Directed Graph Exploration
نویسندگان
چکیده
We study the problem of exploring all nodes of an unknown directed graph. A searcher has to construct a tour that visits all nodes, but only has information about the parts of the graph it already visited. The goal is to minimize the cost of such a tour. In this paper, we present upper and lower bounds for both the deterministic and the randomized online version of exploring all nodes of directed graphs. Our bounds are sharp or sharp up to a small constant, depending on the specific model. Essentially, exploring a directed graph has a multiplicative overhead linear in the number of nodes. If one wants to search for just a node in unweighted directed graphs, a greedy algorithm with quadratic multiplicative overhead can only be improved by a factor of at most two. We were also able to show that randomly choosing a starting point does not improve lower bounds beyond a small constant factor.
منابع مشابه
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Prime graph of a ring R is a graph whose vertex set is the whole set R any any two elements $x$ and $y$ of $R$ are adjacent in the graph if and only if $xRy = 0$ or $yRx = 0$. Prime graph of a ring is denoted by $PG(R)$. Directed prime graphs for non-commutative rings and connectivity in the graph are studied in the present paper. The diameter and girth of this graph are also studied in the pa...
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