Introduction To Algorithms, Third Edition (international Edition)
Introduction To Algorithms, Third Edition (international Edition)
3rd Edition
ISBN: 9780262533058
Author: Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein
Publisher: TRILITERAL
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Chapter 24, Problem 4P

(a)

Program Plan Intro

To show that the time complexity of the computation of d(s, v) in the graph G (V, E) where v belongs to V and δ(s,v)|E| is O (E) in scaling algorithm problem.

(b)

Program Plan Intro

To show that the time complexity of the computation of d1(s, v) in the graph G (V, E) where v belongs to V and δ(s,v)|E| is O (E) in scaling algorithm problem.

(c)

Program Plan Intro

To show that 2δi1(s,v)δi(s,v)2δi1(s,v) +V1 , for a given graph G (V, E).

(d)

Program Plan Intro

To show that for i = 2, 3, ......., k and every( u, v ) belongs toV of the given graph G (V, E), the "reweighted" value wi’ ( u, v ) of edge ( u, v )is a nonnegative integer.

(e)

Program Plan Intro

To show that δi(s,v)=δi(s,v)+2δi1(s,v) , where is the shortest path between the pair of vertices s and v using weight function wi .

(f)

Program Plan Intro

To explain that computation time of di(s, v) from di-1(s, v) takes O (E) time and d(s, v) takes O (E lg W) time.

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