*Suppose Ci,i = 0 and that otherwiseSuppose that W satisfies the quadrangle inequality, na...
*Suppose Ci,i = 0 and that otherwise
Suppose that W satisfies the quadrangle inequality, namely, for all i ≤ i′ ≤ j ≤ j′,
Suppose further, that W is monotone: If i ≤ i′ and j ≤ j′, then Wi,j ≤ Wi′,j′.
a. Prove that C satisfies the quadrangle inequality.
b. Let Ri,j be the largest k that achieves the minimum Ci,k−1 + Ck,j. (That is, in case of ties, choose the largest k.) Prove that
c. Show that R is nondecreasing along each row and column.
d. Use this to show that all entries in C can be computed in O(N2) time.
e. Which of the dynamic programming algorithms can be solved in O(N2) using these techniques?
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