Mixing
Mathematical notation of continuous path creation (TSP)
$begingroup$
Recently, I have been studying TSP algorithms and I would like to ask how is it best to describe the nearest neighbour algorithm in the math formation.
The foundation of the algorithm is basic, start with required node and visit the closest non-visited node. Repeat till all the nodes are visited.
I have troubles how to describe this algorithm using the mathematic notation.
I would like to start with something like this:
Let's say we have n vertices as a input: $V={v_1, v_2, dots, v_n}$ and a set of edges $E$. Define A as set of unvisited nodes = $U = {v_1, v_2, dots, v_n} = V$.
Then choose the starting node $v_i$ and change the sets in following way:
$U = U - {v_i}$. Find the closest non-visited neighbor from the current node as x = $v_j notin U | min{(v_i, v_j) in E}$ (this mathematical notation may not be totally correct, I will edit i).
So the question is, if I define the closest unvisited neighbor as $x$ for example, how should I start and expand the current path until solution is found?
Is something like this correct? $P = P1:P2:P3$ where $P1 = {(v_1, v_2)}$ etc.?
What do you recommend?
Thanks.
graph-theory notation
asked Jan 27 at 20:36
BraveDistributionBraveDistribution
11
$endgroup$
add a comment |
$begingroup$
Recently, I have been studying TSP algorithms and I would like to ask how is it best to describe the nearest neighbour algorithm in the math formation.
The foundation of the algorithm is basic, start with required node and visit the closest non-visited node. Repeat till all the nodes are visited.
I have troubles how to describe this algorithm using the mathematic notation.
I would like to start with something like this:
Let's say we have n vertices as a input: $V={v_1, v_2, dots, v_n}$ and a set of edges $E$. Define A as set of unvisited nodes = $U = {v_1, v_2, dots, v_n} = V$.
Then choose the starting node $v_i$ and change the sets in following way:
$U = U - {v_i}$. Find the closest non-visited neighbor from the current node as x = $v_j notin U | min{(v_i, v_j) in E}$ (this mathematical notation may not be totally correct, I will edit i).
So the question is, if I define the closest unvisited neighbor as $x$ for example, how should I start and expand the current path until solution is found?
Is something like this correct? $P = P1:P2:P3$ where $P1 = {(v_1, v_2)}$ etc.?
What do you recommend?
Thanks.
graph-theory notation
asked Jan 27 at 20:36
BraveDistributionBraveDistribution
11
$endgroup$
$begingroup$
Recommend not trying to make up notation and just using words.
$endgroup$
– Misha Lavrov
Jan 27 at 21:23
add a comment |
$begingroup$
Recently, I have been studying TSP algorithms and I would like to ask how is it best to describe the nearest neighbour algorithm in the math formation.
The foundation of the algorithm is basic, start with required node and visit the closest non-visited node. Repeat till all the nodes are visited.
I have troubles how to describe this algorithm using the mathematic notation.
I would like to start with something like this:
Let's say we have n vertices as a input: $V={v_1, v_2, dots, v_n}$ and a set of edges $E$. Define A as set of unvisited nodes = $U = {v_1, v_2, dots, v_n} = V$.
Then choose the starting node $v_i$ and change the sets in following way:
$U = U - {v_i}$. Find the closest non-visited neighbor from the current node as x = $v_j notin U | min{(v_i, v_j) in E}$ (this mathematical notation may not be totally correct, I will edit i).
So the question is, if I define the closest unvisited neighbor as $x$ for example, how should I start and expand the current path until solution is found?
Is something like this correct? $P = P1:P2:P3$ where $P1 = {(v_1, v_2)}$ etc.?
What do you recommend?
Thanks.
graph-theory notation
asked Jan 27 at 20:36
BraveDistributionBraveDistribution
11
$endgroup$
Recently, I have been studying TSP algorithms and I would like to ask how is it best to describe the nearest neighbour algorithm in the math formation.
The foundation of the algorithm is basic, start with required node and visit the closest non-visited node. Repeat till all the nodes are visited.
I have troubles how to describe this algorithm using the mathematic notation.
I would like to start with something like this:
Let's say we have n vertices as a input: $V={v_1, v_2, dots, v_n}$ and a set of edges $E$. Define A as set of unvisited nodes = $U = {v_1, v_2, dots, v_n} = V$.
Then choose the starting node $v_i$ and change the sets in following way:
$U = U - {v_i}$. Find the closest non-visited neighbor from the current node as x = $v_j notin U | min{(v_i, v_j) in E}$ (this mathematical notation may not be totally correct, I will edit i).
So the question is, if I define the closest unvisited neighbor as $x$ for example, how should I start and expand the current path until solution is found?
Is something like this correct? $P = P1:P2:P3$ where $P1 = {(v_1, v_2)}$ etc.?
What do you recommend?
Thanks.
graph-theory notation
graph-theory notation
asked Jan 27 at 20:36
BraveDistributionBraveDistribution
11
asked Jan 27 at 20:36
BraveDistributionBraveDistribution
11
asked Jan 27 at 20:36
BraveDistributionBraveDistribution
11
asked Jan 27 at 20:36
BraveDistributionBraveDistribution
11
asked Jan 27 at 20:36
BraveDistributionBraveDistribution
11
11
$begingroup$
Recommend not trying to make up notation and just using words.
$endgroup$
– Misha Lavrov
Jan 27 at 21:23
add a comment |
$begingroup$
Recommend not trying to make up notation and just using words.
$endgroup$
– Misha Lavrov
Jan 27 at 21:23
$begingroup$
Recommend not trying to make up notation and just using words.
$endgroup$
– Misha Lavrov
Jan 27 at 21:23
$begingroup$
Recommend not trying to make up notation and just using words.
$endgroup$
– Misha Lavrov
Jan 27 at 21:23
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3090087%2fmathematical-notation-of-continuous-path-creation-tsp%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3090087%2fmathematical-notation-of-continuous-path-creation-tsp%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
Recommend not trying to make up notation and just using words.
$endgroup$
– Misha Lavrov
Jan 27 at 21:23