Critical Edges Research Articles

Maximum shortest path interdiction problem by upgrading edges on trees under weighted $$l_1$$ norm

Network interdiction problems by deleting critical edges have wide applicatio ns. However, in some practical applications, the goal of deleting edges is difficult to achieve. We consider the maximum shortest path interdiction problem by upgrading edges on trees (MSPIT) under unit/weighted $$l_1$$ norm. We aim to maximize the the length of the shortest path from the root to all the leaves by increasing the weights of some edges such that the upgrade cost under unit/weighted $$l_1$$ norm is upper-bounded by a given value. We construct their mathematical models and prove some properties. We propose a revised algorithm for the problem (MSPIT) under unit $$l_1$$ norm with time complexity O(n), where n is the number of vertices in the tree. We put forward a primal dual algorithm in $$O(n^2)$$ time to solve the problem (MSPIT) under weighted $$l_1$$ norm, in which a minimum cost cut is found in each iteration. We also solve the problem to minimize the cost to upgrade edges such that the length of the shortest path is lower bounded by a value and present an $$O(n^2)$$ algorithm. Finally, we perform some numerical experiments to compare the results obtained by these algorithms.

Selecting the Best Links for Lane-reversal in Wide-area Evacuation Based on the Critical Edge Model of Dynamic Maximum Flow Increase

Based on the theory of dynamic flow, we study the optimization problem of dynamic reverse lane, that is, the selection of the road section and the optimization of the time period of lane reverse operation. We abstract an evacuation road network as a directed network with variable capacity, and define the critical dynamical edge for increasing the dynamical maximum flow value of such network. We can get alternative links and corresponding time period for lane-reversal operation by searching critical dynamical edges for increasing the dynamical maximum flow value. We present a modified algorithm to find such critical dynamical edges on the basis of the maximal capacity path algorithm for the static maximum flow problem. We also give a numerical example and test the effects through traffic simulation. The results show that evacuation time can be effectively decreased through taking dynamical reversal lane scheme in regional evacuation.

On 4-chromatic Schrijver graphs: their structure, non-3-colorability, and critical edges

We investigate 4-chromatic Schrijver graphs from various points of view and color-critical edges in Schrijver graphs in general. In particular, we present the following results. Our proof of non-3-colorability of 4-chromatic Schrijver graphs is based on a complete description of their structure that we present as well. This was already also given (in somewhat different terms) by Braun and even earlier in an unpublished manuscript by Li.

An integrated method for DEM simplification with terrain structural features and smooth morphology preserved

ABSTRACT As a key focus of cartography and terrain analysis, the simplification of a digital elevation model (DEM) is used to preserve the pattern features of the terrain surface while suppressing its details over multiple scales. Statistical filtering and structural analysis methods are commonly used for this process. The structural analysis method performs well in identifying terrain structural edges, while it tends to discard the smooth morphology of a terrain surface. In addition, the filter that aims to reduce noise on a surface may over-smooth the terrain structural edges. Therefore, to preserve both the terrain structural edges and smooth morphology, we propose to combine the techniques of statistical filtering and structural analysis. Specifically, all the critical elevation points and structural edges are first detected from the DEM surface by using the structural analysis method. Then, the iterative guided normal filter is used to smooth the generalized DEM with the guidance of the structure of the original surface. After this process, the terrain structure is retained in the smooth surface of the DEM. The experimental results with a real-world dataset show that our method can inherit the merits of both structural analysis and statistical filter in preserving terrain features for multi-scale DEM representations.

Identification of Critical Nodes and Edges in a Network Based on Clustering

Network structures present within themselves specific characterization of their topological structures and connectivity. The properties of a given network change significantly as failure of its nodes and edges takes place. The failure of a node and/or edge reinstates the properties for the entire network. This paper aims to identify critical nodes and edges, the failure of which brings maximum change in the network properties. Clustering has been applied in this study for the identification process. The methodology discussed in this article would be helpful in tracking multi-states which a network undergoes due to failure of its nodes and edges. The proposed methodology would provide a holistic view for criticality of nodes and edges at both local and global level for a network. An optimum maintenance plan could then be devised for the critical nodes and edges to provide the system with a robust and resilient network. The proposed approach could be applied in power grid transmission, supply chain management, transportation and communication networks, oil, gas, power and water distribution networks to ensure continuous information and commodity flow through the networks. The methodology has been demonstrated with a case study in water distribution network. By applying the methodology, top five critical nodes and edges have been identified for the water distribution system.

Repairing 3D Binary Images Using the FCC Grid

A 3D image I is well-composed if it does not contain critical edges or vertices (where the boundary of I is non-manifold). The process of transforming an image into a well composed one is called repairing. We propose to repair 3D images by associating the face-centered cubic grid (FCC grid) with the cubic grid. We show that the polyhedral complex in the FCC grid, obtained by our repairing algorithm, is well-composed and homotopy equivalent to the complex naturally associated with the given image I with edge-adjacency (18-adjacency). We illustrate an application on two tasks related to the repaired image: boundary reconstruction and computation of its Euler characteristic.

An Improved Critical-Edge Model for Finding Optimal Contraflow Links Considering the Influence of Intersections

A reversible roadway (contraflow) is one in which the direction of traffic flow in one or more lanes is reversed to the opposing direction for some period of time. Reversible roadways are most commonly used for accommodating directionally imbalanced traffic associated with daily commuter periods. Reversible lanes also have been widely used, in recent years, for evacuating major metropolitan regions threatened by hurricanes and other disasters. One important problem in the practice of evacuation traffic organization is the choice of road links for contraflow. Most research on the choice of contraflow links does not consider the influence of intersections, which leads to overestimation of evacuation capacity especially in congested urban road networks. We abstract an evacuation road network as a special network with directional node-weights by considering the capacity of intersection movements as directed weights of nodes. We define the critical edge for increasing the maximum flow value of such network as the one that can maximize the range of flow value increase by expanding its capacity. We obtain alternative links for contraflow by searching critical edges in such network. We presented a modified algorithm for finding such critical edges on the basis of the maximal capacity path algorithm for the classical maximum flow problem. We also provided a numerical example and tested the effects through traffic simulation. Our results show that the results considering the influence of intersections are more reasonable than those ignoring it and that taking the intersection effects into account enables us to reduce the total evacuation time.

Finding Critical Links for Closeness Centrality

Closeness centrality is a class of distance-based measures in the network analysis literature to quantify reachability of a given vertex (or a group of vertices) by other network agents. In this paper, we consider a new class of critical edge detection problems, in which given a group of vertices that represent an important subset of network elements of interest (e.g., servers that provide an essential service to the network), the decision maker is interested in identifying a subset of critical edges whose removal maximally degrades the closeness centrality of those vertices. We develop a general optimization framework, in which the closeness centrality measure can be based on any nonincreasing function of distances between vertices, which, in turn, can be interpreted as communication efficiency between them. Our approach includes three well-known closeness centrality measures as special cases: harmonic centrality, decay centrality, and [Formula: see text]-step reach centrality. Furthermore, for quantifying the centrality of a group of vertices we consider three different approaches for measuring the reachability of the group from any vertex in the network: minimum distance to a vertex in the group, maximum distance to a vertex in the group, and the average centrality of vertices in the group. We study the theoretical computational complexity of the proposed models and describe the corresponding mixed integer programming formulations. For solving medium- and large-scale instances of the problem, we first develop an exact algorithm that exploits the fact that real-life networks often have rather small diameters. Then we propose two conceptually different heuristic algorithms. Finally, we conduct computational experiments with real-world and synthetic network instances under various settings, which reveal interesting insights and demonstrate the advantages and limitations of the proposed models and algorithms. The online appendices are available at https://doi.org/10.1287/ijoc.2018.0829 .

A SPECTRUM OF SERIES–PARALLEL GRAPHS WITH MULTIPLE EDGE EVOLUTION

AbstractWe discuss a rich family of directed series–parallel (SP) graphs grown by the simultaneous random series or parallel development of multiple edges. The family portrays a spectrum that spans a wide range of SP graphs: from simple models, where only as few as one edge is chosen for evolution at each discrete point in time, to complex hierarchical lattice networks grown by a take-all strategy, where all the edges in the existing network are developed.The family of SP graphs we discuss is grown from an initial seed graph with τ0 edges under an arbitrary building sequence, $\{k_{n}\}_{n=1}^{\infty}$, of nonnegative integers (with $k_n \le \tau _0 + \sum\nolimits_{i = 1}^n {k_i} $, for arbitrary τ0 ≥ 1), that specifies the number of edges subjected to evolution at time n. We study the average north polar degree and show that we can go beyond averages to strong laws. We also find the exact average number of critical edges. The asymptotics of the critical edges are facilitated under the regularity condition that $k_n/\sum\nolimits_{i = 1}^n {k_i} $ converges to a constant (as n → ∞), a natural condition easily met by practical strategies, such as single-edge evolution and take-all choice, and much in between.

Optimal disintegration strategy in multiplex networks.

Network disintegration comprises the problem of identifying the critical nodes or edges whose removal will lead to a network collapse. The solution of this problem is significant for strategies for dismantling terrorist organizations and for immunization in disease spreading. Network disintegration has received considerable attention in isolated networks. Here, we consider the generalization of optimal disintegration strategy problems to multiplex networks and propose a disintegration strategy based on tabu search. Experiments show that the disintegration effect of our strategy is clearly superior to those of typical disintegration strategies. Moreover, our approach sheds light on the properties of the nodes within the optimal disintegration strategies.

Characteristics of Changes of Transportation Performance for Pairs of Critical Edges

When the robustness of a public service system design is tested, we can often use scenarios where possible random failures can occur and they can influence the time the service is accessible which is provided for system users. The construction of a suitable scenario is based on the choice of links of the transportation network which influence the system performance in a substantial way. In such scenarios one or multiple arcs can be affected by this failure. In our contribution we present characteristics of pairs of critical arcs that can be used to develop an algorithm for the creation of critical scenarios.

Identifying critical edges in complex networks

The critical edges in complex networks are extraordinary edges which play more significant role than other edges on the structure and function of networks. The research on identifying critical edges in complex networks has attracted much attention because of its theoretical significance as well as wide range of applications. Considering the topological structure of networks and the ability to disseminate information, an edge ranking algorithm BCCMOD based on cliques and paths in networks is proposed in this report. The effectiveness of the proposed method is evaluated by SIR model, susceptibility index S and the size of giant component σ and compared with well-known existing metrics such as Jaccard coefficient, Bridgeness index, Betweenness centrality and Reachability index in nine real networks. Experimental results show that the proposed method outperforms these well-known methods in identifying critical edges both in network connectivity and spreading dynamic.

Efficient disintegration strategy in directed networks based on tabu search

The problem of network disintegration, which aims at identifying the critical nodes or edges whose removal will lead to a network collapse, has attracted much attention due to its wide applications. This paper focuses on the disintegration of directed networks. We propose a disintegration strategy based on tabu search. Experiments show that the disintegration effect of our strategy is obviously better than those of typical disintegration strategies based on local structural properties. Moreover, we find that the critical nodes identified to remove in directed networks are not those nodes with large degree or betweenness centrality that always are the crucial properties in undirected network.

Image smoothing via truncated gradient regularisation

Edge-preserving image smoothing aims at maintaining the fundamental constituents, i.e. salient edges of a given image, while removing the noise and insignificant details in the meantime. It is often employed at the pre-processing step of many image processing tasks, including reconstruction, segmentation, recognition and three-dimensional content generation, to name just a few. Recently, a sparse gradient counting scheme in an optimisation framework has attracted much attention, and it confines the discrete number of intensity changes among neighbouring pixels. This l 0 -regularised sparsity pursuit scheme performs favourably in a global optimisation manner. However, it often achieves unsatisfactory performance at diminishing trivial details and at smoothing discrete regions. In this study, a new image smoothing scheme with truncated l 0 regularisation is proposed, which is especially effective for sharpening critical edges. For objective evaluation of the smoothing performance, images are linearly quantised into several layers to generate the experimental images, then these quantised images are smoothed using several methods for reconstructing the smoothly changed shape and intensity of the original images. Compared with the l 0 smoothing scheme, extensive experimental results demonstrate that the proposed method performs much better at preserving main structures and removing trivial details.

Current-flow efficiency of networks

Many real-world networks, from infrastructure networks to social and communication networks, can be formulated as flow networks. How to realistically measure the transport efficiency of these networks is of fundamental importance. The shortest-path-based efficiency measurement has limitations, as it assumes that flow travels only along those shortest paths. Here, we propose a new metric named current-flow efficiency, in which we calculate the average reciprocal effective resistance between all pairs of nodes in the network. This metric takes the multipath effect into consideration and is more suitable for measuring the efficiency of many real-world flow equilibrium networks. Moreover, this metric can handle a disconnected graph and can thus be used to identify critical nodes and edges from the efficiency-loss perspective. We further analyze how the topological structure affects the current-flow efficiency of networks based on some model and real-world networks. Our results enable a better understanding of flow networks and shed light on the design and improvement of such networks with higher transport efficiency.

Link-Prediction Enhanced Consensus Clustering for Complex Networks.

Many real networks that are collected or inferred from data are incomplete due to missing edges. Missing edges can be inherent to the dataset (Facebook friend links will never be complete) or the result of sampling (one may only have access to a portion of the data). The consequence is that downstream analyses that “consume” the network will often yield less accurate results than if the edges were complete. Community detection algorithms, in particular, often suffer when critical intra-community edges are missing. We propose a novel consensus clustering algorithm to enhance community detection on incomplete networks. Our framework utilizes existing community detection algorithms that process networks imputed by our link prediction based sampling algorithm and merges their multiple partitions into a final consensus output. On average our method boosts performance of existing algorithms by 7% on artificial data and 17% on ego networks collected from Facebook.

Privacy Preserving Approach of Published Social Networks Data with Vertex and Edge Modification Algorithm

Background/Objectives: The main objectives are to preserve the privacy of the published data by modifying the graph by adding the smallest number of edges. Methods/Statistical analysis: In this study, a quantitative criterion for anonymity cost is defined. If the anonymity cost is numerically measurable, comparison and then selection of the best state can be possible. To calculate the cost of anonymity, due to generalization of the information on the labels of vertices, we use the NCP .This method provides a quantitative value of the lost information due to the generalization of the labels. Findings: In this research, social networks with a variety of connections and critical edges among individuals have been taken into account, and the purpose is to preserve the privacy of the published data by modifying the graph by adding the smallest number of edges. After applying anonymity for each k anonymity vertex, in addition to the same degree of vertices, connections of the vertices become identical as well. After anonymity, social network becomes resistant to neighborhood attacks. Greedy algorithm was developed for this purpose, which had an optimized performance using the modified graph and was efficient in terms of time complexity and memory consumption. The main purpose of this research is to establish the optimal balance between the privacy of entities, Usefulness of the data and the cost of anonymity. Applications/ Improvements: In order to reduce the cost of anonymityand alsoto have the lowest rate of lost information: generalization of the information on the labels of edgeshave been removed, As well as, adding and removing vertex in this methodnot permitted.

Communicability angles reveal critical edges for network consensus dynamics.

We consider the question of determining how the topological structure influences a consensus dynamical processes taking place on a network. By considering a large data set of real-world networks we first determine that the removal of edges according to their communicability angle, an angle between position vectors of the nodes in an Euclidean communicability space, increases the average time of consensus by a factor of 5.68 in real-world networks. The edge betweenness centrality also identifies, in a smaller proportion, those critical edges for the consensus dynamics; i.e., its removal increases the time of consensus by a factor of 3.70. We justify theoretically these findings on the basis of the role played by the algebraic connectivity and the isoperimetric number of networks on the dynamical process studied and their connections with the properties mentioned before. Finally, we study the role played by global topological parameters of networks on the consensus dynamics. We determine that the network density and the average distance-sum, which is analogous of the node degree for shortest-path distances, account for more than 80% of the variance of the average time of consensus in the real-world networks studied.

Efficient, Decentralized Detection of Qualitative Spatial Events in a Dynamic Scalar Field.

This paper describes an efficient, decentralized algorithm to monitor qualitative spatial events in a dynamic scalar field. The events of interest involve changes to the critical points (i.e., peak, pits and passes) and edges of the surface network derived from the field. Four fundamental types of event (appearance, disappearance, movement and switch) are defined. Our algorithm is designed to rely purely on qualitative information about the neighborhoods of nodes in the sensor network and does not require information about nodes’ coordinate positions. Experimental investigations confirm that our algorithm is efficient, with overall communication complexity (where n is the number of nodes in the sensor network), an even load balance and low operational latency. The accuracy of event detection is comparable to established centralized algorithms for the identification of critical points of a surface network. Our algorithm is relevant to a broad range of environmental monitoring applications of sensor networks.

Imitation and efficient contagion

This paper is about the diffusion of cooperation in an infinite population of networked individuals repeatedly playing a Prisoner's Dilemma. We formulate conditions on payoffs and network structure such that, starting from an initial seed group, imitative learning results in the overall adoption of cooperation—efficient contagion. Key to this result is the pattern of interaction among players who are at the same distance from the initial seed group. We find that the more these agents interact among themselves rather than with players who are closer to or further away from the initial seed group, the easier it is for efficient contagion to take place. We highlight the importance of cycles for efficient contagion, and show that the presence of critical edges prevents it. We also find that networks organized as dense clusters sparsely connected to one another tend to resist efficient contagion. Finally, we find that the likelihood of efficient contagion in a network increases when information neighborhoods extend beyond interaction neighborhoods.