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In this way, thepathdecompositionnodes containing "v" correspond to the representative points in the interval for "v".
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Each node of the path tree corresponds to a path of the heavypathdecomposition.
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In a heavypathdecomposition, each non-leaf node selects one heavy edge, the edge to the child that has the greatest number of descendants (breaking ties arbitrarily).
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Subsequent applications of heavypathdecompositionhave included solving the level ancestor problem, finding a path near all nodes of a given graph, and decoding grammar-based codes, among others.
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If "p" is a path of the heavypathdecomposition, then the parent of "p" in the path tree is the path containing the parent of the head of "p".
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