Abstract: Network concepts are increasingly used in biology and genetics. For example, the clustering coefficient has been used to understand network architecture; the connectivity (also known as degree) has been used to screen for cancer targets; and the topological overlap matrix has been used to define modules and to annotate genes. Dozens of potentially useful network concepts are known from graph theory. Here we study network concepts in special types of networks, which we refer to as approximately factorizable networks. In these networks, the pairwise connection strength (adjacency) between 2 network nodes can be factored into node specific contributions, named node 'conformity'. The node conformity turns out to be highly related to the connectivity. To provide a formalism for relating network concepts to each other, we define three types of network concepts: fundamental-, conformity-based-, and approximate conformity-based concepts. Fundamental concepts include the standard definitions of connectivity, density, centralization, heterogeneity, clustering coefficient, and topological overlap. The approximate conformity-based analogs of fundamental network concepts have several theoretical advantages. First, they allow one to derive simple relationships between seemingly disparate networks concepts. For example, we derive simple relationships between the clustering coefficient, the heterogeneity, the density, the centralization, and the topological overlap. The second advantage of approximate conformity-based network concepts is that they allow one to show that fundamental network concepts can be approximated by simple functions of the connectivity in module networks. Using protein-protein interaction, gene co-expression, and simulated data, we show that a) many networks comprised of module nodes are approximately factorizable and b) in these types of networks, simple relationships exist between seemingly disparate network concepts. Our results are implemented in freely available R software code, which can be downloaded from the following webpage: http://www.genetics.ucla.edu/labs/horvath/ModuleConformity/ModuleNetworks

Abstract: Since the 1960s, automated approaches to examination timetabling have been explored and a wide variety of approaches have been investigated and developed. In this paper we build upon a recently presented, sequential solution improvement technique which searches efficiently over a very large set of “adjacent” (neighbourhood) solutions. This solution search methodology, originally developed by Ahuja and Orlin, has been applied successfully in the past to a number of difficult combinatorial optimisation problems. It is based on an improvement graph representation of solution adjacency and identifies improvement moves by finding cycle exchange operations using a modified shortest path label-correcting algorithm. We have drawn upon Ahuja–Orlin’s basic methodology to develop an effective automated exam timetabling technique. We have evaluated our approach against the latest methodologies in the literature on standard benchmark problems. We demonstrate that our approach produces some of the best known results on these problems.

Abstract: This paper presents a new approach to automatic segmentation of foreground objects from an image sequence by integrating techniques of background subtraction and motion-based foreground segmentation. First, a region-based motion segmentation algorithm is proposed to obtain a set of motion-coherence regions and the correspondence among regions at different time instants. Next, we formulate the classification problem as a graph labeling over a region adjacency graph based on Markov random fields (MRFs) statistical framework. A background model representing the background scene is built and then is used to model a likelihood energy. Besides the background model, a temporal coherence is also maintained by modeling it as the prior energy. On the other hand, color distributions of two neighboring regions are taken into consideration to impose spatial coherence. Then, the a priori energy of MRFs takes both spatial and temporal coherence into account to maintain the continuity of our segmentation. Finally, a labeling is obtained by maximizing the a posteriori energy of the MRFs. Under such formulation, we integrate two different kinds of techniques in an elegant way to make the foreground detection more accurate. Experimental results for several video sequences are provided to demonstrate the effectiveness of the proposed approach

Abstract: In many applications, the properties of an object being modeled are stored as labels on vertices or edges of a graph. In this paper, we consider succinct representation of labeled graphs. Our main results are the succinct representations of labeled and multi-labeled graphs (we consider vertex labeled planar triangulations, as well as edge labeled planar graphs and the more general k-page graphs) to support various label queries efficiently. The additional space cost to store the labels is essentially the information-theoretic minimum. As far as we know, our representations are the first succinct representations of labeled graphs. We also have two preliminary results to achieve the main results. First, we design a succinct representation of unlabeled planar triangulations to support the rank/select of edges in ccw (counter clockwise) order in addition to the other operations supported in previous work. Second, we design a succinct representation for a k-page graph when k is large to support various navigational operations more efficiently. In particular, we can test the adjacency of two vertices in O(lg k lg lg k) time, while previous work uses O(k) time (10; 14). © Springer-Verlag Berlin Heidelberg 2007.

Abstract: Power optimization is a crucial concern for modern circuit designs. Multiple supply voltages (MSV's) provide an effective technique for the power optimization. This paper addresses the voltage-island generation problem for MSV designs at the post-floorplanning stage. We first present a general formulation of this problem that considers level-shifter planning and power-network routing resources. Without loss of solution quality, we propose an economical graph-based representation that needs only a linear number of nodes to the block number to model the block adjacency in a floorplan for the voltage-island generation. In contrast, previous works need a quadratic number of nodes. To tackle the addressed problem, we employ an ILP formulation which consists of (1) level-shifter aware wirelength estimation to capture the timing overhead, (2) voltage-island-clustering inequalities to avoid complicated constraint transformations, and (3) inequalities to capture the power-network routing-resource usage. Compared with previous works, our algorithm can produce better voltage islands in terms of power-network routing resources. Experimental results show that our algorithm can effectively reduce the power-network routing resource by up to 19.46% with a reasonable overhead of 4.03% more power consumption and using reasonable running time.

Abstract: Selecting the proper process conditions for the injection-molding process is treated as a multiobjective optimization problem, where different objectives, such as minimizing the injection pressure, volumetric shrinkage/warpage, or cycle time, present trade-off behaviors. As such, various optima may exist in the objective space. This paper presents the development of an integrated simulation-based optimization system that incorporates the design of computer experiments, Gaussian process (GP) for regression, multiobjective genetic algorithm (MOGA), and levels of adjacency to adaptively and automatically search for the Pareto-optimal solutions for different objectives. Since the GP approach can provide both the predictions and the estimations of the predictions simultaneously, a nondominated sorting procedure on the predicted variances at each iteration step is performed to intelligently select extra samples that can be used as additional training samples to improve the GP surrogate models. At the same time, user-defined adjacency constraint percentages are employed for evaluating the convergence of iteration. The illustrative applications in this paper show that the proposed optimization system can help mold designers to efficiently and effectively identify optimal process conditions. © 2007 Wiley Periodicals, Inc. Adv Polym Techn 26:71–85, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/adv.20092

Abstract: We present algorithms for computing the p-rank of integer matrices. They are designed to be particularly effective when p is a small prime, the rank is relatively low, and the matrix itself is large and dense and may exceed virtual memory space. Our motivation comes from the study of difference sets and partial difference sets in algebraic design theory. The p-rank of the adjacency matrix of an associated strongly regular graph is a key tool for distinguishing difference set constructions and thus answering various existence questions and conjectures. For the p-rank computation, we review several memory efficient methods, and present refinements suitable to the small prime, small rank case. We give a new heuristic approach that is notably effective in practice as applied to the strongly regular graph adjacency matrices. It involves projection to a matrix of order slightly above the rank. The projection is extremely sparse, is chosen according to one of several heuristics, and is combined with a small dense certifying component. Our algorithms and heuristics are implemented in the LinBox library. We also briefly discuss some of the software design issues and we present results of experiments for the Paley and Dickson sequences of strongly regular graphs.

Abstract: An analysis of one-dimensional adjacency effects is presented. This classical problem is shown to be amenable to closed form error analysis when one-dimensional adjacency correction schemes are used. In particular the error made when surface reflectance is retrieved using an infinite target assumption is given in closed form. This allows deductions for the behaviour of the error as a function of wavelength and optical thickness. Typical length-scales of the adjacency effects are deduced and the range and magnitude of the error are also given in closed form.

Abstract: A zero eigenvalue in the spectrum of the adjacency matrix of the graph representing an unsaturated carbon framework indicates the presence of a nonbonding π orbital (NBO). A graph with at least one zero in the spectrum is singular; nonzero entries in the corresponding zero-eigenvalue eigenvector(s) (kernel eigenvectors) identify the core vertices. A nut graph has a single zero in its adjacency spectrum with a corresponding eigenvector for which all vertices lie in the core. Balanced and uniform trivalent (cubic) nut graphs are defined in terms of (−2, +1, +1) patterns of eigenvector entries around all vertices. In balanced nut graphs all vertices have such a pattern up to a scale factor; uniform nut graphs are balanced with scale factor one for every vertex. Nut graphs are rare among small fullerenes (41 of the 10 190 782 fullerene isomers on up to 120 vertices) but common among the small trivalent polyhedra (62 043 of the 398 383 nonbipartite polyhedra on up to 24 vertices). Two constructions are describ...

Abstract: A method for segmenting at least a pair of regions of an image, such method comprising: obtaining data of the image; computing watersheds of the image from intensity gradients of such image data; extracting a watershed region adjacency graph from the computed watersheds, such graph comprising a plurality of nodes corresponding to the watersheds and node interconnecting edges; assigning weights to the interconnecting edges; identifying each of the pair of regions in the image; identifying the nodes corresponding to the pair of identified regions in the adjacency graph; applying constrained graph-partitioning in the adjacency graph using the edge-weights to label unmarked nodes corresponding to each one of the pair of regions; and extrapolating the obtained label nodes on the graph to the image to segment each one of the pair of regions of the image.

Abstract: This paper describes a complete implementation of the Approximate Cell Decomposition approach to path planning. The method presented overcomes a primary bottleneck associated with this approach, which is determining cell adjacency. This increased efficiency is achieved by employing a technique found in Geographic Information Systems known as tesseral addressing.

Abstract: A new radial space-filling method for visualizing cluster hierarchies is presented. The method, referred to as a radial clustergram, arranges the clusters into a series of layers, each representing a different level of the tree. It uses adjacency of nodes instead of links to represent parent−child relationships and allocates sufficient screen real estate to each node to allow effective visualization of cluster properties through color-coding. Radial clustergrams combine the most appealing features of other cluster visualization techniques but avoid their pitfalls. Compared to classical dendrograms and hyperbolic trees, they make much more efficient use of space; compared to treemaps, they are more effective in conveying hierarchical structure and displaying properties of nodes higher in the tree. A fisheye lens is used to focus on areas of interest, without losing sight of the global context. The utility of the method is demonstrated using examples from the fields of molecular diversity and conformational...

Abstract: Traditional aspect graphs are topology-based and are impractical for articulated objects. In this work we learn a small number of aspects, or prototypical views, from video data. Groundtruth segmentations in video sequences are utilized for both training and testing aspect models that operate on static images. We represent aspects of an articulated object as collections of line segments. In learning aspects, where object centers are known, a linear matching based on line location and orientation is used to measure similarity between views. We use K-medoid to find cluster centers. When using line aspects in recognition, matching is based on pairwise cues of relative location, relative orientation as well adjacency and parallelism. Matching with pairwise cues leads to a quadratic optimization that we solve with a spectral approximation. We show that our line aspect matching is capable of locating people in a variety of poses. Line aspect matching performs significantly better than an alternative approach using Hausdorff distance, showing merits of the line representation.

Abstract: In this paper, we first give a relation between the adjacency spectral radius and the $Q$-spectral radius of a graph. Then using this result, we further give some new sharp upper bounds on the adjacency spectral radius of a graph in terms of degrees and the average 2-degrees of vertices. Some known results are also obtained.

Abstract: We present a novel force-directed method for drawing an intersecting clustered graph. This is based upon simulation of a virtual physical system. The graph can express complicated structures such as inclusion and intersection between vertices/clusters as well as adjacency, and it is used in diverse fields such as creativity support, software engineering, and semantic Web. We describe definitions, aesthetics, model, algorithm, performance evaluation, and applications.

Abstract: The watershed partition of an image often results in over-segmentation. This well-known phenomenon is due to variations of intensity that do not correspond to object boundaries and produce spurious local minima in the image gradient magnitude. Filtering minima or merging watershed regions is then necessary to obtain a higher-level description of the data. In this paper, we propose new solutions to this problem by applying two interactive multilabel partitioning techniques to the adjacency graph of the watershed regions. In our first approach, the partition is derived from the probability that a "random walker" starting at an arbitrary node, first reaches a node with a pre-assigned label. In the second approach, we compute a geodesic partition of the graph using competing wavefronts starting at prescribed nodes. Both methods are based on existing segmentation techniques previously implemented on image lattices. Using a watershed adjacency graph greatly reduces their memory footprint and computational cost. We demonstrate the practicality and versatility of this approach with several experiments on 2D and 3D datasets.

Abstract: An injection or die-casting mould is an assembly of parts containing an impression into which molten material is injected. In this article, the undercuts present in mould parts are divided into basically two parts: completely visible and partially visible. A graph-based approach is proposed to identify these undercuts even for the free form objects. Unlike conventional graph based methods a new polyhedron face adjacency graph (PFAG) is proposed with the key concept of visibility of undercuts by using Bezier surface. A rule-based approach is also discussed to automatically generate an optimal parting surfaceof irregular moulded parts. Since the generation of parting surface plays an important and effective role in mould – die design, thus it is essential to develop a simple and robust algorithm based on proposed methodology, which can effectively tackle the problem. Different case studies show that the proposed method can recognize various undercut features without much difficulty.

Abstract: We define morphological operators on weighted graphs in order to speed up image transformations such as floodings, levelings and waterfall hierarchies. The image is represented by its region adjacency graph in which the nodes represent the catchment basins of the image and the edges link neighboring regions. The weights of the nodes represent the level of flooding in each catchment basin ; the weights of the edges represent the altitudes of the pass points between adjacent regions.

Abstract: We present a complete, exact and efficient implementation to compute the adjacency graph of an arrangement of quadrics, i.e. surfaces of algebraic degree 2. This is a major step towards the computation of the full 3D arrangement. We enhanced an implementation for an exact parameterization of the intersection curves of two quadrics, such that we can compute the exact parameter value for intersection points and from that the adjacency graph of the arrangement. Our implementation is complete in the sense that it can handle all kinds of inputs including all degenerate ones, i.e. singularities or tangential intersection points. It is exact in that it always computes the mathematically correct result. It is efficient measured in running times, i.e. it compares favorably to the only previous implementation.

Abstract: Numerical comparison of spaces with one another is often achieved with set scalar measures such as global and local integration, connectivity, etc., which capture a particular quality of the space but therefore lose much of the detail of its overall structure. More detailed methods such as graph edit distance are difficult to calculate, particularly for large plans. This paper proposes the use of the graph spectrum, or the ordered eigenvalues of a graph adjacency matrix, as a means to characterise the space as a whole. The result is a vector of high dimensionality that can be easily measured against others for detailed comparison. Several graph types are investigated, including boundary and axial representations, as are several methods for deriving the spectral vector. The effectiveness of these is evaluated using a genetic algorithm optimisation to generate plans to match a given spectrum, and evolution is seen to produce plans similar to the initial targets, even in very large search spaces. Results indicate that boundary graphs alone can capture the gross topological qualities of a space, but axial graphs are needed to indicate local relationships. Methods of scaling the spectra are investigated in relation to both global local changes to plan arrangement. For all graph types, the spectra were seen to capture local patterns of spatial arrangement even as global size is varied.

Abstract: The raindrop method of searching a solution space for feasible and efficient forest management plans has been demonstrated as being useful under a limited set of circumstances, mainly where adjacency restrictions are accommodated using the unit restriction model. We expanded on this work and applied the model (in a modified form) to a problem that had both wood flow and area restriction adjacency constraints, then tested the problem formulation on six hypothetical forests of different sizes and age class distributions. Threshold accepting and tabu search were both applied to the problems as well. The modified raindrop method’s performance was best when applied to forests with normal age class distributions. 1-opt tabu search worked best on forests with young age class distributions. Threshold accepting and the raindrop method both performed well on forests with older age class distributions. On average, the raindrop method produced higher quality solutions for most of the problems, and in all but one case where it did not, the solutions generated were not significantly different than the heuristic that located a better solution. The advantage of the raindrop method is that it uses only two parameters and does not require extensive parameterization. The disadvantage is the amount of time it needs to solve problems with area restriction adjacency constraints. We suggest that it may be advantageous to use this heuristic on problems with relatively simple spatial forest planning constraints, and problems that do not involve young initial age class distributions. However, generalization of the performance of the raindrop method to other forest planning problems is problematic, and will require examination by those interested in pursuing this planning methodology. Given that our tests of the raindrop method are limited to a small set of URM and ARM formulations, one should view the combined set of work as additional insight into the potential performance of the method on problems of current interest to the forest planning community.

Abstract: The small screens on increasingly used mobile devices challenge the traditional visualization methods designed for desktops. This paper presents a method called "Radial Edgeless Tree" (RELT) for visualizing trees in a 2- dimensional space. It combines the existing connection tree drawing with the space-filling approach to achieve the efficient display of trees in a small geometrical area, such as the screen that are commonly used in mobile devices. We recursively calculate a set of non-overlapped polygonal nodes that are adjacent in the hierarchical manner. Thus, the display space is fully used for displaying nodes, while the hierarchical relationships among the nodes are presented by the adjacency (or boundary-sharing) of the nodes. It is different from the other traditional connection approaches that use a node-link diagram to present the parent-child relationships which waste the display space. The hierarchy spreads from north-west to south-east in a top-down manner which naturally follows the traditional way of human perception of hierarchies. We discuss the characteristics, advantages and limitations of this new technique and suggestions for future research.