2-3 graphs which have Vizings adjacency property by Winter P. A.

By Winter P. A.

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In this case, we need to compute the distance between the labels of the nodes and edges in order to define the cost of a label substitution. Clearly, the cost of the label substitution is application-dependent. In the case of numerical labels, it may be natural to define the distances based on numerical distance functions between the two graphs. In general, the cost of the edits is also application dependent, since different applications may use different notions of similarity. Thus, domain-specific techniques are often used in order to define the edit costs.

The idea is to compute a minimum image based support of a given pattern. For this case, we compute the number of unique nodes of the graph to which a node of the given pattern is mapped. This measure continues to satisfy the anti-monotonicity property, and can therefore be used in order to determine the underlying frequent patterns. An efficient algorithm with the use of this measure has been proposed in [31]. As in the case of standard frequent pattern mining, a number of variations are possible for the case of finding graph patterns, such as determining maximal patterns [100], closed patterns [198], or significant patterns [98, 157, 198].

We then use multiple trees to cover an entire graph. Agrawal et al. [10]’s optimal tree cover achieves ????(log ????) query time, where ???? is the number of nodes in the graph. Instead of using trees, Jagadish et al. [105] proposes to decompose a graph into pairwise Graph Data Management and Mining: A Survey of Algorithms and Applications 21 disjoint chains, and then use chains to cover the graph. The intuition of using a chain is similar to using a tree: if ???? can reach ???? on a chain, then ???? can reach any node that comes after ???? on that chain.

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