Force-directed Approach Research Articles

A Force-Directed Approach to Seeking Route Recommendation in Ride-on-Demand Service Using Multi-Source Urban Data

The rapidly-growing business of ride-on-demand (RoD) service such as Uber, Lyft and Didi proves the effectiveness of their new service model – using mobile apps and dynamic pricing to coordinate between drivers, passengers and the service provider, to manipulate the supply and demand, and to improve service responsiveness as well as quality. Despite its success, dynamic pricing creates a new problem for drivers: how to seek for passengers to maximize revenue under dynamic prices. Seeking route recommendation has already been studied extensively in traditional taxi service, but most studies do not consider the effects of taxis and passengers on the seeking taxi simultaneously. Further, in RoD service it is necessary to consider more factors such as dynamic prices, the status of other transportation services, etc. In this paper, we employ a force-directed approach to model, by analogy, the relationship between vacant cars and passengers as that between positive and negative charges in electrostatic field. We extract features from multi-source urban data to describe dynamic prices, the status of RoD, taxi and public transportation services, and incorporate them into our model. The model is then used in route recommendation in every intersection so that a driver in a vacant RoD car knows which road segment to take next. We conduct extensive experiments based on our multi-source urban data, including RoD service operational data, taxi GPS trajectory data and public transportation distribution data, and results not only show that our approach outperforms existing baselines, but also justify the need to incorporate multi-source urban data and dynamic prices.

How to Draw a Planarization

We study the problem of computing straight-line drawings of non-planar graphs with few crossings. We assume that a crossing-minimization algorithm is applied first, yielding a planarization, i.e., a planar graph with a dummy vertex for each crossing, that fixes the topology of the resulting drawing. We present and evaluate two different approaches for drawing a planarization in such a way that the edges of the input graph are as straight as possible. The first approach is based on the planarity-preserving force-directed algorithm ${\rm I{\small M}P{\small R}E{\small D}}$ [Simonetto et al. Computer Graphics Forum 2011], the second approach, which we call Geometric Planarization Drawing, iteratively moves vertices to their locally optimal positions in the given initial drawing. Our evaluation shows that both approaches significantly improve the initial drawing and that our geometric approach outperforms the force-directed approach. To the best of our knowledge, this is the first paper concerned with the generation of a straight-line drawing that respects an arbitrary planarization.

Techniques for Drawing Geographic One-Line Diagrams: Substation Spacing and Line Routing

Visualization of electric power transmission systems centers on the one-line diagram, which is a simplified logical depiction of the circuit's connections and elements. Such a graph drawing is useful for supporting the study, analysis, and presentation of power system data. This paper proposes an automated way to generate one-line diagrams, given substation identifiers with geographic tags and the system bus-branch model. Two approaches to drawing the substations are given: a force-directed approach and a greedy approach, which in different ways modify the position and size of substations as drawn. For transmission line routing between substations, a Delaunay-based method is employed, which segments the transmission line drawings to avoid overlapping with substations and other lines. These methods show good visual properties in spacing, geographic context, relatively straight lines, and computational speed. The result is that large power systems, real and synthetic, can be easily and quickly visualized with a diagram that merges geographic context with logical clarity.

Analysis of the Usage of Magnetic Force-directed Approach and Visual Techniques for Interactive Context-based Drawing of Multi-attributed Graphs

Abstract In this article, the authors perform an analysis in order to assess adaptation of magnetic force-directed algorithms for context-based information extraction from multi-attributed graphs during visualization sessions. Theoretic standings behind magnetic force-directed approach are stated together with review on how particular features of respective algorithms in combination with appropriate visual techniques are especially suitable for improved processing and presenting of knowledge that is captured in form of graphs. The complexity of retrieving multi-attributed information within the proposed approach is handled with dedicated tools, such as selective attraction of nodes to MFE (Magnetic Force Emitter) based on search criteria, localization of POI (Point of Interest) regions, graph node anchoring, etc. Implicit compatibility of aforementioned tools with interactive nature of data exploration is distinguished. Description of case study, based on bibliometric network analysis is given, which is followed by the review of existing related works in this field. Conclusions are made and further studies in the field of visualization of multi-attributed graphs are defined.

EulerForce: Force-directed layout for Euler diagrams

Euler diagrams use closed curves to represent sets and their relationships. They facilitate set analysis, as humans tend to perceive distinct regions when closed curves are drawn on a plane. However, current automatic methods often produce diagrams with irregular, non-smooth curves that are not easily distinguishable. Other methods restrict the shape of the curve to for instance a circle, but such methods cannot draw an Euler diagram with exactly the required curve intersections for any set relations. In this paper, we present eulerForce, as the first method to adopt a force-directed approach to improve the layout and the curves of Euler diagrams generated by current methods. The layouts are improved in quick time. Our evaluation of eulerForce indicates the benefits of a force-directed approach to generate comprehensible Euler diagrams for any set relations in relatively fast time.

A fast successive over-relaxation algorithm for force-directed network graph drawing

Force-directed approach is one of the most widely used methods in graph drawing research. There are two main problems with the traditional force-directed algorithms. First, there is no mature theory to ensure the convergence of iteration sequence used in the algorithm and further, it is hard to estimate the rate of convergence even if the convergence is satisfied. Second, the running time cost is increased intolerablely in drawing large- scale graphs, and therefore the advantages of the force-directed approach are limited in practice. This paper is focused on these problems and presents a sufficient condition for ensuring the convergence of iterations. We then develop a practical heuristic algorithm for speeding up the iteration in force-directed approach using a successive over-relaxation (SOR) strategy. The results of computational tests on the several benchmark graph datasets used widely in graph drawing research show that our algorithm can dramatically improve the performance of force-directed approach by decreasing both the number of iterations and running time, and is 1.5 times faster than the latter on average.

Towards high-quality, untangled meshes via a force-directed graph embedding approach

Abstract High quality meshes are crucial for the solution of partial differential equations (PDEs) via the finite element method (or other PDE solvers). The accuracy of the PDE solution, and the stability and conditioning of the stiffness matrix depend upon the mesh quality. In addition, the mesh must be untangled in order for the finite element method to generate physically valid solutions. Tangled meshes, i.e., those with inverted mesh elements, are sometimes generated via large mesh deformations or in the mesh generation process. Traditional techniques for untangling such meshes are based on geometry and/or optimization. Optimization-based mesh untangling techniques first untangle the mesh and then smoothe the resulting untangled mesh in order to obtain high quality meshes; such techniques require the solution of two optimization problems. In this paper, we study how to modify a physical, force-directed method based upon the Fruchterman-Reingold (FR) graph layout algorithm so that it can be used for untangling. The objectives of aesthetic graph layout, such as minimization of edge intersections and near equalization of edge lengths, follow the goals of mesh untangling and generating good quality elements, respectively. Therefore, by using the force-directed method, we can achieve both steps of mesh untangling and mesh smoothing in one operation. We compare the effectiveness of our method with that of the optimization-based mesh untangling method in [1] and implemented in Mesquite by untangling a suite of unstructured triangular, quadrilateral, and tetrahedral finite element volume meshes. The results show that the force-directed method is substantially faster than the Mesquite mesh untangling method without sacrificing much in terms of mesh quality for the majority of the test cases we consider in this paper. The force-directed mesh untangling method demonstrates the most promise on convex geometric domains. Further modifications will be made to the method to improve its ability to untangle meshes on non-convex domains.

A Force-Directed Scheduling based architecture generation algorithm and design tool for FPGAs

The derivation of efficient, custom architectures for implementing algorithms on Field Programmable Gate Array platforms presents several research challenges. We focus on the derivation of efficient streaming architectures from dataflow graphs, targeting multi-cycle, fully pipelined functional units. In this paper, we present a Force-Directed Scheduling based algorithm for deriving area-efficient architectures from dataflow graphs based on replication and critical path relaxation. We have implemented this algorithm in a design tool called CHARGER, which integrates schedule generation with post-schedule communications infrastructure generation and Hardware Description Language generation. We compare the performance of our algorithm against that of a traditional Force-Directed Scheduling approach by generating architectures from algorithms selected from embedded computing and scientific computing.

Target Identification Through Human Pointing Gesture Based on Human-Adaptive Approach

We propose a human-adaptive approach for calculating human pointing targets, integrating (1) calculating the user’s subjective pointing direction from finger direction, (2) integrating sensory information obtained from user pointing and contextual information such as user action sequences, and (3) arranging target candidates based on the user’s characteristics of pointing and action sequences. The user's subjective pointing direction is approximated by the linear function with the finger direction. Integration of sensory and contextual information using a probabilistic model enables the system to calculate the target accurately. Using a force-directed approach, we obtained good placement in which false estimations are decreased and not moved much from initial placement. Experimental results demonstrate the usefulness of our proposal.

Elastic Flow in an Application Specific Network-on-Chip

A Network-on-Chip (NoC) is increasingly needed to interconnect the large number and variety of Intellectual Property (IP) cells that make up a System-on-Chip (SoC). The network must be able to communicate between cells in di erent clock domains, and do so with minimal space, power, and latency overhead. In this paper, we describe an asynchronous NoC using an elastic-flow protocol, and methods of automatically generating a topology and router placement. We use the communication profile of the SoC design to drive the binary-tree topology creation and the physical placement of routers, and a force-directed approach to determine router locations. The nature of elastic-flow removes the need for large router bu ers, and thus we gain a significant power and space advantage compared to traditional NoCs. Additionally, our network is deadlock-free, and paths have bounded worst-case communication latencies.

Smashing Peacocks Further: Drawing Quasi-Trees from Biconnected Components

Quasi-trees, namely graphs with tree-like structure, appear in many application domains, including bioinformatics and computer networks. Our new SPF approach exploits the structure of these graphs with a two-level approach to drawing, where the graph is decomposed into a tree of biconnected components. The low-level biconnected components are drawn with a force-directed approach that uses a spanning tree skeleton as a starting point for the layout. The higher-level structure of the graph is a true tree with meta-nodes of variable size that contain each biconnected component. That tree is drawn with a new area-aware variant of a tree drawing algorithm that handles high-degree nodes gracefully, at the cost of allowing edge-node overlaps. SPF performs an order of magnitude faster than the best previous approaches, while producing drawings of commensurate or improved quality.

IPSep-CoLa: An Incremental Procedure for Separation Constraint Layout of Graphs

We extend the popular force-directed approach to network (or graph) layout to allow separation constraints, which enforce a minimum horizontal or vertical separation between selected pairs of nodes. This simple class of linear constraints is expressive enough to satisfy a wide variety of application-specific layout requirements, including: layout of directed graphs to better show flow; layout with non-overlapping node labels; and layout of graphs with grouped nodes (called clusters). In the stress majorization force-directed layout process, separation constraints can be treated as a quadratic programming problem. We give an incremental algorithm based on gradient projection for efficiently solving this problem. The algorithm is considerably faster than using generic constraint optimization techniques and is comparable in speed to unconstrained stress majorization. We demonstrate the utility of our technique with sample data from a number of practical applications including gene-activation networks, terrorist networks and visualization of high-dimensional data.

Effective enforcement of path-delay constraints in performance-driven placement

We propose a performance-driven cell placement method based on a modified force-directed approach. A pseudolink is added to connect the source and sink flip-flops of every critical path to enforce their closeness. Given user-specified input-output pad locations at the chip boundaries and starting with all core cells in the chip center, we iteratively move one cell at a time to its force-equilibrium location assuming all other cells are fixed. The process stops when no cell can be move farther than a threshold distance. Next, cell rows are formed one at a time starting from the top and bottom. After forming these two cell rows (top/bottom), all remaining movable core cells' force-equilibrium locations are updated. The row-formation-and-update process continues until all rows are formed and, hence, a legal placement is obtained. We have integrated the proposed approach into an industrial automatic placement-and-route flow. Experimental results on benchmark circuits up to 191-K cell (500-K gate) show that the critical path delay can be improved by as much as 17%. Our layout quality is independent of initial placement. We also study the effect on both layout quality and central processing unit time consumption due to the amount of pseudolinks added. We found that the introduction of pseudolink indeed significantly improves the layout quality. We also empirically demonstrated that the proposed approach is effective in reducing the total half-perimeter wirelength metric.

A force-directed algorithm that preserves edge-crossing properties

We present an iterative drawing algorithm for undirected graphs, based on a force-directed approach, that preserves edge-crossing properties. This algorithm ensures that two edges cross in the final drawing if and only if these edges crossed in the initial layout. Therefore no new edge crossings are introduced. We describe applications of this technique to improve classical algorithms for drawing planar graphs and for dynamic graph drawing.

Pin assignment for multi-FPGA systems

Multi-FPGA systems have tremendous potential, providing a high-performance computing substrate for many different applications. One of the keys to achieving this potential is a complete, automatic mapping solution that creates high-quality mappings in the shortest possible time. In this paper, we consider one step in this process, the assignment of inter-FPGA signals to specific I/O pins on the FPGAs in a multi-FPGA system. We show that this problem can neither be handled by pin assignment methods developed for other applications nor standard routing algorithms. Although current mapping systems ignore this issue, we show that an intelligent pin assignment method can achieve both quality and mapping speed improvements over random approaches. Intelligent pin assignment methods already exist for multi-FPGA systems, but are restricted to topologies where logic-bearing FPGAs cannot be directly connected. In this paper, we provide three new algorithms for the pin assignment of multi-FPGA systems with arbitrary topologies. We compare these approaches on several mappings to current multi-FPGA systems, and show that the force-directed approach produces better mappings, in significantly shorter time, than any of the other approaches.