Q1: We define the capacity of a path in a weighted graph G(V, E) to be the minimum weight of an edge along that path. For example, the capacity of the path [V0, V1, V2] in the graph below is 5 and the capacity of the path V1, V0, V3, V2 is 3. A maximum-capacity path between u and v is a simple path between u and v whose capacity is larger than or equal to those of all paths from u to v. In the graph below, the maximum capacity path from V0 to V3 is [V0, V1, V2, V3].
Q1: We define the capacity of a path in a weighted graph G(V, E) to be the minimum weight of an edge along that path. For example, the capacity of the path [V0, V1, V2] in the graph below is 5 and the capacity of the path V1, V0, V3, V2 is 3. A maximum-capacity path between u and v is a simple path between u and v whose capacity is larger than or equal to those of all paths from u to v. In the graph below, the maximum capacity path from V0 to V3 is [V0, V1, V2, V3].
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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![Q1:
We define the capacity of a path in a weighted graph G(V, E) to be the minimum weight of
an edge along that path. For example, the capacity of the path [V0, V1, V2] in the graph
below is 5 and the capacity of the path V1, V0, V3, V2 is 3. A maximum-capacity path
between u and v is a simple path between u and v whose capacity is larger than or equal to
those of all paths from u to v. In the graph below, the maximum capacity path from V0 to
V3 is [V0, V1, V2, V3].
(a) Show that if [a, b, ... , u, v] is a maximum-capacity path from a to v, then a maximum-
capacity path from a to u followed by the edge (u, v) is a maximum-capacity path from
a to v.
(b) Is it true that if [a, b, c, u, v] is a maximum-capacity path from a to v, then [a, b, c, u]
is a maximum-capacity path from a to u? Why?
(c) Can you think of an algorithm you have seen before that can be modified to find the
maximum-capacity paths from a particular vertex s to all other vertices in the graph?
How?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc80fba05-5ea3-4445-9af4-8c572b2e977b%2Fd1251273-d04c-4ef8-895a-b656e851346c%2Ff0q5nrm_processed.png&w=3840&q=75)
Transcribed Image Text:Q1:
We define the capacity of a path in a weighted graph G(V, E) to be the minimum weight of
an edge along that path. For example, the capacity of the path [V0, V1, V2] in the graph
below is 5 and the capacity of the path V1, V0, V3, V2 is 3. A maximum-capacity path
between u and v is a simple path between u and v whose capacity is larger than or equal to
those of all paths from u to v. In the graph below, the maximum capacity path from V0 to
V3 is [V0, V1, V2, V3].
(a) Show that if [a, b, ... , u, v] is a maximum-capacity path from a to v, then a maximum-
capacity path from a to u followed by the edge (u, v) is a maximum-capacity path from
a to v.
(b) Is it true that if [a, b, c, u, v] is a maximum-capacity path from a to v, then [a, b, c, u]
is a maximum-capacity path from a to u? Why?
(c) Can you think of an algorithm you have seen before that can be modified to find the
maximum-capacity paths from a particular vertex s to all other vertices in the graph?
How?
![10
Vo
3
V2
25
V3
V4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc80fba05-5ea3-4445-9af4-8c572b2e977b%2Fd1251273-d04c-4ef8-895a-b656e851346c%2Fbv7bsfi_processed.png&w=3840&q=75)
Transcribed Image Text:10
Vo
3
V2
25
V3
V4
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