From 884d4cb59ba51aff8fd4e8127b6faa2f4951b04c Mon Sep 17 00:00:00 2001
From: Martin Mares <mj@ucw.cz>
Date: Mon, 28 Jan 2008 12:47:00 +0100
Subject: [PATCH] More bibliography.

---
 biblio.bib | 75 +++++++++++++++++++++++++++++++++++++++++++++++++++++-
 mst.tex    |  5 ++++
 2 files changed, 79 insertions(+), 1 deletion(-)

diff --git a/biblio.bib b/biblio.bib
index 3d8c3e4..368963e 100644
--- a/biblio.bib
+++ b/biblio.bib
@@ -28,7 +28,7 @@
  address = {New York, NY, USA},
 }
 
-@inproceedings { fw90trans,
+@inproceedings { fw:transdich,
    author = "M. Fredman and D. E. Willard",
    title = "{Trans-dichotomous algorithms for minimum spanning trees and shortest paths}",
    booktitle = "{Proceedings of FOCS'90}",
@@ -241,6 +241,15 @@
     year = "1995",
     url = "citeseer.ist.psu.edu/king95simpler.html" }
 
+@article{ king:verifytwo,
+  title={{A Simpler Minimum Spanning Tree Verification Algorithm}},
+  author={King, Valerie},
+  journal={Algorithmica},
+  volume={18},
+  pages={263--270},
+  year={1997}
+}
+
 @book { schrijver,
     author = "Alexander Schrijver",
     title = "{Combinatorial Optimization --- Polyhedra and Efficiency}",
@@ -386,3 +395,67 @@
   year={2001},
   publisher={McGraw-Hill}
 }
+
+@inproceedings{ pettie:onlineverify,
+  author = "S. Pettie",
+  title = "An inverse-{A}ckermann style lower bound for the online minimum spanning
+    tree verification problem",
+  booktitle = "Proc. 43rd Annual Symp. on the Foundations of Computer Science, Vancouver, Canada",
+  year = "2002",
+  url = "citeseer.ist.psu.edu/article/pettie02inverseackermann.html"
+}
+
+@article{ dixon:verify,
+    author = "Brandon Dixon and Monika Rauch and Robert Endre Tarjan",
+    title = "Verification and Sensitivity Analysis of Minimum Spanning Trees in Linear Time",
+    journal = "SIAM J. Comput.",
+    volume = "21",
+    number = "6",
+    pages = "1184-1192",
+    year = "1992",
+    url = "citeseer.ist.psu.edu/dixon92verification.html"
+}
+
+inproceedings{ pettie:minirand,
+ author = {Seth Pettie and Vijaya Ramachandran},
+ title = {Minimizing randomness in minimum spanning tree, parallel connectivity, and set maxima algorithms},
+ booktitle = {SODA '02: Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms},
+ year = {2002},
+ isbn = {0-89871-513-X},
+ pages = {713--722},
+ location = {San Francisco, California},
+ publisher = {Society for Industrial and Applied Mathematics},
+ address = {Philadelphia, PA, USA}
+}
+
+@article{ buchsbaum:verify,
+  title={{Linear-time pointer-machine algorithms for least common ancestors, MST verification, and dominators}},
+  author={Buchsbaum, A.L. and Kaplan, H. and Rogers, A. and Westbrook, J.R.},
+  journal={Proceedings of the thirtieth annual ACM symposium on Theory of computing},
+  pages={279--288},
+  year={1998},
+  publisher={ACM Press New York, NY, USA}
+}
+
+@article{ bacala:parametric,
+  title={{Linear-time algorithms for parametric minimum spanning tree problems on planar graphs}},
+  author={Fern{\'a}ndez-Baca, D. and Slutzki, G.},
+  journal={Theoretical Computer Science},
+  volume={181},
+  number={1},
+  pages={57--74},
+  year={1997},
+  publisher={Elsevier}
+}
+
+@inproceedings{ katriel:cycle,
+  author = "I. Katriel and P. Sanders and J. Tr{\"a}ff",
+  title = "A practical minimum spanning tree algorithm using the cycle property",
+  booktitle = "11th European Symposium on Algorithms(ESA)",
+  number = "2832",
+  series = "LNCS",
+  pages = "679--690",
+  publisher = "Springer",
+  year = "2003",
+  url = "citeseer.ist.psu.edu/katriel03practical.html"
+}
diff --git a/mst.tex b/mst.tex
index 9c21ffa..eff6a01 100644
--- a/mst.tex
+++ b/mst.tex
@@ -1089,7 +1089,11 @@ If $m/n \ge \log^{(k)} n$, then $\beta(m,n)\le k$.
 
 \FIXME{Reference to Q-Heaps.}
 
+%--------------------------------------------------------------------------------
+
+\section{Verification of minimality}
 
+\FIXME{\cite{pettie:onlineverify} online lower bound}
 
 % use \para
 % G has to be connected, so m=O(n)
@@ -1101,5 +1105,6 @@ If $m/n \ge \log^{(k)} n$, then $\beta(m,n)\le k$.
 % use \delta(X) notation
 % mention disconnected graphs
 % unify use of n(G) vs. n
+% Euclidean MST
 
 \endpart
-- 
2.39.2