Forschungsgemeinschaft Research Group ADYN [411362735].

Global migration topology analysis and modeling of directed flow network 2006–2010

We applied the network theory to the global world migration phenomenon, seen as a directed network (flow of migrants between world countries from 2006 to 2010) and measured different centralities statistics: in and out-degree, in and out-closeness, and clustering coefficient. One of the important findings is that distributions of out-degree and in-degree for immigration and emigration are completely different aspects of the same phenomenon. The out-degree distribution is uniform with a Gaussian distribution when the in-degree distribution is compound by several groups depending on the in-degree and the in-weight. The receptor countries-nodes, which have large values of in-weight, can be divided into two groups: the developed countries (with low clustering coefficient but large values of the in-degree) and a small group of countries (with high clustering coefficient and small in-degree values). The countries-nodes with large out-weight can be divided into two subgroups with a high clustering coefficient. One of these groups is well connected and forms with the group of the developed countries an in-subgroup of diameter 2 thanks to the double links between them. The second group is characterized by low values of the in-degree (some with null value) and is connected to the rest of the network mainly by out-degrees. Finally, the Latin American countries may be seen as a homogeneous fifth group.

Optimal K-node disruption on a node-capacitated network

This paper examines a network disruption model from the perspective of a network attacker, who wishes to identify the subset of $$ K $$ nodes to disable on a node-capacitated directed flow network (e.g., air transport) such that the disrupted flow is maximized. Such models can also be used by a network defender who wishes to identify the nodes whose disruption would have the greatest impact on network performance. In this problem, the system flow is constrained not only by the disruption to nodes, but also by the limited capacity on nodes that are not disrupted. This paper presents multiple mixed-integer linear programming formulations for this problem, including a novel path-based formulation, and novel multi-commodity flow-based formulations. Computational testing is provided, demonstrating that the multi-commodity based formulation is able to solve relatively large-sized network instances, with the best performance obtained by a two-step procedure that utilizes an approximation to obtain an initial solution for the provably-optimal multi-commodity flow based formulation.

Flow motifs reveal limitations of the static framework to represent human interactions

Networks are commonly used to define underlying interaction structures where infections, information, or other quantities may spread. Although the standard approach has been to aggregate all links into a static structure, some studies have shown that the time order in which the links are established may alter the dynamics of spreading. In this paper, we study the impact of the time ordering in the limits of flow on various empirical temporal networks. By using a random walk dynamics, we estimate the flow on links and convert the original undirected network (temporal and static) into a directed flow network. We then introduce the concept of flow motifs and quantify the divergence in the representativity of motifs when using the temporal and static frameworks. We find that the regularity of contacts and persistence of vertices (common in email communication and face-to-face interactions) result on little differences in the limits of flow for both frameworks. On the other hand, in the case of communication within a dating site and of a sexual network, the flow between vertices changes significantly in the temporal framework such that the static approximation poorly represents the structure of contacts. We have also observed that cliques with 3 and 4 vertices containing only low-flow links are more represented than the same cliques with all high-flow links. The representativity of these low-flow cliques is higher in the temporal framework. Our results suggest that the flow between vertices connected in cliques depend on the topological context in which they are placed and in the time sequence in which the links are established. The structure of the clique alone does not completely characterize the potential of flow between the vertices.

Performance modelling of serial production lines with inspection/repair stations

The authors derived a set of analytical models for serial production lines with multiple operation stations and multiple inspection/repair stations. Multiple defect types may be acquired by the production units from the raw stock as well as during processing at operation stations. The analytical models are steady-state equations for outgoing quality level, throughput rate and scrap rates. The analytical models are based on (1) traffic rate equations of the flow through a production line when represented as a directed flow network and (2) probabilistic models of changes in defect attributes of the production units as they flow. The formulas may be used for evaluating inspection configuration designs including the formulation of optimal cost models.

On a function for the vulnerability of a directed flow network

AbstractThe concept of vulnerability of a network, by which we mean the susceptibility of the network to attack, is very useful for the design of networks such as computer networks and communication networks. In this paper, a directed flow network, in which a nonnegative real number called edge capacity or capacity is associated with each edge is considered. If an edge in a network is destroyed, the value of maximum flow between two vertices in the network is decreased in general. If the decrease of the value of maximum flow by the destruction is large, the degree of influence of the edge on the vulnerability of the network is considered to be large. Two indices measuring the degree of influence of an edge on the vulnerability in the above sense are proposed and their properties are studied in this paper. Furthermore, the two indices are generalized to functions measuring the degree of influence of an edge on the vulnerability in a network.

An O( n2log n) parallel max-flow algorithm

A synchronized parallel algorithm for finding maximum flow in a directed flow network is presented. Its depth is O( n 3 ( log n) p) , where p ( p ≤ n) is the number of processors used. This problem seems to be more involved than most of the problems for which efficient parallel algorithms exist. The parallel algorithm induces a new rather simple sequential O( n 3) algorithm. This algorithm is very much parallel oriented. It is quite difficult to conceive and analyze it, if one is restricted to the sequential point of view.