Layered Graph Research Articles

Monitoring the evolutionary aspect of the Gene Ontology to enhance predictability and usability

BackgroundMuch effort is currently made to develop the Gene Ontology (GO). Due to the dynamic nature of information it addresses, GO undergoes constant updates whose results are released at regular intervals as separate versions. Although there are a large number of computational tools to aid the development of GO, they are operating on a particular version of GO, making it difficult for GO curators to anticipate the full impact of particular changes along the time axis on a larger scale. We present a method for tapping into such an evolutionary aspect of GO, by making it possible to keep track of important temporal changes to any of the terms and relations of GO and by consequently making it possible to recognize associated trends.ResultsWe have developed visualization methods for viewing the changes between two different versions of GO by constructing a colour-coded layered graph. The graph shows both versions of GO with highlights to those GO terms that are added, removed and modified between the two versions. Focusing on a specific GO term or terms of interest over a period, we demonstrate the utility of our system that can be used to make useful hypotheses about the cause of the evolution and to provide new insights into more complex changes.ConclusionsGO undergoes fast evolutionary changes. A snapshot of GO, as presented by each version of GO alone, overlooks such evolutionary aspects, and consequently limits the utilities of GO. The method that highlights the differences of consecutive versions or two different versions of an evolving ontology with colour-coding enhances the utility of GO for users as well as for developers. To the best of our knowledge, this is the first proposal to visualize the evolutionary aspect of GO.

Fault detection and isolation in robotic manipulator via hybrid neural networks

Fault diagnosis systems are important for industrial robots, especially those operated in remote and hazardous environment. Faults in robotic manipulator can cause economic and serious damages. So the Robots need the ability to independently as well as effectively detect and tolerate internal failures in order to continue performing their tasks without the need for immediate human intervention. This saves time and cost involved in repairing the robot. This type of autonomous fault tolerance is also useful for industrial robots in that it decreases down-time by tolerating failures, identifies faulty components or subsystems to speed up the repair process, and prevents the robot from damaging the products being manufactured. So an attempt is made to develop a robust fault detection system to identify and isolate the faults in robot manipulator. In this paper, two artificial neural networks are employed to identify and isolate the faults. A learning architecture, approximation of dynamic behavior of robot manipulator, is used to generate the residual vector, by comparing with actual measured values. First, A multi layer perceptron feed forward network, whose structure is characterized by layered graph, trained with back propagation algorithm is applied to reproduce the dynamic behavior, then counter propagation network which learns a near optimal look uptable approximation to the mapping being approximated. The counter propagation network has the ability to compress a huge amount of data in a few weights and parameters. Simulations employing a SCORBOT ER 5u plus five links robotic manipulator are showed demonstrating that the system can detect and isolate correctly faults that occur in non-trained trajectories. The main contribution of this work is the first application of fault detection and isolation to robot manipulator with non-additive fault. (Received in January 2007, accepted in October 2007. This paper was with the authors 3 months for 2 revisions.)

On the Parameterized Complexity of Layered Graph Drawing

We consider graph drawings in which vertices are assigned to layers and edges are drawn as straight line-segments between vertices on adjacent layers. We prove that graphs admitting crossing-free h-layer drawings (for fixed h) have bounded pathwidth. We then use a path decomposition as the basis for a linear-time algorithm to decide if a graph has a crossing-free h-layer drawing (for fixed h). This algorithm is extended to solve related problems, including allowing at most k crossings, or removing at most r edges to leave a crossing-free drawing (for fixed k or r). If the number of crossings or deleted edges is a non-fixed parameter then these problems are NP-complete. For each setting, we can also permit downward drawings of directed graphs and drawings in which edges may span multiple layers, in which case either the total span or the maximum span of edges can be minimized. In contrast to the Sugiyama method for layered graph drawing, our algorithms do not assume a preassignment of the vertices to layers.

Expressive security policy rules using Layered Conceptual Graphs

A method must be provided to support the analysis of security policy rules interdependencies in a (possibly distributed) environment. We propose a Conceptual Graphs based language that will allow us to represent the structure of information and to employ reasoning for consistency checking. We motivate our choice of language by the gained expressivity, the potential for depicting policy associations rigourously and by associated reasoning capabilities. We explain our approach in the context of security requirements for medical systems. We evaluate our work theoretically, by means of an example of a real world policy rule.

Cooperation enhanced by the difference between interaction and learning neighborhoods for evolutionary spatial prisoner’s dilemma games

We study an evolutionary prisoner's dilemma game with two layered graphs, where the lower layer is the physical infrastructure on which the interactions are taking place and the upper layer represents the connections for the strategy adoption (learning) mechanism. This system is investigated by means of Monte Carlo simulations and an extended pair-approximation method. We consider the average density of cooperators in the stationary state for a fixed interaction graph, while varying the number of edges in the learning graph. According to the Monte Carlo simulations, the cooperation is modified substantially in a way resembling a coherence-resonance-like behavior when the number of learning edges is increased. This behavior is reproduced by the analytical results.

Refactorisation methods for TTCN-3

In this paper we introduce automatic methods for restructuring source codes written in test description languages. We modify the structure of these sources without making any changes to their behavior. This technique is called refactorisation. There are many approaches to refactorisation. The goal of our refactorisation methods is to increase the maintainability of source codes. We focus on TTCN-3 (Testing and Test Control Notation), which is a rapidly spreading test description language nowadays. A TTCN-3 source consists of a data description (static) part and a test execution (dynamic) part. We have developed models and refactorisation methods based on these models, separately for the two parts. The static part is mapped into a layered graph structure, while the dynamic part is mapped to a CEFSM (Communicating Extended Finite State Machine) – based model.

Multicasting for all-optical multifiber networks

All-optical wavelength-routed WDM WANs can support the high bandwidth and the long session duration requirements of the application scenarios such as interactive distance learning or on-line diagnosis of patients simultaneously in different hospitals. However, multifiber and limited sparse light splitting and wavelength conversion capabilities of switches result in a difficult optimization problem. We attack this problem using a layered graph model. The problem is defined as a k-edge-disjoint degree-constrained Steiner tree problem for routing and fiber and wavelength assignment of k multicasts. A mixed integer linear programming formulation for the problem is given, and a solution using CPLEX is provided. However, the complexity of the problem grows quickly with respect to the number of edges in the layered graph, which depends on the number of nodes, fibers, wavelengths, and multicast sessions. Hence, we propose two heuristics layered all-optical multicast algorithm [(LAMA) and conservative fiber and wavelength assignment (C-FWA)] to compare with CPLEX, existing work, and unicasting. Extensive computational experiments show that LAMA's performance is very close to CPLEX, and it is significantly better than existing work and C-FWA for nearly all metrics, since LAMA jointly optimizes routing and fiber-wavelength assignment phases compared with the other candidates, which attack the problem by decomposing two phases. Experiments also show that important metrics (e.g., session and group blocking probability, transmitter wavelength, and fiber conversion resources) are adversely affected by the separation of two phases. Finally, the fiber-wavelength assignment strategy of C-FWA (Ex-Fit) uses wavelength and fiber conversion resources more effectively than the First Fit.

Modeling and solving the rooted distance-constrained minimum spanning tree problem

In this paper we discuss models and methods for solving the rooted distance constrained minimum spanning tree problem which is defined as follows: given a graph G = ( V , E ) with node set V = { 0 , 1 , … , n } and edge set E , two integer weights, a cost c e and a delay w e associated with each edge e of E , and a natural (time limit) number H , we wish to find a spanning tree T of the graph with minimum total cost and such that the unique path from a specified root node, node 0, to any other node has total delay not greater than H . This problem generalizes the well known hop-constrained spanning tree problem and arises in the design of centralized networks with quality of service constraints and also in package shipment with service guarantee constraints. We present three theoretically equivalent modeling approaches, a column generation scheme, a Lagrangian relaxation combined with subgradient optimization procedure, both based on a path formulation of the problem, and a shortest path (compact) reformulation of the problem which views the underlying subproblem as defined in a layered extended graph. We present results for complete graph instances with up to 40 nodes. Our results indicate that the layered graph path reformulation model is still quite good when the arc weights are reasonably small. Lagrangian relaxation combined with subgradient optimization procedure appears to work much better than column generation and seems to be a quite reasonable approach to the problem for large weight, and even small weight, instances.

Introduction to the Special Issue on the Integration of AI and OR Techniques in CP for Combinatorial Optimization (CPAIOR 2005)

The Second International Conference on Integration of Artificial Intelligence (AI) and Operations Research (OR) Techniques in Constraint Programming (CP) for Combinatorial Optimization Problems (CPAIOR 2005) was held in Prague, Czech Republic, during May 30–June 1, 2005. The interest of the research community in this conference is witnessed by the high number of submissions received, almost reaching 100 papers submitted to CPAIOR 2005. From these submissions, we chose 26 papers to be published in full in the proceedings and only five papers to be extended into a journal form, and submitted to this Special Issue. These papers are explained here in greater depth than was possible in the conference proceedings. The first three papers have a theme in common: global constraints and filtering algorithms. Global constraints play a significant role in Constraint Programming and in hybrid approaches. They are a vehicle for embedding OR techniques in CP and they are crucial to the solution of hard combinatorial problems. The first paper in this group is entitled Filtering Algorithms for the NValue Constraint by Bessiere et al. The paper shows some approximations for computing a bound on the total number of different values an array of variables can assume. The approximations are compared as far as filtering and complexity are concerned. The second paper in the global constraint group is entitled A Cost-Regular Based Hybrid Column Generation Approach by Demassey et al. It proposes a costbased version of the regular constraint, where the longest and the shortest path are computed in the layered graph of the regular constraint. The constraint is particularly useful for solving sub-problems in hybrid Column Generation approaches. The constraint is applied to Employee Timetabling Problems to show its effectiveness.

Segmentation and tracking of multiple video objects

This paper describes a technique that produces a content-based representation of a video shot composed by a background (still) mosaic and one or more foreground moving objects. Segmentation of moving objects is based on ego-motion compensation and on background modelling using tools from robust statistics. Region matching is carried out by an algorithm that operates on the Mahalanobis distance between region descriptors in two subsequent frames and uses singular value decomposition to compute a set of correspondences satisfying both the principle of proximity and the principle of exclusion. The sequence is represented as a layered graph, and specific techniques are introduced to cope with crossing and occlusion. Examples of MPEG-4 (main profile) encoding are reported.

From the Dandelion Code to the Rainbow code: a class of bijective spanning tree representations with linear complexity and bounded locality

There are many ways to represent spanning trees in genetic algorithms (GAs). Among them are Cayley codes, which represent each tree on n vertices as a string of (n-2) integers from the set [1,n]. In 2003, Thompson showed that the Dandelion Code, a Cayley code with high locality, offers consistently better performance in a GA than all other known Cayley codes, including the Pru/spl uml/fer Code and the Blob Code. In this paper, we study the Dandelion Code and its properties. We give linear-time implementations of the decoding and encoding algorithms, and prove that the representation has bounded locality and asymptotically optimal locality, unlike all other known Cayley codes. We then modify the Dandelion Code to create bijective spanning tree representations for graph topologies other than the complete graph. Two variations are described: the bipartite Dandelion Code (for encoding the spanning trees of a complete bipartite graph) and the Rainbow Code (for encoding the spanning trees of a complete layered graph). Both variations inherit the Dandelion Code's desirable properties, and have the potential to outperform existing GA representations for computationally hard transportation problems (including the Fixed Charge Transportation Problem) and multistage transportation problems, particularly on large instances.

On a class of Koszul algebras associated to directed graphs

In [I. Gelfand, V. Retakh, S. Serconek, R.L. Wilson, On a class of algebras associated to directed graphs, Selecta Math. (N.S.) 11 (2005), math.QA/0506507] I. Gelfand and the authors of this paper introduced a new class of algebras associated to directed graphs. In this paper we show that these algebras are Koszul for a large class of layered graphs.

On a class of algebras associated to directed graphs

To any directed graph we associate an algebra with edges of the graph as generators and with relations defined by all pairs of directed paths with the same origin and terminus. Such algebras are related to factorizations of polynomials over noncommutative algebras. We also construct a basis for our algebras associated to layered graphs.

SLEA: a novel scheme for routing in overlay IP/WDM networks

This paper studies the routing problems in Internet protocol/wavelength-division-multiplexing (IP/WDM) networks based on the overlay routing algorithm (ORA) and the integrated routing algorithm (IRA), respectively. Although IRA usually outperforms ORA in terms of blocking performance, IRA exhibits disadvantages in control information exchange, network privacy issue, and wavelength port efficiency. In this paper, a new mechanism called the short lightpath establishment approach (SLEA) is proposed for ORA in order to tackle the problems in IRA and achieve similar (or even better) network performance at the same time. The main idea of SLEA is to ensure that each new lightpath created by ORA is restricted by an optical hop constraint when a subwavelength-granularity connection is routed in the optical layer. It follows that SLEA essentially avoids per-connection-based greedy treatment and improves network wide resource utilization by eliminating inefficient long optical bypasses. To implement SLEA in ORA, the Dijsktra's algorithm has been modified based on an extended layered graph model. SLEA does not introduce any additional signaling and computational complexity. The analysis and simulation in this paper show that there exists an optimal optical hop constraint for each particular network configuration such that SLEA-based ORA (SLEA-ORA) can efficiently utilize the network resource of concern. As a result, with the optimal optical hop constraint, SLEA-ORA could outperform ORA and IRA in terms of the bandwidth-blocking ratio (BBR) and the average number of IP hops of label-switched paths (LSPs).

Confluent Layered Drawings

We combine the idea of confluent drawings with Sugiyama-style drawings in order to reduce the edge crossings in the resultant drawings. Furthermore, it is easier to understand the structures of graphs from the mixed-style drawings. The basic idea is to cover a layered graph by complete bipartite subgraphs (bicliques), then replace bicliques with tree-like structures. The biclique cover problem is reduced to a special edge-coloring problem and solved by heuristic coloring algorithms. Our method can be extended to obtain multi-depth confluent layered drawings.

Crossing-constrained hierarchical drawings

We study the problem of computing hierarchical drawings of layered graphs when some pairs of edges are not allowed to cross. We show that deciding the existence of a drawing satisfying at least k non-crossing constraints from a given set is NP-hard, even if the graph is 2-layered and even when the permutation of the vertices on one side of the bipartition is fixed. We then propose simple constant-ratio approximation algorithms for the optimization version of the problem, which requires to find a maximum realizable subset of constraints, and we discuss how to extend the well-known hierarchical approach for creating layered drawings of directed graphs so as to minimize the number of edge crossings while maximizing the number of satisfied constraints.

Dynamic routing, wavelength, and fibre selection algorithms for multifibre WDM grooming networks

The problem of dynamic routing in a multifibre time-slotted wavelength routed WDM network is considered. Requests to establish a connection are dynamic and each connection requests an integer multiple of some basic unit. Each wavelength has the capacity of carrying a multiple of these channels, where each channel is represented by a time-slot as in TDM networks. The network is represented as a layered graph model with multiple layers, where each layer represents a specific wavelength. Each link in the layered graph has one or more fibres and an associated cost. The cost of layered graph links could be a function of the loading state of the respective wavelength across the available fibres. Algorithms are proposed for fibre selection and for setting link costs, and a modified Dijkstra algorithm on the layered graph is used to select a route on the layered graph for a new connection request. The selected route on the layered graph represents the physical path and the selected wavelength. The performance of these algorithms is evaluated for a realistic mesh network topology for various combinations of the number of wavelengths, the number of fibres per link, the number of time-slots per wavelength, and the offered load for both uniform and non-uniform traffic loads. The best performing fibre selection and link cost update methods are identified. The proposed algorithm for routing and wavelength assignment in mesh optical WDM grooming networks outperforms previously proposed work in the literature.

An Efficient Implementation of Sugiyama's Algorithm for Layered Graph Drawing

Sugiyama's algorithmic framework for layered graph drawing is commonly used in practical software. The extensive use of dummy vertices to break long edges between non-adjacent layers often leads to unsatisfactorial performance. The worst-case running-time of Sugiyama's approach is O(|V||E|log|E|) requiring O(|V||E|) memory, which makes it unusable for the visualization of large graphs. By a conceptually simple new technique we are able to keep the number of dummy vertices and edges linear in the size of the graph and hence reduce the worst-case time complexity of Sugiyama's approach by an order of magnitude to O((|V|+|E|)log|E|) requiring O(|V|+|E|) space.

Visual Understanding of Metabolic Pathways Across Organisms Using Layout in Two and a Half Dimensions

Summary We propose a method for visualizing a set of related metabolic pathways across organisms using 2 1/2 dimensional graph visualization. Interdependent, twodimensional layouts of each pathway are stacked on top of each other so that biologists get a full picture of subtle and significant differences among the pathways. The (dis)similarities between pathways are expressed by the Hamming distances of the underlying graphs which are used to compute a stacking order for the pathways. Layouts are determined by a global layout of the union of all pathway graphs using a variant of the proven Sugiyama approach for layered graph drawing. Our variant layout approach allows edges to cross if they appear in different graphs.

Automatic Layout of UML Class Diagrams in Orthogonal Style

Unified modelling language (UML) diagrams have become increasingly important in engineering and re-engineering processes for software systems. Of particular interest are UML class diagrams whose purpose is to display generalizations, associations, aggregations, and compositions in one picture. The combination of directed and undirected relations poses a special challenge to a graph layout tool. Current approaches for the automatic layout of class diagrams are based on the layered graph drawing paradigm. These algorithms produce good results for class diagrams with large and deep structural information, that is, diagrams with a large and deep inheritance hierarchy. However, they do not perform satisfactorily in absence of this information. We suggest to use the topology-shape—metrics paradigm for automatic layout of class diagrams, which has been used very successfully for drawing undirected graphs in orthogonal style. Moreover, we introduce the algorithms UML-Kandinsky and GoVisual fitting into this paradigm. Both algorithms work for class diagrams with rich structural information as well as for class diagrams with few or no structural information. Therefore, they improve the existing algorithms significantly.