show that if d1,...,dn are nonnegative real numbers adding up to 1, then the expressionn i=1 1/(di + 1) is minimal for d1 = d2 = =d n =1/n.show that if d1,...,dn are nonnegative real numbers adding up to 1, then the expressionn i=1 1/(di + 1) is minimal for d1 = d2 = =d n =1/n.
Answers
Answer:
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Answer:
Answer: (D)
Explanation: A generic algorithm or method to solve this question is
1: procedure isV alidDegreeSequence(L)
2: for n in list L do
3: if L doesn’t have n elements next to the current one then return false
4: decrement next n elements of the list by 1
5: arrange it back as a degree sequence, i.e. in descending order
6: if any element of the list becomes negative then return false
7: return true
Rationale behind this method comes from the properties of simple graph. Enumerating the f alse returns, 1) if L doesn’t have enough elements after the current one or 2) if any element of the list becomes negative, then it means that there aren’t enough nodes to accommodate edges in a simple graph fashion, which will lead to violation of either of the two conditions of the simple graph (no self-loops and no multiple-edges between two nodes), if not others