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L = ({ g },...)
After executing line 1 of DECOMPOSE:
R
TRAVERSE_UP({g}) returns (TRUE, {{ d, e, f }, { h, i, j, k, l, m, n}}, TRUE, FALSE)
R
After executing line 11 of DECOMPOSE,
{a } {b } { c }
{ g}
{a } {b } { c }
T:
{d } { e } { f } {h } { i }
{m } {n }
T:
type(R ) = BRACE.
{ g}
{d } { e } { f } {h } { i }
{m } {n }
{ j } {k } {l }
{ j } {k } {l }
L = ({ k}, { l }, { j}, {j , k , l }, { h }, { i }, {m }, {n}, {d} ,... ) at line 2
TRAVERSE_UP({k } ) returns (FALSE, {}, TRUE, TRUE)at line 6.
TRICKLE_DOWN({{ d, e, f}, {h, i, j, k, l, m, n}})
TRAVERSE_DOWN({ d, e, f }) returns (FALSE, {}, TRUE, TRUE)
R
T:
After executing line 18,
{ h } {i }
{m } {n }
After executing line 9 of TRICKLE_DOWN,
bipartite({j, k, l }) = FALSE.
{ j } {k } { l }
{a } {b } { c }
T:
{ g}
type({ d, e, f }) = BRICK.
{d } { e } { f } {h } { i }
L = ({ j, k, l }, { h}, { i}, {m}, {n }, { d } ,... )
{ j } {k } {l }
TRAVERSE_UP({ j, k, l }) returns (TRUE, {{ j, k, l }}, FALSE, FALSE)
TRAVERSE_DOWN({h, i, j, k, l, m, n}) returns (TRUE, {{ j, k, l}} , TRUE, FALSE)
T:
{ h } {i }
{m } {n }
type({ h, i, j, k, l, m, n}) = BRACE.
bipartite({h, i, j, k, l, m, n }) = FALSE.
{m } {n }
{h } { i }
{ j } {k } { l }
{m } {n }
{ j } {k } {l }
TRICKLE_DOWN({{ j, k, l }})
L = ({ d }, { f }, {e }, { g }, { a },...)
TRAVERSE_DOWN({j, k, l }) returns (FALSE, {}, TRUE, TRUE)
TRAVERSE_UP({d }) returns (FALSE, {}, TRUE, TRUE)
R
{a } {b } { c }
T:
bipartite({ d, e, f }) = FALSE.
{ g}
{d } { e } { f } {h } { i }
{m } {n }
type({ j, k, l}) = BRICK.
{h } { i }
{m } {n }
{ j } {k } {l }
Legend:
{ j } {k } {l }
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DECOMPOSE terminates
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Subtour elimination polytopes and graphs of inscribable type

Transcription

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