The Implementation of Eulerian Coverings of a Graph for Solving Routing Problems
Abstract
In terms of graph theory, the urban transport network can be adequately represented as a graph. All crossroads in the city are considered to be the vertices of the graph, and streets are the edges. Using this model, one can set and effectively solve many routing problems: (1) constructing the routes between given starting and ending points, satisfying the rules of the road (allowed turns at crossroads and a given sequence of driving through the streets), (2) finding the way, passing through all the streets of the city in accordance with the rules of the road and a given sequence of turns at crossroads (an algorithm for constructing an permissible Eulerian chain), (3) constructing a minimal cardinality set of routes running through all the streets of the city (Eulerian cover of any graph with permissible chains). The paper provides a formalization of these problems and effective algorithms for solving them.
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