The monotone restriction (MR) on the heuristic function is defined as h (nj ) 2 h (ni ) – c (ni , nj). Please prove the following: 1. If h(n) < h*(n), A* terminates by finding an optimal path (if a solution exists), 2. If A* uses h(n)

The monotone restriction (MR) on the heuristic function is defined as h (nj ) 2 h (ni ) – c (ni , nj). Please prove the following: 1. If h(n) < h(n), A terminates by finding an optimal path (if a solution exists), 2. If A* uses h(n)

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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Question

The monotone restriction (MR) on the heuristic function is defined as
h (nj ) 2 h (ni ) - c (ni , nj ).
Please prove the following:
1. If h(n) <h*(n), A* terminates by finding an optimal path (if a solution exists),
2. If A* uses h(n) < h*(n) with the MR, then f is non-decreasing along any path
3. If h satisfies the monotone restriction (MR), then whenever A* expands a
node, it has already found an optimal path to this node.

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