Show that the set of edges used to label vertices in Steps 2a and 2b of the augmenting flow algorithm form a tree rooted at a
Show that the set of edges used to label vertices in Steps 2a and 2b of the augmenting flow algorithm form a tree rooted at a
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
Related questions
Question
Show that the set of edges used to label vertices in Steps 2a and 2b of the
augmenting flow
![Augmenting Flow Algorithm
1. Give vertex a the labels (–, 0).
Call the vertex being scanned p with second label A(p). Initially, p=a.
(a) Check each incoming edge e = (q", p). If f(e) > 0 and q is unlabeled, then
label q with [p¯, A(q)], where A(q)= min[A(p), f(e)].
(b) Check each outgoing edge e=(p",q). If s(e)= k(e) – f(e) > 0 and q is
unlabeled, then label q with [p+, A(q)], where A(q) =min[A(p), s(e)].
3. If z has been labeled, go to Step 4. Otherwise choose another labeled vertex to
be scanned (which was not previously scanned) and go to Step 2. If there are no
more labeled vertices to scan, let P be the set of labeled vertices, and now (P, P)
is a saturated a-z cut. Moreover, |If|=k(P, P), and thus f is maximum.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11354d02-9b20-4649-a9ed-bf7044846b0d%2Fc6c43337-6149-4efd-bd55-48d964dac718%2Ff702a_processed.png&w=3840&q=75)
Transcribed Image Text:Augmenting Flow Algorithm
1. Give vertex a the labels (–, 0).
Call the vertex being scanned p with second label A(p). Initially, p=a.
(a) Check each incoming edge e = (q", p). If f(e) > 0 and q is unlabeled, then
label q with [p¯, A(q)], where A(q)= min[A(p), f(e)].
(b) Check each outgoing edge e=(p",q). If s(e)= k(e) – f(e) > 0 and q is
unlabeled, then label q with [p+, A(q)], where A(q) =min[A(p), s(e)].
3. If z has been labeled, go to Step 4. Otherwise choose another labeled vertex to
be scanned (which was not previously scanned) and go to Step 2. If there are no
more labeled vertices to scan, let P be the set of labeled vertices, and now (P, P)
is a saturated a-z cut. Moreover, |If|=k(P, P), and thus f is maximum.
Transcribed Image Text:Find an a-z chain K of slack edges by backtracking from z as in the shortest
path algorithm. Then an a–z flow chain fr along K of A(z) units is the desired
augmenting flow. Increase the flow in the edges of K by A(z) units (decrease flow
if edge is backward directed in K).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 5 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Recommended textbooks for you
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education