Jump to content
  • Advertisement
Sign in to follow this  
sectrix

Understanding the D* lite whitepaper

This topic is 2141 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

If you intended to correct an error in the post then please contact us.

Recommended Posts

I'm writing a tool for a game I play, and I've found I need a good pathfinding algorithm.

I've already written an A* and a Dijkstra routine, but I've found them to be far too slow. It takes them about 20 and 13 seconds respectively to find the shortest path along the longer routes.

I've come across D* lite as a possible better solution, but there's very little information on the web. Some of what I did find came from here several years ago, so, here's to hoping those members are still around.

I found and read Koenig's 2002 paper about it, (this one), and I understand all of the LPA* pseudo code except for two lines:

- Calculate keys()
In the calculateKeys function, it reads: Return[ min( g(s), rhs(s) ) + h(s, s[sub]goal[/sub]) ; min ( g(s), rhs(s)) ]. What I don't understand is the ; in the middle. Does the function return two values? Does it perform some sort of operation on the results of the two min statements?

- Update vertex and rhs calculation
The other line I had trouble with was this one: min [sub]s' (is element of) pred(s)[/sub] (g(s'), c(s', s)). I don't get that one at all. The s' in pred() with the smallest g or c?

I feel like I'm going to get a lot of blank stares, but, any ideas anyone?

Share this post


Link to post
Share on other sites
Advertisement
Does the function return two values?


It returns a pair or 2D vector; the authors have opted for [a;b] over (a,b) to improve legibility.

The other line I had trouble with was this one: min [sub]s' (is element of) pred(s)[/sub] (g(s'), c(s', s)). I don't get that one at all. The s' in pred() with the smallest g or c?[/quote]

I don't see this line. I do see min [sub]s' (is element of) pred(s)[/sub] (g(s') + c(s', s)) - i.e. the minimum of the expression on the right over all predecessors of s.

EDIT: slightly clearer wording. Edited by TheUnbeliever

Share this post


Link to post
Share on other sites
I see. So the second line is basically: the minimum s' in predecessors of u, as calculated by ( g(s') + c (s', u) ).

Excellent, thank you so much for that.

One follow up question then.

When comparing: U.TopKey < calculateKeys, ie: (X1, Y1) < (X2, Y2), is this (X1 < X2) AND (Y1 < Y2), or (X1 < X2) OR (Y1 < Y2), or something else entirely? Edited by sectrix

Share this post


Link to post
Share on other sites
the minimum s' in predecessors of u, as calculated by ( g(s') + c (s', u) ).


Not quite. That would be written 'argmin', whereas we just have 'min'. This is the minimum value of g(s') + c(s',u) for any predecessor s', not the predecessor itself.

When comparing: U.TopKey < calculateKeys, ie: (X1, Y1) < (X2, Y2), is this (X1 < X2) AND (Y1 < Y2), or (X1 < X2) OR (Y1 < Y2), or something else entirely?[/quote]

Explained from around the middle of the first paragraph on page 478, starting at 'keys are compared according to a lexicographic ordering.'

Share this post


Link to post
Share on other sites
OK, I had it backwards then. It's the minimum of ( g(s') + c(s', u) ) as calculated with all s' in predecessors of u.

And the key comparison is: (X1, Y1) <= (X2, Y2) iff (X1 < X2) OR [X1 = X2 AND Y1 <= Y2].
Have I got it right?


And it seems that everywhere in the pseudo code where there is a < with a dot above it represents this lexicographic comparison, correct?

Share this post


Link to post
Share on other sites
Sign in to follow this  

  • Advertisement
×

Important Information

By using GameDev.net, you agree to our community Guidelines, Terms of Use, and Privacy Policy.

Participate in the game development conversation and more when you create an account on GameDev.net!

Sign me up!