Reachability In Networks Research Articles

Reachability in Simple Neural Networks

We investigate the complexity of the reachability problem for (deep) neural networks: does it compute valid output given some valid input? It was recently claimed that the problem is NP-complete for general neural networks and specifications over the input/output dimension given by conjunctions of linear inequalities. We recapitulate the proof and repair some flaws in the original upper and lower bound proofs. Motivated by the general result, we show that NP-hardness already holds for restricted classes of simple specifications and neural networks. Allowing for a single hidden layer and an output dimension of one as well as neural networks with just one negative, zero and one positive weight or bias is sufficient to ensure NP-hardness. Additionally, we give a thorough discussion and outlook of possible extensions for this direction of research on neural network verification.

Bounded Confidence and Cohesion-Moderated Pressure: A General Model for the Large-Scale Dynamics of Ordered Opinion.

Due to the development of social media, the mechanisms underlying consensus and chaos in opinion dynamics have become open questions and have been extensively researched in disciplines such as sociology, statistical physics, and nonlinear mathematics. In this regard, our paper establishes a general model of opinion evolution based on micro-mechanisms such as bounded confidence, out-group pressure, and in-group cohesion. Several core conclusions are derived through theorems and simulation results in the model: (1) assimilation and high reachability in social networks lead to global consensus; (2) assimilation and low reachability result in local consensus; (3) exclusion and high reachability cause chaos; and (4) a strong "cocoon room effect" can sustain the existence of local consensus. These conclusions collectively form the "ideal synchronization theory", which also includes findings related to convergence rates, consensus bifurcation, and other exploratory conclusions. Additionally, to address questions about consensus and chaos, we develop a series of mathematical and statistical methods, including the "energy decrease method", the "cross-d search method", and the statistical test method for the dynamical models, contributing to a broader understanding of stochastic dynamics.

Reachability in choice networks

In this paper, we investigate the problem of determining s−t reachability in choice networks. In the traditional s−t reachability problem, we are given a weighted network tuple G=〈V,E,c,s,t〉, with the goal of checking if there exists a path from s to t in G. In an optional choice network, we are given a choice set S⊆E×E, in addition to the network tuple G. In the s−t reachability problem in choice networks (OCRD), the goal is to find whether there exists a path from vertex s to vertex t, with the caveat that at most one edge from each edge-pair (x,y)∈S is used in the path. OCRD finds applications in a number of domains, including routing in wireless networks and sensor placement. We analyze the computational complexities of the OCRD problem and its variants from a number of algorithmic perspectives. We show that the problem is NP-complete in directed acyclic graphs with bounded pathwidth. Additionally, we show that its optimization version is NPO PB-complete. Additionally, we show that the problem is fixed-parameter tractable in the cardinality of the choice set S. In particular, we show that the problem can be solved in time O∗(1.42|S|). We also consider weighted versions of the OCRD problem and detail their computational complexities; in particular, the optimization version of the WOCRD problem is NPO-complete. While similar results have been obtained for related problems, our results improve on those results by providing stronger results or by providing results for more limited graph types.

Migrating From Legacy to Software Defined Networks: A Network Reliability Perspective

Designing survivable communication networks to achieve carrier-grade five-nines reliability is of paramount importance for the network operators. This article addresses service reliability and its related aspects such as nodal reachability, network connectivity, and edge-disjoint routing in both traditional networks and software defined networks (SDNs). The proposed roadmap is based on two phases: Fundamental analytical phase and performance evaluation phase. In the first phase, a graph operator is defined to analyze the characteristics of the reliability metric and its associated reachability feature. This phase will focus on both the macro- and micro-level properties of reliability. In the second phase, we exploit the analysis in the former phase to get an insight into the performance evaluation of traditional and SDN-based networks against the reliability metric, and then calculate the statistical significance of the mean difference of their reliability values. Reliability under edge-disjoint paths to avoid resource competition is also investigated. Various types of topologies are utilized to test the service reliability of both architecture designs. Extensive simulation results show that SDN-based networks have comparable performance to its legacy counterpart against the operational reliability metric. Our findings not only shed light on enhancing reliability using edge-disjoint paths under link failure scenarios but also expected to benefit the operators to achieve their service level objectives while migrating from legacy to SDN-based platform.

Modelling Reachability in Transport Networks: Using Alternative Visual Representations in Interactive Linked‐Views to Gain Valuable Insights

Most people use maps for navigation. Geographic maps visually represent physical distance between locations. These maps sometimes provide a false impression of travel times. Two cities geographically close to each other might be “far apart” in terms of travel time because of slower connections, whereas two cities geographically distant might be “nearby” in terms of travel time because of faster connections. Under such circumstances, visualizing a transport network using time as a distance measure can make the transport network more understandable. This study integrates several (carto)graphic representations—a time line, a distance line, a time prism, a time cartogram, and a geographic map—in an interactive linked-views environment to model reachability in transport networks. A prototype is implemented in a web environment using D3.js. The implementation can be applied to any transport network. In this research, the approach is illustrated with railroad network data for the Dutch province of Overijssel. The solution provides an alternative and insightful perspective for analyzing the data. In addition to complementing a wide variety of methods to visualizing travel times, the approach could be applied in areas such as spatial analysis and transport planning.

Concurrency and reachability in treelike temporal networks

Network properties govern the rate and extent of various spreading processes, from simple contagions to complex cascades. Recently, the analysis of spreading processes has been extended from static networks to temporal networks, where nodes and links appear and disappear. We focus on the effects of accessibility, whether there is a temporally consistent path from one node to another, and reachability, the density of the corresponding accessibility graph representation of the temporal network. The level of reachability thus inherently limits the possible extent of any spreading process on the temporal network. We study reachability in terms of the overall levels of temporal concurrency between edges and the structural cohesion of the network agglomerating over all edges. We use simulation results and develop heterogeneous mean-field model predictions for random networks to better quantify how the properties of the underlying temporal network regulate reachability.

Last train scheduling for maximizing passenger destination reachability in urban rail transit networks

As urban rail transit (URT) systems usually do not operate for the whole day, the last train service offers the last daily chance for late-night passengers to utilize URT services to reach their target destination stations. This paper formally introduces and models the destination-reachability based last train timetabling problem (DR-LTTP in abbreviation) in URT networks, which involves both the last train timetabling and the passenger assignment. The DR-LTTP is formulated as a mixed integer linear programming and can be solved by existing commercial optimization software. The model is illustrated with a simple numerical example on a minimum spanning tree network, and comparison experiments are conducted between DR-LTTP model and station-transferability based last train timetabling problem (ST-LTTP in abbreviation). Finally, a real case study with Beijing URT network is conducted to test the performance of our model.

On demand knowledge‐based memory‐aided rebroadcast algorithm for multimedia voice data transmission in MANET

SummaryMANET refers to wireless networks in which mobile nodes can be easily adapted to change the location dynamically due to their mobility and offers flexibility in the network configuration. An efficient mechanism for reliable exchanging of the multimedia voice messages through MANET nodes is achieved by route discovery of broadcasting operation. A major problem in such systems is the broadcast overhead and retransmission associated with high dense network and less reachability in sparse network. In systems of vastly dynamic nature, to reduce this broadcast overhead in nodes and to increase the reachability in static or semi static nodes in an environment, an enhanced mechanism shore up called On Demand Knowledge‐Based Memory‐Aided Rebroadcast Algorithm for Multimedia voice Data Transmission in MANET (OMRA) is herewith proposed, which operates on both dense and sparse network. In this scheme, hello multimedia voice messages are broadcast to collect one‐hop neighbor information such as mobility factor, node velocity, node density ratio and uncovered neighbors. Additionally, it determines and preserves inquiry data of mobile nodes when the mobility factor is low ensue in sparse network. By considering these varying nature the rebroadcast delay and rebroadcast probability are adjusted adaptively to decide whether to rebroadcast the inward multimedia voice messages. This paper concentrates only on broadcasting the multimedia voice message through MANET nodes in a reliable manner. The performance study of this work is analyzed by various existing algorithms in the literature such as flooding, Gossip1, DBA, and NCPR. The experimental results proves that the proposed OMRA has got an edge over the existing broadcast schemes in terms of broadcast overhead and retransmission of multimedia voice messages, especially to increase reachability in sparse networks.

Mining k-reachable sets in real-world networks using domination in shortcut graphs

We propose a technique for mining minimum sets with bounded reachability in real-world networks, i.e. the smallest vertex sets such that any other vertex is at distance at most k from at least one vertex of this set. Our technique uses a simple but efficient mechanism. We first introduce new edges to shorten the paths in our network to obtain a shortcut graph. As the next step, we search for the minimum dominating set in the shortcut graph. For this purpose, a variety of algorithmic approaches is applied and computationally studied. To the best of our knowledge, this approach and the impact of shortcut graph structure on the problem have not been systematically explored yet. Experimental results are presented for local samples of two social networks, as well as large network science graphs, including several research collaboration networks. Different profiles of k-reachable sets were found for different networks. We find that k-reachable set sizes sharply decline with increasing k and decreasing graph diameters in the context of shortcut graphs obtained from social networks, as well as the largest connected components of research collaboration networks. However, there are also real-world networks, which seem to have slightly different profiles.

Controllability emerging from conditional path reachability in complex networks

SummaryControllability of complex networks is a fundamental requirement to orientate the networks toward a sustainable way of development. Determination of link weights and calculation of eigenvalues of large‐scale matrices are two inevitable problems in applying the exact controllability framework in complex networks. Here, we introduce a novel controllability analysis approach based on the controllability index and the reachability matrix to identify the minimum set of driver nodes, in order to achieve complete regulation of arbitrary networks with general configurations. An effective algorithm is theoretically developed via using only the 0–1 binary structure of the network. Theoretical analysis and numerical examples show that our proposed algorithm possesses structural adaptability and control robustness under the weighted perturbation. Copyright © 2017 John Wiley & Sons, Ltd.

Sufficient conditions for reachability in automata networks with priorities

In this paper, we develop a framework for an efficient under-approximation of the dynamics of Asynchronous Automata Networks (AANs). An AAN is an Automata Network with synchronised transitions between automata, where each transition changes the local state of exactly one automaton (but any number of synchronising local states are allowed). The work we propose here is based on static analysis by abstract interpretation, which allows to prove that reaching a state with a given property is possible, without the same computational cost of usual model checkers: the complexity is polynomial with the total number of local states and exponential with the number of local states within a single automaton. Furthermore, we address AANs with classes of priorities, and give an encoding into AANs without priorities, thus extending the application range of our under-approximation. Finally, we illustrate our method for the model checking of large-scale biological networks.

Under-approximation of Reachability in Multivalued Asynchronous Networks

The Process Hitting is a recently introduced framework designed for the modelling of concurrent systems. Its originality lies in a compact representation of both components of the model and its corresponding actions: each action can modify the status of a component, and is conditioned by the status of at most one other component. This allowed to define very efficient static analysis based on local causality to compute reachability properties. However, in the case of cooperations between components (for example, when two components are supposed to interact with a third one only when they are in a given configuration), the approach leads to an over-approximated interleaving between actions, because of the pure asynchronous semantics of the model.To address this issue, we propose an extended definition of the framework, including priority classes for actions. In this paper, we focus on a restriction of the Process Hitting with two classes of priorities and a specific behaviour of the components, that is sufficient to tackle the aforementioned problem of cooperations. We show that this class of Process Hitting models allows to represent any Asynchronous Discrete Networks, either Boolean or multivalued. Then we develop a new refinement for the under-approximation of the static analysis to give accurate results for this class of Process Hitting models. Our method thus allows to efficiently under-approximate reachability properties in Asynchronous Discrete Networks; it is in particular conclusive on reachability properties in a 94 components Boolean network, which is unprecedented.

LIRT: A Lightweight Scheme for Indistinguishability, Reachability, and Timeliness in Wireless Sensor Control Networks

Wireless sensor control networks (WSCNs) are important scenarios and trends in mobile wireless sensor networks. Compared with traditional wireless sensor networks, WSCNs have two specific characteristics: entities in networks are extended from passive sensors to active sensors (e.g., actuators and actors) and the transmitting messages are extended from data only to data plus (e.g., data and control instructions). Thus new security problems arises. In this paper, we make the first attempt to specify the security requirements for WSCNs, namely, indistinguishability, reachability, and timeliness. In addition, several new attacks in WSCN, distinguishing risks, dropping attacks, and disordering attacks, are pointed out at the first time. A lightweight scheme LIRT is proposed with tailored design to guarantee the indistinguishability, reachability, and timeliness in WSCNs. Extensive and rigorous analysis on LIRT justifies its security strength and performance measures.

SURF: A distributed channel selection strategy for data dissemination in multi-hop cognitive radio networks

In this paper, we propose an intelligent and distributed channel selection strategy for efficient data dissemination in multi-hop cognitive radio network. Our strategy, SURF, classifies the available channels and uses them efficiently to increase data dissemination reliability in multi-hop cognitive radio networks. The classification is done on the basis of primary radio unoccupancy and of the number of cognitive radio neighbors using the channels. Through extensive NS-2 simulations, we study the performance of SURF compared to four related approaches. Simulation results confirm that our approach is effective in selecting the best channels for efficient communication (in terms of less primary radio interference) and for highest dissemination reachability in multi-hop cognitive radio networks.

Computing weight constraint reachability in large networks

Reachability is a fundamental problem on large-scale networks emerging nowadays in various application domains, such as social networks, communication networks, biological networks, road networks, etc. It has been studied extensively. However, little existing work has studied reachability with realistic constraints imposed on graphs with real-valued edge or node weights. In fact, such weights are very common in many real-world networks, for example, the bandwidth of a link in communication networks, the reliability of an interaction between two proteins in PPI networks, and the handling capacity of a warehouse/storage point in a distribution network. In this paper, we formalize a new yet important reachability query in weighted undirected graphs, called weight constraint reachability (WCR) query that asks: is there a path between nodes $$a$$ and $$b$$ , on which each real-valued edge (or node) weight satisfies a range constraint. We discover an interesting property of WCR, based on which, we design a novel edge-based index structure to answer the WCR query in $$O(1)$$ time. Furthermore, we consider the case when the index cannot entirely fit in the memory, which can be very common for emerging massive networks. An I/O-efficient index is proposed, which provides constant I/O (precisely four I/Os) query time with $$O(|V|\log |V|)$$ disk-based index size. Extensive experimental studies on both real and synthetic datasets demonstrate the efficiency and scalability of our solutions in answering the WCR query.

Characterising temporal distance and reachability in mobile and online social networks

The analysis of social and technological networks has attracted a lot of attention as social networking applications and mobile sensing devices have given us a wealth of real data. Classic studies looked at analysing static or aggregated networks, i.e., networks that do not change over time or built as the results of aggregation of information over a certain period of time. Given the soaring collections of measurements related to very large, real network traces, researchers are quickly starting to realise that connections are inherently varying over time and exhibit more dimensionality than static analysis can capture. In this paper we propose new temporal distance metrics to quantify and compare the speed (delay) of information diffusion processes taking into account the evolution of a network from a global view. We show how these metrics are able to capture the temporal characteristics of time-varying graphs, such as delay, duration and time order of contacts (interactions), compared to the metrics used in the past on static graphs. We also characterise network reachability with the concepts of in- and out-components. Then, we generalise them with a global perspective by defining temporal connected components. As a proof of concept we apply these techniques to two classes of time-varying networks, namely connectivity of mobile devices and interactions on an online social network.

Network reliability and the probabilistic estimation of damage from fire spread

An efficient generalization of Shanthikumar's upper bound on two-terminal reliability is developed, that leads to efficient methods for the probabilistic assessment of damage from fire spread and other invasive hazards in segmented structures. The methods exploit a basic relationship between the fire spread problem and the probability of reachability in communications networks. The upper bound employs noncrossing cuts of the network.

Calculating bounds on reachability and connectedness in stochastic networks

AbstractIn this article, computational procedures are presented for generating bounds on measures of network reliability. The two measures considered, reachability and connectedness, are the probability that there is an operating path from a node to all other nodes in a directed (respectively undirected) stochastic network. Our bounds, which are given in terms of polynomials in p, the common arc failure probability, are based on recent bounding results developed by the authors for the class of shellable independence systems. Two pairs of bounds are given: weaker bounds whose computation time is bounded by a polynomial in the size of the network and tighter bounds whose computation time is bounded by a polynomial in the size of the network and the number of minimum‐cardinality network cuts. Computational results are also given which evaluate the quality of the bounds. The generation of the bounds involves several interesting path and cut counting problems.