lds revisited
(aka chinese whispers)
Send reinforcements. We’re going to advance.
Send three and fourpence. We’re going
to a dance!
Motivation (rooted in footnote 279/1998)
lds (improved) for non-binary domains
• present the algorithm• how does it perform
A refresher
• Chronological Backtracking (BT)• what’s that then?• when/why do we need it?
Quick Intro
Limited Discrepancy Search (lds)• what’s that then
Then the story
An example problem (to show bt)
Colour each of the 5 nodes, such that if they are adjacent, they take different colours
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A Tree Trace of BT (assume domain ordered {R,B,G})
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A Tree Trace of BT (assume domain ordered {R,B,G})
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A Tree Trace of BT (assume domain ordered {R,B,G})
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A Tree Trace of BT (assume domain ordered {R,B,G})
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A Tree Trace of BT (assume domain ordered {R,B,G})
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A Tree Trace of BT (assume domain ordered {R,B,G})
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A Tree Trace of BT (assume domain ordered {R,B,G})
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A Tree Trace of BT (assume domain ordered {R,B,G})
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A Tree Trace of BT (assume domain ordered {R,B,G})
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A Tree Trace of BT (assume domain ordered {R,B,G})
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A Tree Trace of BT (assume domain ordered {R,B,G})
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A Tree Trace of BT (assume domain ordered {R,B,G})
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A Tree Trace of BT (assume domain ordered {R,B,G})
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LDS
• show the search process• assume binary branching• assume we have 4 variables only
Limited Discrepancy Search (LDS) Ginsberg & Harvey
Take no discrepancies (go with the heuristic)
What’s a heuristic
Limited Discrepancy Search (LDS) Ginsberg & Harvey
Take no discrepancies
Limited Discrepancy Search (LDS) Ginsberg & Harvey
Take no discrepancies
Limited Discrepancy Search (LDS) Ginsberg & Harvey
Take no discrepancies
Limited Discrepancy Search (LDS) Ginsberg & Harvey
Take 1 discrepancy
Limited Discrepancy Search (LDS) Ginsberg & Harvey
Take 1 discrepancy
Limited Discrepancy Search (LDS) Ginsberg & Harvey
Take 1 discrepancy
Limited Discrepancy Search (LDS) Ginsberg & Harvey
Take 1 discrepancy
Limited Discrepancy Search (LDS) Ginsberg & Harvey
Take 1 discrepancy
Limited Discrepancy Search (LDS) Ginsberg & Harvey
Take 1 discrepancy
Limited Discrepancy Search (LDS) Ginsberg & Harvey
Take 1 discrepancy
Limited Discrepancy Search (LDS) Ginsberg & Harvey
Take 1 discrepancy
Limited Discrepancy Search (LDS) Ginsberg & Harvey
Take 1 discrepancy
Limited Discrepancy Search (LDS) Ginsberg & Harvey
Take 1 discrepancy
Limited Discrepancy Search (LDS) Ginsberg & Harvey
Take 1 discrepancy
Limited Discrepancy Search (LDS) Ginsberg & Harvey
Take 1 discrepancy
Now take 2 discrepancies
Limited Discrepancy Search (LDS) Ginsberg & Harvey
Take 2 discrepancies
Limited Discrepancy Search (LDS) Ginsberg & Harvey
Take 2 discrepancies
Limited Discrepancy Search (LDS) Ginsberg & Harvey
Take 2 discrepancies
And now for the Chinese whispers
Motivation for lds
Motivation for lds
First proposal
For discrepancies 0 to n
First proposal
For discrepancies 0 to n
k is remaining discrepancies
First proposal
For discrepancies 0 to n
k is remaining discrepancies
Go with heuristic
First proposal
For discrepancies 0 to n
k is remaining discrepancies
Go with heuristic
Go against then go with
The lds search process: how it goes
The lds search process: how it goes
NOTE: lds revisits search states with k discrepanciesWhen searching with > k discrepancies
My pseudo code
lds revisits nodes: Korf’s improvement (AAAI 96)
Korf’s improvement
Korf’s 1st mistake!
Woops!
Do you see it? He’s taking his discrepancies late/deep!
Korf’s 1st mistake!
Wrong way round Richard
Richard, was that a bug?
Yip, but so?
Korf’s 2nd bug
Richard, you know there is another bug?
Woops!
Richard, you know there is another bug?
Richard, are you there?
My pseudo code
Toby, do you do it late or early?
Chris, late or early?
Wafa, late or early?
Wafa’s response
My pseudo code
I think this has not been reported
Are all discrepancies the same?
Does it make a difference if we take discrepancies late or early?
Measuring discrepancies
Putting a cost on a discrepancy
No experiments done yet
Car sequencingDoes it matter if we take discrepancies late or early?
(basically, is H&G’s motivation for lds correct?)
Car Sequencing Problem
Assessed exercise 2
My empirical study on car sequencing problemsUsing various search algorithms, heuristics.
Question: does the order (late/early) that we take discrepancies in lds matter?
Well, did you see a pattern?
If there is no pattern what does this say about H&G’s hypothesis?
And, if no pattern, why is lds any good?
See anything?
Is this work worthy of more effort?
What does this tell us about how we do research?
• we can just follow on without question• we can forget the basic/initial hypothesis• we can forget to really look at our results• we can be frightened or disinterested in –ve results• we can publish papers with multiple errors• we are human