Matroids.

diff --git a/PLAN b/PLAN
index e333a50b7a908bcf5726d16c8f02e9f4ed7d4d0b..f351b240fe936caf31d403ce50eff138b730f520 100644 (file)
--- a/PLAN
+++ b/PLAN
@@ -68,12 +68,6 @@ Related:
 - K best trees
 - degree-restricted cases and arborescences
 - bounded expansion classes?
-- mention matroids
-
-Models:
-
-- add references to the C language
-- all data structures should mention space complexity
 
 Ranking:
 

diff --git a/biblio.bib b/biblio.bib
index f97c59c401510ba4027b1d2d5e916e01c2e0c1a2..3dead5b6834094149ef2e152504f2d8e4d6f1589 100644 (file)
--- a/biblio.bib
+++ b/biblio.bib
@@ -1477,3 +1477,9 @@
     type = "Memo"
 }
 
+@book{ oxley:matroids,
+  title={{Matroid Theory}},
+  author={Oxley, J.G.},
+  year={1992},
+  publisher={Oxford University Press}
+}

diff --git a/mst.tex b/mst.tex
index 871d92df1e529adc4397ffc6b8530c2c717811f4..3f715954dd69cdaeb575751369442f8f562971f9 100644 (file)
--- a/mst.tex
+++ b/mst.tex
@@ -316,6 +316,15 @@ direction, when~$e$ is not contained in~$T_{min}$, it is $T_{min}$-heavy (by
 Theorem \ref{mstthm}), so it is the heaviest edge on the cycle $T_{min}[e]+e$.
 \qed
 
+\rem
+The MST problem is a~special case of the problem of finding the minimum basis
+of a~weighted matroid. Surprisingly, when we modify the Red-Blue procedure to
+use the standard definitions of cycles and cuts in matroids, it will always
+find the minimum basis. Some of the other MST algorithms also easily generalize to
+matroids and in some sense matroids are exactly the objects where ``the greedy approach works''. We
+will however not pursue this direction in our work, referring the reader to the Oxley's monograph
+\cite{oxley:matroids} instead.
+
 %--------------------------------------------------------------------------------
 
 \section{Classical algorithms}\id{classalg}%