Outgoing Edges Research Articles

Marking shortest paths on pushdown graphs does not preserve MSO decidability

In this paper we consider pushdown graphs, i.e. infinite graphs that can be described as transition graphs of deterministic real-time pushdown automata. We consider the case where some vertices are designated as being final and we build, in a breadth-first manner, a marking of edges that lead to such vertices (i.e., for every vertex that can reach a final one, we mark all out-going edges laying on some shortest path to a final vertex).Our main result is that the edge-marked version of a pushdown graph may itself no longer be a pushdown graph, as we prove that the MSO theory of this enriched graph may be undecidable.

Spiral structures in the rotor-router walk

We study the rotor-router walk on the infinite square lattice with the outgoing edges at each lattice site ordered clockwise. In the previous paper (Papoyan et al 2015 J. Phys. A: Math. Theor. 48 285203), we considered the loops created by rotors and labeled the sites where the loops become closed. The sequence of labels in the rotor-router walk was conjectured to form a spiral structure asymptotically obeying an Archimedean property. In the present paper, we select a subset of labels called ‘nodes’ and consider the spirals formed by them. The new spirals are directly related to tree-like structures, which represent the evolution of the cluster of vertices visited by the walk. We show that the average number of visits to the origin by the moment is where is the average number of spiral rotations.

Completeness Results for Generalized Communication-free Petri Nets with Arbitrary Arc Multiplicities

We investigate gcf-Petri nets, a generalization of communication-free Petri nets allowing arbitrary edge multiplicities, and characterized by the sole restriction that each transition has at most one incoming edge. We use canonical firing sequences with nice properties for gcf-PNs to show that the RecLFS, (zero-)reachability, covering, and boundedness problems of gcf-PNs are in PSPACE. By showing, how PSPACE-Turing machines can be simulated by gss-PNs, a subclass of gcf-PNs where additionally all transitions have at most one outgoing edge, we ultimately prove the PSPACE-completess of these problems for gss/gcf-PNs. Last, we show PSPACE-hardness as well as a doubly exponential space bound for the containment and equivalence problems of gss/gcf-PNs.

Further Considerations about Relationship between Framework and Application Components

A large number of software applications are used over ten years, and are subjected to continuous maintenance activities to improve their operability, functionality, stability and so on. Through such maintenance activities, the internal structure of the software system becomes more complex. We believe that studying how the complexity has evolved is important for understanding the actual maintenance activities. In a previous experiment, we analyzed how code clones and use relations between application and framework components change through a longitudinal study of open source software. However, we performed our analysis over only one set of framework and application, so we would like to discuss how our findings generalize. In this paper, we replicate the previous experiment, targeting several open source projects. By comparing with the result of the past experiment, we will discuss about generalities of our findings. Moreover, we study the differences between the trends for both incoming and outgoing edges, how use relations increase and decrease through long term development, and how code clones are introduced in the software in the early period of the development. These analyses have a certain level of commonality for understanding actual developers' activities.

Directed triadic closure and edge deletion mechanism induce asymmetry in directed edge properties

Many directed real world networks, such as the WWW, genetic regulation networks and economic networks exhibit significant differences between the properties of the incoming and outgoing edges, while the differences exhibited by other networks, such as Social Netw. are far more limited. This phenomenon is most evident in the differences between the distributions of incoming and outgoing degrees and direct clustering coefficients. There is currently no generic network generation model that would reproduce and tune these observed dissimilarities. We propose and empirically validate a simple and realistic model that can explain the emergence of the dissimilarities between the incoming and outgoing network degrees and clustering coefficients by combining directed triadic closure, random edge addition and directed edge removal. Surprisingly, we find that the difference between in and out degree distributions is attributed to asymmetries in the edge removal, highlighting the neglected yet crucial importance of edge removal mechanisms to the static and dynamic properties of real world networks. The model is governed by only two parameters: the first tunes the randomness of the edge addition mechanism, while the second controls the difference between the in and out degrees. The combination of these parameters reproduces the observed variety of directed degree distributions and clustering coefficients. Further comparisons of the model’s microscopic dynamics against the empirically observed evolution of real world social network confirms that while quite simple, the model properly describes both the edge addition and deletion processes in directed networks.

Analysis of a system of nonlocal conservation laws for multi-commodity flow on networks

We consider a system of scalar nonlocal conservation laws on networks that model a highly re-entrant multi-commodity manufacturing system as encountered in semi-conductor production.Every single commodity is modeled by a nonlocal conservation law, and the corresponding PDEs are coupled via a collective load, the work in progress. We illustrate the dynamics for two commodities. In the applications, directed acyclic networks naturally occur, therefore this type of networks is considered. On every edge of the network we have a system of coupled conservation laws with nonlocal velocity. At the junctions the right hand side boundary data of the foregoing edges is passed as left hand side boundary data to the following edges and PDEs. For distributing junctions, where we have more than one outgoing edge, we impose time dependent distribution functions that guarantee conservation of mass. We provide results of regularity, existence and well-posedness of the multi-commodity network model for $L^{p}$-, $BV$- and $W^{1,p}$-data. Moreover, we define an $L^{2}$-tracking type objective and show the existence of minimizers that solve the corresponding optimal control problem.

Exact and Approximation Algorithms for Optimal Equipment Selection in Deploying In-Building Distributed Antenna Systems

We consider a combinatorial optimization problem in passive In-Building Distributed Antenna Systems (IB-DAS) deployment for indoor mobile broadband service. These systems have a tree topology, in which a central base station is connected to a number of antennas located at tree leaves via cables represented by the tree edges. Each inner node corresponds to a power equipment, of which the available types differ in the number of output ports and/or by power gain at the ports. This paper focuses on the equipment selection problem that amounts to, for a given passive DAS tree topology, selecting a power equipment type for each inner node and assigning the outgoing edges of the node to the equipment ports. The performance metric is the power deviation at the antennas from the target values. We consider as objective function the minimization of either the total or the largest power deviation over all antennas. Our contributions are the development of exact pseudo-polynomial time algorithms and (additive) fully-polynomial time approximation schemes for both objectives. Numerical results are provided to illustrate the algorithms. We also extend some results to account for equipment cost.

Rock-Paper-Scissors Meets Borromean Rings

Directed graphs with an odd number of vertices n, where each vertex has both (n − 1)/2 incoming and outgoing edges, have a rich structure. We were lead to their study by both the Borromean rings and the game rockpaper-scissors. An interesting interplay between groups, graphs, topological links, and matrices reveals the structure of these objects, and for larger values of n, extensive computation produces some surprises. Perhaps most surprising is how few of the larger graphs have any symmetry and those with symmetry possess very little. In the final section, we dramatically sped up the computation by first computing a “profile” for each graph.

Optimized Proposed Algorithm for Graph Traversal

This paper includes a flexible algorithm for traversing a directed and an undirected graph. Graph traversal is defined as the problem of visiting all the nodes in a graph in a particular manner, updating and/or checking their values along the way. The Breadth first search along with Depth first search are the most widely used algorithms for traversing a graph. In this article, an algorithm is proposed for traversing a graph taking in consideration the vertex with the maximum outgoing edges. Instead of beginning from the root node and then gaining access to visit the neighbors of the currently visited node, the algorithms looks for the vertex with the maximum edges and then continue traversing all the neighboring vertices of that vertex. This paper presents an algorithm to traverse an undirected or a directed graph and calculates the time and space complexity of the algorithm. The work proposed here intends to find a new algorithm that can be universally applied to all types of graphs General Terms Your general terms must be any term which can be used for general classification of the submitted material such as Pattern Recognition, Security, Algorithms.

In-out interaction complexity metrics for component-based software

In the current state of software engineering, component-based software development is one of the most alluring paradigms for developing large and complex software products. In this software engineering methodology pre-engineered, pre-tested, context-based, adaptable, deployable software components are assembled according to a predefined architecture. Rather than developing a system from scratch, component-based software development emphasizes the integration of these components according to the user's requirements and specifications. In component-based software, the components interact to access and provide services and functionality to each other. Currently, the emphasis of industry and researchers is on developing impressive and efficient metrics and measurement tools to analyze the interaction complexity among these components. To represent the request and the response of services among components, we have used outgoing edges and incoming edges respectively. In this paper we have defined these interactions as In-Interactions and Out-Interactions. The metrics proposed in this paper are solely based on the interactions among the components. In this work some simple methods and metrics for computing the complexity of composable components are suggested. The metrics discussed in this paper include the computation of interaction complexities as Total-Interactions of a component, Total- Interactions of component-based software, Interaction-Ratio of a component, Interaction-Ratio of component-based software, Average- Interaction among components and Interaction-Percentage of components.

Enumerations of plane trees with multiple edges and Raney lattice paths

An N-ary plane multitree is a rooted tree whose subtrees at any vertex are linearly ordered, and every node has at most N outgoing edges to its children, and two nodes can be connected by multiple edges. An N-Raney path of length n is a lattice path running from (0,1) to (n,0) consisting of steps (1,k) for k∈Z such that k≤N, and for which all points except the last one lie above the x-axis.We show a bijection between N-Raney paths of length n and (N+1)-ary plane multitrees of n nodes. We show also a bijection between Raney paths and Raney sequences of integers whose sum is +1 and every partial sum is positive.These two bijections are a main tool to derive formulas for the number of N-ary plane multitrees with specified number of nodes, edges, and leaves. Some statistical properties are considered. It is shown that when N and n tend to infinity, the ratio of the number of leaves to the total number of nodes in all N-ary plane multitrees with n nodes is 1/e.

Local rewiring rules for evolving complex networks

The effects of link rewiring are considered for the class of directed networks where each node has the same fixed out-degree. We model a network generated by three mechanisms that are present in various networked systems; growth, global rewiring and local rewiring. During a rewiring phase a node is randomly selected, one of its out-going edges is detached from its destination then re-attached to the network in one of two possible ways; either globally to a randomly selected node, or locally to a descendant of a descendant of the originally selected node. Although the probability of attachment to a node increases with its connectivity, the probability of detachment also increases, the result is an exponential degree distribution with a small number of outlying nodes that have extremely large degree. We explain these outliers by identifying the circumstances for which a set of nodes can grow to very high degree.

Computing $$k$$ k shortest paths from a source node to each other node

The single-pair K shortest path (KSP) problem can be described as finding $$k$$k least cost paths through a graph between two given nodes in a non-decreasing order, while single-source KSP algorithms aim to find KSPs from a given node to each other node. However, little effort has been devoted to the single-source KSP approaches. This paper proposes a novel single-source KSP algorithm in a given directed weighted graph where loops are allowed. The proposed method is designed to compute a set of shortest paths with exactly $$k$$k distinctive lengths in a non-decreasing order. Meanwhile, it can also find all shortest paths with the length less than a given threshold. Inspired by water flowing principle, we imagine that there are waters flowing from a source node to each other node along edges at a constant speed. When the water reaches a node, the node will generate new waters flowing along its outgoing edges. By stepping back the traces of the water, the ordered shortest paths can be obtained. We also address the correctness and effectiveness of the method. Simulations are carried out using synthetic data and practical graph data, which demonstrate the considerable performance of the proposed approach especially for single-source KSP problems.

The use of network analysis to study complex animal communication systems: a study on nightingale song.

The singing of song birds can form complex signal systems comprised of numerous subunits sung with distinct combinatorial properties that have been described as syntax-like. This complexity has inspired inquiries into similarities of bird song to human language; but the quantitative analysis and description of song sequences is a challenging task. In this study, we analysed song sequences of common nightingales (Luscinia megarhynchos) by means of a network analysis. We translated long nocturnal song sequences into networks of song types with song transitions as connectors. As network measures, we calculated shortest path length and transitivity and identified the 'small-world' character of nightingale song networks. Besides comparing network measures with conventional measures of song complexity, we also found a correlation between network measures and age of birds. Furthermore, we determined the numbers of in-coming and out-going edges of each song type, characterizing transition patterns. These transition patterns were shared across males for certain song types. Playbacks with different transition patterns provided first evidence that these patterns are responded to differently and thus play a role in singing interactions. We discuss potential functions of the network properties of song sequences in the framework of vocal leadership. Network approaches provide biologically meaningful parameters to describe the song structure of species with extremely large repertoires and complex rules of song retrieval.

Synthesis of Stochastic Flow Networks

A stochastic flow network is a directed graph with incoming edges (inputs) and outgoing edges (outputs), tokens enter through the input edges, travel stochastically in the network, and can exit the network through the output edges. Each node in the network is a splitter, namely, a token can enter a node through an incoming edge and exit on one of the output edges according to a predefined probability distribution. Stochastic flow networks can be easily implemented by DNA-based chemical reactions, with promising applications in molecular computing and stochastic computing. In this paper, we address a fundamental synthesis question: Given a finite set of possible splitters and an arbitrary rational probability distribution, design a stochastic flow network, such that every token that enters the input edge will exit the outputs with the prescribed probability distribution. The problem of probability transformation dates back to von Neumann's 1951 work and was followed, among others, by Knuth and Yao in 1976. Most existing works have been focusing on the "simulation" of target distributions. In this paper, we design optimal-sized stochastic flow networks for "synthesizing" target distributions. It shows that when each splitter has two outgoing edges and is unbiased, an arbitrary rational probability \frac{a}{b} with a\leq b\leq 2^n can be realized by a stochastic flow network of size n that is optimal. Compared to the other stochastic systems, feedback (cycles in networks) strongly improves the expressibility of stochastic flow networks.

In- and Out-Degree Distributions of Nodes and Coverage in Random Sector Graphs

In a random sector graph, the presence of an edge between two nodes depends on their distance and spatial orientation. This kind of graph is widely used for modeling wireless sensor networks where communication among nodes is directional. In particular, it is applied to describe both the radio frequency transmission among nodes equipped with directional antennas and the line-of-sight transmission in optical sensor networks. Important properties of a wireless sensor network, such as connectivity and coverage, can be investigated by studying the degree of the nodes of the corresponding random sector graph. In detail, the in-degree value represents the number of incoming edges, whereas the out-degree considers the outgoing edges. This paper mathematically characterizes the average degree of a random sector graph and the probability distributions of the in-degree and out-degree of the nodes. Furthermore, it derives the coverage probability of the network. All the formulas are validated through extensive simulations, showing an excellent match between theoretical results and experimental data.

Edge removal balances preferential attachment and triad closing

Most network formation analysis studies are centered on edge addition. However, edges in real world networks often have a rapid turnover with a large number of edges added and removed between each node addition or removal steps. In such a case, quasiequilibrium is obtained between edge addition and deletion. Edges have been shown to be added to nodes with a high degree and between pairs of nodes with a high number of common neighbors. If not balanced by a degree dependent edge removal, the preference for high degree nodes and node pairs with many common neighbors is expected to increase the average degree of high degree nodes and their clustering coefficient until very large cliques will be formed. Since such large cliques are not formed in real world networks, we conclude that the edge removal probability around high degree nodes and between node pairs with many common neighbors should be higher than around other nodes. We here show the existence of such a balancing mechanism through the relation between the future edge removal probability around nodes and their degree and a similar relation between the edge removal probability and the number of common neighbors of node pairs. In some networks, this preferential detachment process represents an explicit saturation process, and in others, it represents a random deletion process accompanied by a sublinear edge preferential attachment process. A more complex mechanism emerges in directed networks where the preferential detachment can be proportional to the in and out degrees of the nodes involved. In such networks, preferential detachment is stronger for the incoming edges than for the outgoing edges. We hypothesize multiple possible mechanisms that could explain this phenomenon.

Computing Dynamic Slices of Object-Oriented Programs using Dependency Information

a days, object-oriented programs are becoming very popular amongst the developers and hence almost all software are designed using the object-oriented paradigm. Advanced features of object-oriented programming has made it complicated to understand, test, debug and maintain. To better manage these software, slicing techniques have been proved to be quite efficient. This paper proposed an algorithm for dynamic slicing of object-oriented software. It uses SDG(System Dependence Graph) and DG(Dynamic Graph) as the intermediate program representation while computing the dynamic slices. In this paper dynamic slicing algorithm is based on traversing through the outgoing control dependence edges and incoming data dependence edges of Dynamic Graph. The major advantage of the proposed algorithm is that the time required to compute the dynamic slice of the object- oriented programs is directly proportional to the number of dependencies (control and/or data) arising during the run time. Also the proposed algorithm depends on the numbers of nodes present in the intermediate program representation.

A critical study of network models for neural networks and their dynamics

We use three network models, Erdős–Rényi, Watts–Strogatz and structured nodes, to generate networks sharing several topological features with the neural network of C. elegans (our target network). A new topological measurement, incoming and outgoing edges heat maps, is introduced and used to compare the considered networks. We run these networks as random recurrent neural networks and study their dynamics.We find out that none of the considered network models generates networks similar to the target one both in their topological features and dynamics. Moreover, we find that the dynamics of the target network are very robust to the rewiring of its edges.

Oblivious Algorithms for the Maximum Directed Cut Problem

This paper introduces a special family of randomized algorithms for Max DICUT that we call oblivious algorithms. Let the bias of a vertex be the ratio between the total weight of its outgoing edges and the total weight of all its edges. An oblivious algorithm selects at random in which side of the cut to place a vertex v, with probability that only depends on the bias of v, independently of other vertices. The reader may observe that the algorithm that ignores the bias and chooses each side with probability 1/2 has an approximation ratio of 1/4, whereas no oblivious algorithm can have an approximation ratio better than 1/2 (with an even directed cycle serving as a negative example). We attempt to characterize the best approximation ratio achievable by oblivious algorithms, and present results that are nearly tight. The paper also discusses natural extensions of the notion of oblivious algorithms, and extensions to the more general problem of Max 2-AND.