Finding a maximum-density path in a tree under the weight and length constraints

Let T=(V,E) be a tree with n nodes such that each node v is associated with a value-weight pair(val"v,w"v), where the valueval"v is a real number and the weightw"v is a positive integer. The density of a path P= is defined as @?"i"="1^kval"i/@?"i"="1^kw"i. The weight of P, denoted by w(P), is @?"i"="1^kw"i. Given a tree of n nodes, two integers w"m"i"n and w"m"a"x, and a length lower bound L, we present a pseudo-polynomial O(w"m"a"xnL)-time algorithm to find a maximum-density path P in T such that w"m"i"n=

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