Critical Edges Research Articles

Critical edges for the assignment problem: Complexity and exact resolution

This paper investigates two problems related to the determination of critical edges for the minimum cost assignment problem. Given a complete bipartite balanced graph with n vertices on each part and with costs on its edges, kMost Vital Edges Assignment consists of determining a set of k edges whose removal results in the largest increase in the cost of a minimum cost assignment. A dual problem, Min Edge Blocker Assignment, consists of removing a subset of edges of minimum cardinality such that the cost of a minimum cost assignment in the remaining graph is larger than or equal to a specified threshold. We show that kMost Vital Edges Assignment is NP-hard to approximate within a factor c<2 and Min Edge Blocker Assignment is NP-hard to approximate within a factor 1.36. We also provide an exact algorithm for kMost Vital Edges Assignment that runs in O(nk+2). This algorithm can also be used to solve exactly Min Edge Blocker Assignment.

Scan matching online cell decomposition for coverage path planning in an unknown environment

This paper presents a novel sensor-based online coverage path-planning algorithm that guarantees the complete coverage of an unknown rectilinear workspace for the task of a mobile robot. The proposed algorithm divides the workspace of the robot into cells at each scan sample. This division can be classified as an exact cell decomposition method, which incrementally constructs cell decomposition while the robot covers an unknown workspace. To guarantee complete coverage, a closed map representation based on a feature extraction that consists of a set of line segments called critical edges is proposed. In this algorithm, cell boundaries are formed by extended critical edges, which are the sensed partial contours of walls and objects in the workspace. The robot uses a laser scanner to sense the critical edges. Sensor measurement is sampled twice in each cell. Scan matching is performed to merge map information between the reference scan and the current scan. At each scan sample, a two-direction oriented rectilinear decomposition is achieved in the workspace and presented by a closed map representation. The construction order of the cells is very important in this incremental cell decomposition algorithm. To choose the next target cell from candidate cells, the robot checks for redundancy in the planned path and for possible positions of the ending points of the current cell. The key point of the algorithm is memorizing the covered space to define the next target cell from possible cells. The path generation within the defined cell is determined to minimize the number of turns, which is the main factor in saving time during the coverage. Therefore, the cell’s long boundary should be chosen as the main path of the robot. This algorithm is verified by an experiment under the LABVIEW environment.

Anti-Missile Network Edge Importance Research

The problem about cooperation anti-missile network of warship fleet has been the research hotspot. In order to evaluate the edges for the warship fleet cooperation anti-missile network, a new approach for evaluating the critical edges is proposed by considering the influence of endpoint nodes. The method that edge betweenness is used as the index of evaluating critical edge is incomplete. Aimed at the built operation network, the method is used in the case. The result indicates that the method is reasonable and effective.

Key potential-oriented criticality analysis for complex military organization based on FINC-E model

The complex social organizations, which can self-organize into the region "at the edge of chaos", neither too ordered nor too random, now have become an interdisciplinary research topic. As a kind of special social organization, the complex military organization usually has its key entities and relations, which should be well protected in case of attacks. In order to do the criticality analysis for the military organization, finding the key entities or relations which can disrupt the functions of the organization, two problems should be seriously considered. First, the military organization should be well modeled, which can work well in the specialized military context; secondly it is critical to define and identify the key entities or relations, which should incorporate the topological centrality and weighted nodes or edges. Different from the traditional military organizations which are usually task-oriented, this paper proposes the Force, Intelligence, Networking, and C2 Extended (FINC-E) Model for complex military organization, with which a more detailed and quantitative analysis for the military organization is available. This model provides the formal representation for the nodes and edges in the military organization, which provides a highly efficient and concise network topology. In order to identify the critical nodes and edges, a method based on key potential is proposed, which acts as the measurement of criticality for the heterogeneous nodes and edges in the complex military organization. The key potential is well defined on the basis of topology structure and of the node's or edge's capability, which helps to transform the organization from the heterogeneity to the homogeneity. In the end, the criticality analysis case study is made for both small-world networked military organization and scale-free networked military organization, showing that the measure of key potential has the advantage over other classical measures in locating the key entities or relations for complex military organization.

A Polynomial Time Exact Algorithm for Overlay-Resistant Self-Aligned Double Patterning (SADP) Layout Decomposition

Double patterning lithography (DPL) technologies have become a must for today's sub-32 nm technology nodes. Currently, there are two leading DPL technologies: self-aligned double patterning (SADP) and litho-etch-litho-etch (LELE). Among them, SADP has the significant advantage over LELE in its ability to avoid overlay, making it the likely DPL candidate for the next technology node of 14 nm. In any DPL technology, layout decomposition is the key problem. While the layout decomposition problem for LELE has been well studied in the literature, only a few attempts have been made to address the SADP layout decomposition problem. In this paper, we present a polynomial time exact (optimal) algorithm to determine if a given layout has SADP decompositions that do not have any overlay at specified critical edges. The previous approaches tried to minimize the total overlay of a given layout, which may be a problematic objective. Furthermore, all previous exact algorithms were computationally expensive exponential time algorithms based on SAT or ILP. Other previous algorithms for the problem were heuristics without having any guarantee that an overlay-free solution can be found even if one exists.

Cancer Missense Mutations Alter Binding Properties of Proteins and Their Interaction Networks

Many studies have shown that missense mutations might play an important role in carcinogenesis. However, the extent to which cancer mutations might affect biomolecular interactions remains unclear. Here, we map glioblastoma missense mutations on the human protein interactome, model the structures of affected protein complexes and decipher the effect of mutations on protein-protein, protein-nucleic acid and protein-ion binding interfaces. Although some missense mutations over-stabilize protein complexes, we found that the overall effect of mutations is destabilizing, mostly affecting the electrostatic component of binding energy. We also showed that mutations on interfaces resulted in more drastic changes of amino acid physico-chemical properties than mutations occurring outside the interfaces. Analysis of glioblastoma mutations on interfaces allowed us to stratify cancer-related interactions, identify potential driver genes, and propose two dozen additional cancer biomarkers, including those specific to functions of the nervous system. Such an analysis also offered insight into the molecular mechanism of the phenotypic outcomes of mutations, including effects on complex stability, activity, binding and turnover rate. As a result of mutated protein and gene network analysis, we observed that interactions of proteins with mutations mapped on interfaces had higher bottleneck properties compared to interactions with mutations elsewhere on the protein or unaffected interactions. Such observations suggest that genes with mutations directly affecting protein binding properties are preferably located in central network positions and may influence critical nodes and edges in signal transduction networks.

Timing-driven logic restructuring for nano-hybrid circuits

As the feature size of the integrated circuits (ICs) scales down, the future of nano-hybrid circuit looks bright in extending Moore's Law. However, mapping a circuit to a nano-fabric structure is vexing due to connectivity constraints. A mainstream methodology is that a circuit is transformed into a nano-fabric preferred structure by buffer insertion to high fan-out gates. However, it may result in timing degradation. Logic replication is a traditional way to split high fan-out gates in logic synthesis but may not be suitable for high fan-out gates with high fan-ins. In this article, a timing-driven logic restructuring framework at the gate level is proposed. The proposed framework identifies the high fan-out gates from a given gate netlist according to the fan-out threshold, following by the restructuring of high fan-out gates through the application of logic replication and buffer insertion. To improve circuit timing from a global perspective, latent critical edges are identified to avoid entrapping critical paths during the restructuring. Experimental results on ISCAS benchmarks indicate that 8.51% timing improvement and 6.13% CPU time reduction can be obtained traded with 4.16% area increase on an average.

Feature-based tool path generation approach for incremental sheet forming process

Incremental sheet forming (ISF) is a highly versatile and flexible process for rapid manufacturing of complex sheet metal parts. Although tool path plays an important role in the ISF process, there is only limited development in the tool path generation strategy and the conventional contour based strategies have been proven to cause problems in surface quality and geometric accuracy. This paper presents a new feature-based tool path generation algorithm for incremental sheet forming process. In this algorithm, tool paths are generated according to the specified critical edges. To obtain a better understanding of forming mechanism using the new tool path generation method, the thickness distribution, geometric accuracy and surface quality of the ISF formed shapes by using the feature-based tool path approach are compared with the traditional ISF tool path method based on three case studies including a truncated cone with double bottoms, a non-symmetrical cone and a car fender. The results suggest that the new tool path stretches the sheet in a different way and results in different thickness distributions. The results of these case studies also demonstrate the advantages of the feature based tool path generation especially in surface quality, geometric accuracy and forming time.

179 Impact of cancer mutations on protein binding and activity

Missense mutations play an important role in carcinogenesis, however, their effect on biomolecular interactions remains unclear. We describe a new framework that uses experimental evidence on structural complexes, the atomic details of binding interfaces, and evolutionary conservation to map the set of human protein–biomolecular interactions (Shoemaker et al., 2012; Tyagi et al., 2012). To analyze the impact of missense cancer mutations on protein interactions, we model the affected protein complexes and estimate the change in binding energy upon mutations. We find that although some missense mutations overstabilize protein complexes, overall, they are destabilizing mostly affecting the electrostatic component of binding energy. Our analysis allows to stratify cancer-related interactions, identify potential driver genes, and propose two dozen additional cancer biomarkers. Furthermore, we observe that interactions of proteins with mutations mapped on interfaces have higher bottleneck properties compared to interactions with mutations elsewhere on the protein. This suggests that genes with mutations directly affecting protein-binding properties are preferably located in central network positions and may influence critical nodes and edges in signal transduction networks. Next, we study the mechanisms of aberrant activation of receptor tyrosine kinases in cancer and estimate the effects of single and double cancer mutations on the stability of active and inactive states (Hashimoto et al., 2012). We show that singleton cancer mutations destabilize active and inactive states, however, inactive states are destabilized more than the active ones potentially leading to kinase activation. In addition, more frequent mutations have a higher activating effect. The activation mechanisms of double mutations are found to be quite different from those of single mutations.

Interplay between (im)perfectness, synchrony and connectivity: The case of reliable message transmission

Reliable message transmission is a fundamental problem in distributed communication networks. Of late, several interesting results have been obtained by modelling the network as a directed graph. An important result among them was due to Bhavani et al. [Unconditionally reliable message transmission in directed networks, 18 in: SODA’08: Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, Philadelphia, PA, USA, 2008, pp. 1048–1055], where it was shown that if a negligible probability of error is allowed, the connectivity required in a synchronous network for unconditionally reliable message transmission (URMT) is significantly reduced.We refer to the variant of URMT studied by them as Monte Carlo URMT; here the receiver is allowed to output an incorrect message with small probability. Another interesting variant which has received little attention so far in the literature is the Las Vegas variant, where the receiver is allowed to abort with a small probability, but never to output an incorrect message.We show that the minimum connectivity requirements for the existence of Las Vegas URMT protocols over synchronous networks are the same as that of Monte Carlo URMT protocols over asynchronous networks—a surprising equivalence between two very different models. Furthermore, we show that the higher connectivity requirements of Las Vegas URMT over asynchronous networks match exactly with that of zero-error (perfect) variant over (a)synchronous networks. We also show that there exists a family of graphs where in the number of critical edges for the ‘easier’ randomized variants are asymptotically higher than that for the perfect variants.Hence, our results demonstrate an interesting interplay between (im)perfectness, synchrony and connectivity for the case of reliable message transmission.

Vortex merger and topological changes in two-dimensional turbulence

On the basis of the critical point analysis, we study the reconnection process of vorticity contours associated with coherent vortices in two-dimensional turbulence. After checking topological integrity by the Euler index theorem, we make use of the critical points and their connectivity (so-called surface networks) to characterize topological changes of vorticity contours. We quantify vortex merger by computing the number of centers and saddles of the vorticity field systematically. Surface networks are topological graphs consisting of the critical points and edges connecting them. They can tell in particular which vortices are going to merge in near future. Moreover, we show how this method can remarkably distinguish the dynamics of the vorticity field in the Navier-Stokes equations and that of the Charney-Hasegawa-Mima equation. The relationship between the number of the critical points and hyperpalinstrophy is discussed by deriving the so-called generalized Rice theorem in the spirit of S. Goto and J. C. Vassilicos [Phys. Fluids 21, 035104-1 (2009)]. The Okubo-Weiss' conditional sampling is used to compare reconnection in elliptic and hyperbolic regions. A comparison has been made between topological changes of the vorticity and that of a passive scalar. A study in inviscid flows with different resolutions is also given.

On New Approaches of Assessing Network Vulnerability: Hardness and Approximation

Society relies heavily on its networked physical infrastructure and information systems. Accurately assessing the vulnerability of these systems against disruptive events is vital for planning and risk management. Existing approaches to vulnerability assessments of large-scale systems mainly focus on investigating inhomogeneous properties of the underlying graph elements. These measures and the associated heuristic solutions are limited in evaluating the vulnerability of large-scale network topologies. Furthermore, these approaches often fail to provide performance guarantees of the proposed solutions. In this paper, we propose a vulnerability measure, pairwise connectivity, and use it to formulate network vulnerability assessment as a graph-theoretical optimization problem, referred to as -disruptor. The objective is to identify the minimum set of critical network elements, namely nodes and edges, whose removal results in a specific degradation of the network global pairwise connectivity. We prove the NP-completeness and inapproximability of this problem and propose an pseudo-approximation algorithm to computing the set of critical nodes and an pseudo-approximation algorithm for computing the set of critical edges. The results of an extensive simulation-based experiment show the feasibility of our proposed vulnerability assessment framework and the efficiency of the proposed approximation algorithms in comparison to other approaches.

A Note on Edge-Domsaturation Number of a Graph

The edge-domsaturation number ds'(G) of a graph G = (V, E) is the least positive integer k such that every edge of G lies in an edge dominating set of cardinality k. In this paper, we characterize unicyclic graphs G with ds'(G) = q – Δ'(G) + 1 and investigate well-edge dominated graphs. We further define γ'–-critical, γ'+-critical, ds'–-critical, ds'+-critical edges and study some of their properties.

Identifying groups of critical edges in a realistic electrical network by multi-objective genetic algorithms

In this paper, an analysis of the vulnerability of the Italian high-voltage (380 kV) electrical transmission network (HVIET) is carried out for the identification of the groups of links (or edges, or arcs) most critical considering the network structure and flow. Betweenness centrality and network connection efficiency variations are considered as measures of the importance of the network links. The search of the most critical ones is carried out within a multi-objective optimization problem aimed at the maximization of the importance of the groups and minimization of their dimension. The problem is solved using a genetic algorithm. The analysis is based only on information on the topology of the network and leads to the identification of the most important single component, couples of components, triplets and so forth. The comparison of the results obtained with those reported by previous analyses indicates that the proposed approach provides useful complementary information.

Fault-Tolerant Bipancyclicity of Faulty Hypercubes Under the Generalized Conditional-Fault Model

Let F_v be a set of faulty nodes in an n-dimensional hypercube, denoted by Q_n. Also, let F_e be a set of faulty edges in which at least one end-node of each edge is faulty. An edge in Q_n is said to be critical if it is either fault-free or in F_e. In this paper, we prove that, for up to 2n-4 faulty nodes and/or edges, an n-dimensional hypercube contains a fault-free cycle of every even length from 4 to 2^n-2oF_vo in which each node is incident to at least two critical edges. Our result improves on the previously best known results reported in the literature.

Performance and reliability of electrical power grids under cascading failures

The stability and reliability of electrical power grids are indispensable to the continuous operation of modern cities and critical for preparedness, response, recovery and mitigation in emergence management. Because present power grids in China are often running near their critical operation points, they are especially vulnerable and sensitive to external disturbances such as hurricanes, earthquakes and terrorist attacks, which may trigger cascading failures or blackouts. This paper describes a quantitative investigation of the stability and reliability of power grids with a focus on cascading failures under external disturbances. The 118-bus (substation) power network in Hainan, China is employed as a case study to investigate the risk of cascading failure of the regional power grids. System performance and reliability of the power grids are evaluated under two hypothetical scenarios (seismic impact and intentional disturbance) that could trigger cascading failures. By identifying the most vulnerable (critical) edges and nodes, the robustness of the power network is evaluated under the triggered cascading failures. It is found that the system reliabilities could decline as much as 95% during the triggered cascading failure. This paper also explores the use of concepts from modern complex network theories such as state transition graph and characteristic length to understand the complex mechanism of cascading failures. The findings could be useful for power industries and emergency managers to evaluate the vulnerability of power systems, understand the risk of blackout induced by cascading failures, and improve the resilience of power systems to external disturbances.

Rethinking the Interplay of Feminism and Secularism in a Neo-Secular Age

The need to re-examine established ways of thinking about secularism and its relationship to feminism has arisen in the context of the confluence of a number of developments including: the increasing dominance of the ‘clash of civilizations’ thesis; the expansion of postmodern critiques of Enlightenment rationality to encompass questions of religion; and sustained critiques of the ‘secularization thesis’. Conflicts between the claims of women's equality and the claims of religion are well-documented vis-à-vis all major religions and across all regions. The ongoing moral panic about the presence of Islam in Europe, marked by a preoccupation with policing Muslim women's dress, reminds us of the centrality of women and gender power relations in the interrelation of religion, culture and the state. Added to postmodern and other critiques of the secular-religious binary, most sociological research now contradicts the equation of modernization with secularization. This article focuses on the challenges that these developments pose to politically oriented feminist thinking and practice. It argues that non-oppressive feminist responses require a new critical engagement with secularism as a normative principle in democratic, multicultural societies. To inform this process, the author maps and links discussions across different fields of feminist scholarship, in the sociology of religion and in political theory. She organizes the main philosophical traditions and fault lines that form the intellectual terrain at the intersection of feminism, religion and politics in two broad groups: feminist critiques of the Enlightenment critique of religion; and feminist scholarship at the critical edges of the Enlightenment tradition. The author argues that notwithstanding the fragmented nature of feminist debates in this area, common ground is emerging across different politically oriented approaches: all emphasize ‘democracy’ and the values that underpin it as the larger discursive frame in which the principle of secularism can be redefined with emancipatory intent in a neo-secular age.

Software Quality Control Based on Genetic Algorithm

Software evaluation has a crucial role in the life cycle of software production system. Producing suitable data for testing the behavior of the software is a subject of many researches in software engineering. In this paper software quality control with criteria of covering application paths is considered and a new method based on genetic algorithm for generating optimal test data is proposed. In this algorithm, the fitness function, population production mechanism and other parameters of genetic algorithm is determined. In addition, the population production stopping criteria is based on critical edges of control flow graph. Critical edges are those that their presence in a control flow graph path represents the presence of other edges and the edges test shows the adequacy of graph test paths. The simulation results on prototype test data show the effectiveness of the proposed method.

Changing of the Number of Minimum Dominating Sets after Edge Addition: Non Critical Edges

Let γ(G) and #γ(G) denote the domination number and the number of all distinct minimum dominating sets of a graph G, respectively. We show that #γ(G + e) ≥ #γ(G) for every edge with γ(G+e) = γ(G). Based on this, we begin an investigation of graphs for which #γ increases whenever an edge is added (we call such graphs #γ+-EA-critical). We prove that if G is #γ+-EA-critical then either G is edgeless or γ(G+e) = γ(G) for all . If p is a number of endvertices of a #γ+-EA-critical graph G of order n ≥ 6, we show that (a) p ≤ γ(G), and (b) p ≤ [n/3] provided G is connected. In both cases, we find the extremal graphs. We also find all #γ+-EA-critical graphs each component of which is either a tree or a unicyclic graph.

Testable Critical Path Selection Considering Process Variation

Critical path selection is very important in delay testing. Critical paths found by conventional static timing analysis (STA) tools are inadequate to represent the real timing of the circuit, since neither the testability of paths nor the statistical variation of cell delays caused by process variation is considered. This paper proposed a novel path selection method considering process variation. The circuit is firstly simplified by eliminating non-critical edges under statistical timing model, and then divided into sub-circuits, while each sub-circuit has only one prime input (PI) and one prime output (PO). Critical paths are selected only in critical sub-circuits. The concept of partially critical edges (PCEs) and completely critical edges (CCEs) are introduced to speed up the path selection procedure. Two path selection strategies are also presented to search for a testable critical path set to cover all the critical edges. The experimental results showed that the proposed circuit division approach is efficient in path number reduction, and PCEs and CCEs play an important role as a guideline during path selection.