Converting a maximum preflow to a maximum flow. We define a maximum preflow X O as a preflow with the maximum possible flow into the sink. (a) Show that for a given maximum preflow xo, some maximum flow x* with the same flow value as xo, satisfies the condition that Xu :s x- for all arcs (i, j) E A. (Hint: Use flow decomposition.) (b) Sug gest a labeling algorithm that converts a maximum preflow into a maximum flow in at most n + m augmentations. (e) Suggest a variant of the shortest augmenting path algo rithm that would convert a maximum preflow into a maximum flow in O(nm) time. (Hi nt: Define distance labels from the source node and show that the algorithm will creat

Converting a maximum preflow to a maximum flow. We define a maximum preflow X O as a preflow with the maximum possible flow into the sink. (a) Show that for a given maximum preflow xo, some maximum flow x* with the same flow value as xo, satisfies the condition that Xu :s x- for all arcs (i, j) E A. (Hint: Use flow decomposition.) (b) Sug gest a labeling algorithm that converts a maximum preflow into a maximum flow in at most n + m augmentations. (e) Suggest a variant of the shortest augmenting path algo rithm that would convert a maximum preflow into a maximum flow in O(nm) time. (Hi nt: Define distance labels from the source node and show that the algorithm will creat

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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Please answer follow up questions.
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