# 0.7 Graphs  (Page 13/21)

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• Completeness

Breadth-first search is complete. This means that if there is a solution breadth-first search will find it regardless of the kind of graph. However, if the graph is infinite and there is no solution breadth-first search will diverge.

• Optimality

For unit-step cost, breadth-first search is optimal. In general breadth-first search is not optimal since it always returns the result with the fewest edges between the start node and the goal node. If the graph is a weighted graph, and therefore has costs associated with each step, a goal next to the start does not have to be the cheapest goal available. This problem is solved by improving breadth-first search to uniform-cost search which considers the path costs. Nevertheless, if the graph is not weighted, and therefore all step costs are equal, breadth-first search will find the nearest and the best solution.

## Applications of bfs

Breadth-first search can be used to solve many problems in graph theory, for example:

• Finding all connected components in a graph.
• Finding all nodes within one connected component
• Copying Collection, Cheney's algorithm
• Finding the shortest path between two nodes u and v (in an unweighted graph)
• Testing a graph for bipartiteness
• (Reverse) Cuthill–McKee mesh numbering

## Finding connected components

The set of nodes reached by a BFS are the largest connected component containing the start node.

## Testing bipartiteness

BFS can be used to test bipartiteness, by starting the search at any vertex and giving alternating labels to the vertices visited during the search. That is, give label 0 to the starting vertex, 1 to all its neighbours, 0 to those neighbours' neighbours, and so on. If at any step a vertex has (visited) neighbours with the same label as itself, then the graph is not bipartite. If the search ends without such a situation occurring, then the graph is bipartite.

## Usage in 2d grids for computer games

BFS has been applied to pathfinding problems in computer games, such as Real-Time Strategy games, where the graph is represented by a tilemap, and each tile in the map represents a node. Each of that node is then connected to each of its neighbour (neighbour in north, north-east, east, south-east, south, south-west, west, and north-west).

It is worth mentioning that when BFS is used in that manner, the neighbour list should be created such that north, east, south and west get priority over north-east, south-east, south-west and north-west. The reason for this is that BFS tends to start searching in a diagonal manner rather than adjacent, and the path found will not be the correct one. BFS should first search adjacent nodes, then diagonal nodes.

## 7.3.4. bellman-ford algorithms

The Bellman–Ford algorithm computes single-source shortest paths in a weighted digraph (where some of the edge weights may be negative). Dijkstra's algorithm accomplishes the same problem with a lower running time, but requires edge weights to be non-negative. Thus, Bellman–Ford is usually used only when there are negative edge weights.

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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