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Travel-time curve is a graph showing the relationship between the distance from the epicenter to the observation point and the travel time. [2] [3] Travel-time curve is drawn when the vertical axis of the graph is the travel time and the horizontal axis is the epicenter distance of each observation point. [4] [5] [6] By examining the travel ...
The contraction hierarchies algorithm has no knowledge about road types but is able to determine which shortcuts have to be created using the graph alone as input. To find a path from to the algorithm can skip over the grey vertices and use the dashed shortcut instead. This reduces the number of vertices the algorithm has to look at.
The main advantage of this approach is that it can make use of efficient shortest path algorithms for deterministic networks. However, the resulting optimal path may not be reliable, because this approach fails to address travel time variability. To tackle this issue, some researchers use travel duration distribution instead of its expected value.
A* (pronounced "A-star") is a graph traversal and pathfinding algorithm that is used in many fields of computer science due to its completeness, optimality, and optimal efficiency. [1] Given a weighted graph , a source node and a goal node, the algorithm finds the shortest path (with respect to the given weights) from source to goal.
TSP can be modeled as an undirected weighted graph, such that cities are the graph's vertices, paths are the graph's edges, and a path's distance is the edge's weight. It is a minimization problem starting and finishing at a specified vertex after having visited each other vertex exactly once.
Dijkstra's algorithm is commonly used on graphs where the edge weights are positive integers or real numbers. It can be generalized to any graph where the edge weights are partially ordered, provided the subsequent labels (a subsequent label is produced when traversing an edge) are monotonically non-decreasing. [10] [11]
Although graph searching methods such as a breadth-first search would find a route if given enough time, other methods, which "explore" the graph, would tend to reach the destination sooner. An analogy would be a person walking across a room; rather than examining every possible route in advance, the person would generally walk in the direction ...
In graphs that have negative cycles, the set of shortest simple paths from v to all other vertices do not necessarily form a tree. For simple connected graphs, shortest-path trees can be used [1] to suggest a non-linear relationship between two network centrality measures, closeness and degree. By assuming that the branches of the shortest-path ...