Abstract
The paper presents a parallel graph exploration algorithm. Automaton on a graph is an analogue of the Turing machine тАФ tape cells correspond to graph vertices, where the automaton can store some data, and moves along the tape correspond to moves along graph arcs. This system can be considered also as an aggregate of finite automatons located in graph vertices and interacting by message sending. Each automaton changes its state according to the data stored in the corresponding vertex, and moves along graph arcs are replaced with messages sent by the automaton of the arcтАЩs starting vertex to the one of the ending vertex. The suggested parallel graph exploration algorithm has worst case working time bound O(n/k+D), where n is the number of vertices, and D is the graph diameter, the maximum length of simple path (non-self intersecting path). As a result the algorithm builds two spanning trees of the graph: the direct spanning tree, which has the root vertex as its tree root and is directed from the root, and the back spanning tree, directed to the root.
Highlights
A task of graph exploration with a goal to uncover a structure of unknown graph by moving along its arcs can be met in many domains
We suggest the algorithm of spanning trees building with the following features: vertex automaton memory is bounded by O(nDlog s), message size is bounded by O(Dlog s), arc capacity is k, algorithm worst case working time is O(n/k + D)
Start message is sent by the root automaton to automata of all other vertices, it contains the vertex vector and initiates vertex automaton operation, which is started by sending Root search messages
Summary
A task of graph exploration with a goal to uncover a structure of unknown graph by moving along its arcs can be met in many domains. In many cases such an exploration can be considered as being performed by agents working in graph vertices and sending each other messages along graph arcs. Usual graph exploration corresponds to possibility for a single message to have a size linear on the number of vertices.
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