Orthogonal Edge Routing for Directed Layered Graphs
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Solution Overview
Problem
Existing graph drawing techniques struggle to produce clear and uncluttered diagrams for complex layered directed graphs, especially when node positions are predetermined, as they often result in high edge crossings and aesthetically unappealing visualizations, particularly for large and cyclic graphs.
Innovation Solution
The method employs a computer-implemented technique for orthogonal edge routing that uses Dijkstra's algorithm to determine the shortest paths for edges and iteratively reduces edge crossings by repositioning segments within layer and lane pipes, ensuring edges do not cross nodes and maintaining clarity by using a grid structure with layer and lane pipes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Object-generated harmful factors
If sophisticated path-finding algorithms are used for edge routing, then edge crossings may be reduced, but the device complexity and computational requirements increase significantly
Solution Approach 1:
The patent segments the edge routing problem into multiple phases: initial routing phase using simple algorithms, and subsequent optimization phases that only address crossing reduction. This segmentation allows the use of computationally simple algorithms in the initial phase while achieving crossing reduction through targeted subsequent optimizations, rather than requiring sophisticated algorithms throughout the entire process.
Solution Approach 2:
The patent performs preliminary routing using simple algorithms to establish initial edge paths before attempting crossing reduction. This preliminary action creates a baseline routing that can then be optimized in subsequent phases, avoiding the need to use complex algorithms from the beginning while still achieving crossing reduction goals.
2Object-generated harmful factors
If node positions are rearranged to eliminate crossings, then edge crossings are reduced, but the node position constraints and diagram clarity requirements are violated
Solution Approach 1:
The patent separates the node positioning function from the edge routing optimization function. Node positions are determined by layout algorithms and remain fixed, while edge routing optimization operates independently on the routing paths. This segmentation allows crossing reduction without requiring node position changes, preserving position precision while reducing crossings.
Solution Approach 2:
The patent introduces intermediate routing elements (such as routing grids, channel definitions, and path waypoints) that mediate between fixed node positions and edge crossing reduction goals. These intermediaries allow the system to achieve crossing reduction through path adjustments rather than node position changes, maintaining position precision while eliminating crossings.
3Object-generated harmful factors
If existing heuristic techniques are used for crossing minimization, then partial crossings reduction is achieved, but the results are unpredictable and aesthetically unappealing for complex graphs
Solution Approach 1:
The patent implements feedback mechanisms where each routing phase evaluates the crossing reduction achieved and adjusts subsequent routing decisions accordingly. The system monitors crossing patterns, identifies problematic areas, and applies targeted routing adjustments in subsequent phases, creating a feedback loop that progressively improves results in a predictable and systematic manner rather than relying on unpredictable heuristics.
Solution Approach 2:
The patent applies periodic action through multiple iterative routing phases, where each phase performs systematic crossing reduction operations in a structured sequence. Rather than using single-pass unpredictable heuristics, the system repeatedly applies refined routing operations across different phases, with each phase building on previous results to achieve progressively better and more predictable outcomes.
Data Source
AI summary
A computer-implemented technique for orthogonal edge routing of directed layered graphs with edge crossings reduction is presented. The pre-arranged nodes are positioned on a rectangular grid consisting of layers across the flow direction and lanes along the flow direction. The layers are separated by rectangular regions defined as layer pipes, and the lanes are separated by rectangular regions defined as lane pipes. Each pipe contains one or more ordered segment tracks. The edges are routed along the shortest paths as orthogonal polylines composed of chained line segments. Each segment is assigned to a pipe. The segments within a pipe are positioned on segment tracks. The edge crossings reduction phase contains iterative procedures to resolve intersections between segments. To resolve the crossings between edges the pairs of conflicting segments are swapped or segments are repositioned on adjacent segment tracks, effectively rubber banding the segments while considering the shortest paths of edges.