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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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