Shortest‐Path Algorithm

In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. Dijkstra's algorithm (and others) is used to find the shortest path between two nodes in a graph. This concept is used in transportation, robotics, networking, etc.

Summary

Things to Remember

In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.
Dijkstra's algorithm (and others) is used to find the shortest path between two nodes in a graph.
This concept is used in transportation, robotics, networking, etc.

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Subjective Questions

Q1:

Write a short note on Ketamine.

Type: Short Difficulty: Easy

Show/Hide Answer

Answer: <h4>Ketamine</h4>
Introduction:
It is a rapidly acting general anesthetic. Ketamine produces a somnolent state in which some patients appear to be awake but dissociated from their environment, unresponsive to pain and having no recall. Somatic pain appears to be more effectively blocked than visceral pain. It produces no muscle relaxation but may produce generalized extensor spasm during emergence from anesthesia. Ketamine causes transient depression of respiratory centre. It causes and increases of systolic and diastolic Bp and heart rate.
Mechanism of action:
It blocks afferent impulses of pain perception, similarly, it suppresses spinal cord activity. Thus, it effects CNS transmitter system. It has anaesthesia with profound analgesia. It is a dissociative anaesthesia. It increases blood pressure and preserves the laryngeal relaxes.
Indication:
<ul>
<li>Induction and the maintenance of anaesthesia for diagnostic procedure</li>
<li>It is mostly used in short surgical operations and minor surgical or diagnostic procedures e.g. burns dressings, incision and drainage of abscesses, closed reduction of fractures. (MUA), dilation and curettage (D+C) and performing biopsies.</li>
<li>Children</li>
</ul>
Preparation:
It is usually available in the form of injection such as:
Ketamine hydrochloride injection 10mg/ml, 100mg/ml
Dose:
<ul>
<li>1-2mg/kg IV</li>
<li>3-5mg/kg IM</li>
<li>10-15mg/kg oral</li>
</ul>
Adverse effect:
<ul>
<li>CNS: hallucination, fasciculations , emergence reaction, delirium, tonic-clonic movements</li>
<li>CVS: hypertension, tachycardia, arrhythmias, increase cardiac output</li>
<li>GIT: excessive salivation, vomiting</li>
<li>Respiratory: respiratory depression, cough reflex depressed</li>
<li>Skeletal: increased skeletal muscle tone, tremor</li>
<li>Skin: skin rash</li>
</ul>
Drug interaction:
<ul>
<li>It may cause hypertension and tachycardia in patients taking Levothyroxine when given Ketamine.</li>
<li>Seizures have been attributed to an interaction between Ketamine and Theophylline.</li>
</ul>
Contraindication:
<ul>
<li>Epilepsy</li>
<li>Hypertension</li>
<li>Increased intracranial pressure</li>
<li>CCF</li>
<li>Glaucoma</li>
<li>CVA</li>
<li>Psychiatric patient</li>
<li>Alcoholism</li>
</ul>
Precaution:
It may cause laryngeal spasm if given fast.
NOTE: Add atropine 10 micrograms/kg,
Avoid in ischemic heart disease heart disease, heart failure and raised intracranial pressure.
During recovery, a patient may go to emergency if hallucination is present.
Advantages:
<ul>
<li>Used as intravenously</li>
<li>Used for short surgical</li>
<li>Respiration is not depressed</li>
</ul>
Disadvantages:
<ul>
<li>Unresponsive to pain</li>
<li>It produces no muscle relaxation</li>
<li>Heart rate, cardiac output, and BP are elevated</li>
<li>Nightmares</li>
<li>Hallucinations</li>
</ul>

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Shortest‐Path Algorithm

In graph theory,the shortest path problem is the problem of finding a pathbetween two vertices(or nodes) in a graphsuch that the sum of the weightsof its constituent edges is minimized, i.e. the total sum of weights of the overall path is the minimum possible. A special example of application may be the problem of finding the shortest path between two intersections on a road map (the graph's vertices correspond to intersections and the edges correspond to road segments, each weighted by the length of its road segment).

Let e_i,j be the edge incident to both v_iand v_j. Given a real-valued weight function f : E -> R, and an undirected graph G, the shortest path from v to v' is the path P=(v₁, v₂, v₃, . . . ,v_n) (where v₁= v and v_n = v') that over all possible n minimizes the sum f(e_i,_i+1) where i runs from 1 to n-1.

(6,4,5,1) and (6,4,3,2,1) are both paths between vertices 6 and 1. But the latter is the shortest path

Shortest path (A,C,E,D,F) between vertices A and F

The common types of shortest path problems are:

Single-Pair Shortest Path Problem
Single-Source Shortest Path Problem
Single-Destination Shortest Path Problem
All-Pairs Shortest Path Problem

The most popular algorithms used to solve such different types of shortest path problems are:

Dijkstra's algorithm
Bellman-Ford algorithm
A* search algorithm
Floyd-Warshall algorithm
Johnson's algorithm

Applications

Used to automatically find directions between physical locations, such as driving directions on web mapping websites like Google Maps.
Used in networking and telecommunications
Robotics
VLSI design
Finding the optimal sequence of choices to reach a certain goal state in a game.

References

1. https://en.wikipedia.org/wiki/Shortest_path_problem

2. Karumanchi, N. "Data Structures and Algorithms Made Easy"

3. Y. Langsam, M. J. Augenstein and A. M Tenenbaum, “Data Structures using C and C++”

4. R. L. Kruse, B. P. Leung, C. L. Tondo, “Data Structure and Program design in C”

Lesson

Graphs

Subject

Computer Engineering

Grade

Engineering

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