Best First Search: Fundamentals and Applications

By Fouad Sabry

What Is Best First Search

The best-first search is an example of a class of search algorithms that investigates a graph by extending the node that seems to hold the most potential in accordance with a predetermined rule.

How You Will Benefit

(I) Insights, and validations about the following topics:

Chapter 1: Best-First Search

Chapter 2: Heuristic in Computer Science

Chapter 3: A* Search Algorithm

Chapter 4: Graph Traversal

Chapter 5: Pathfinding

Chapter 6: Dijkstra's Algorithm

Chapter 7: Greedy Algorithm

Chapter 8: Bidirectional Search

Chapter 9: Beam Search

Chapter 10: Real-Time Web

(II) Answering the public top questions about best first search.

(III) Real world examples for the usage of best first search in many fields.

(IV) 17 appendices to explain, briefly, 266 emerging technologies in each industry to have 360-degree full understanding of best first search' technologies.

Who This Book Is For

Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of best first search.

• Language: English
• Publisher: One Billion Knowledgeable
• Release date: Jun 28, 2023

Book preview

Chapter 1: Best-first search

The term best-first search refers to a category of search algorithms that investigates a network by extending the most interesting node selected in accordance with a predetermined set of guidelines.

Judea Pearl described the best-first search as estimating the promise of node n by a heuristic evaluation function f(n) which, in general, might be dependent on the characterization of n, the explanation of the objective in question, information that had been uncovered by the investigation up until that date, and maybe most significantly, based on any additional information on the issue domain.

Utilizing a priority queue as the traditional method, an efficient selection of the currently best candidate for extension can normally be achieved.

Both the A* search algorithm and the B* search algorithm are examples of best-first search algorithms. Combinatorial search often makes use of best-first algorithms for the purpose of route discovery. Both A* and B* are not examples of a greedy best-first search since they both take into account the distance from the starting point in addition to the distances to the objective that are calculated.

Expansion of the first successor of the parent should be performed using a greedy method. After a new succeeding generation is produced:

If the heuristic of the successor is higher than that of its parent, the successor's heuristic is moved to the head of the queue, and the loop is restarted. The parent's heuristic is then reinserted right behind the successor.

In every other case, the succeeding item is added to the queue (in a location determined by its heuristic value). The technique will determine which, if any, of the parent's successors are still in existence.

An illustration of this method is shown below in the form of pseudocode. In this illustration, queue stands for a priority queue that sorts nodes according to their heuristic distances from the objective. Because this version remembers which nodes it has already traversed, it is suitable for usage with undirected graphs. It is able to be altered in order to recover the route.

procedure GBS(start, target) is:

mark start as visited

add start to queue

while queue is not empty do:

current_node ← vertex of queue with min distance to target

remove current_node from queue

foreach neighbor n of current_node do:

if n not in visited then:

if n is target:

return n

else:

mark n as visited

add n to queue

return failure

{End Chapter 4}

{End Chapter 1}

Chapter 2: Heuristic (computer science)

In the fields of computer science and mathematical optimization, heuristic (from Greek εὑρίσκω I find, discover) is a strategy that was developed to help solve problems more rapidly in situations when traditional approaches are insufficient for finding an approximative solution, or when traditional procedures are unable to locate any specific remedy.

This is accomplished via the use of optimality trading, completeness, accuracy, or accuracy in exchange for velocity.

To some extent, It is possible to see it as a short cut.

A heuristic function, which is usually referred to as simply a heuristic, is a function that rates the many possibilities in search algorithms at each branching stage depending on the information that is available in order to choose which branch to follow. For instance, it might be a close approximation of the precise answer.

The purpose of a heuristic is to generate a solution in a fair amount of time that is adequate for resolving the issue that is currently being considered. This solution may not be the best out of all the possible answers to this issue; instead, it could only be a close approximation of the correct answer. However, despite this, it is still important since locating it will not take an insurmountable amount of time.

Heuristics have the potential to create outcomes on their own, or they may be used with optimization algorithms in order to boost such algorithms' overall effectiveness (e.g., they may be used to generate good seed values).

Heuristics are the only viable option for a variety of complex optimization problems that need to be routinely solved in real-world applications as a result of results about NP-hardness in theoretical computer science. This is because NP-hardness makes it extremely difficult to find optimal solutions.

Since heuristics may be used even in circumstances in which there are no known algorithms, they are an essential part of both the area of artificial intelligence and the process of simulating human thought on a computer.

The following is a list of the trade-off factors that may be used to decide whether or not to employ a heuristic for the solution of a certain problem::

Optimality: Does the heuristic ensure that the optimal solution will be discovered in situations when there are several possible solutions to a given problem? Is it really vital to locate the most effective solution?

Completeness refers to whether or not the heuristic can identify all of the possible solutions to a problem when there are more than one. Do we really need each and every solution? A great number of heuristics are designed to only locate one answer.

Regarding the accuracy and precision of the putative answer, can the heuristic offer a confidence interval for it? Is there an unacceptable amount of room for error on the solution?

Execution time: is this the most effective heuristic that is currently known for resolving problems of this kind? Some heuristics get closer to the correct answer more quickly than others. Some heuristics are just somewhat faster than traditional approaches, and in this instance, the 'overhead' on computing the heuristic could have a detrimental influence.

Because the theory that underpins heuristics is not very detailed, there are some scenarios in which it may be difficult to determine whether or not the answer that was identified by the heuristic is satisfactory.

One method for accomplishing the increase in computing efficiency that is anticipated from the use of a heuristic is to resolve an issue that is easier and whose solution is also a solution to the first problem.

Jon Bentley provides a description of an example of an approximation that may be used to