o Models and machines
o Radix-sorting
o Bit tricks
- . Ranking sets
- . Bitwise B-trees
- . Q-Heaps
+ o Q-Heaps
* Advanced MST Algorithms
o Minor-closed classes
o Fredman-Tarjan algorithm
- . ?? Chazelle ??
- . ?? Pettie ??
- . MST verification
- . Randomized algorithms
+ o MST verification
+ o Linear-time verification
+ o A randomized algorithm
+ o Special cases and related problems
-* Ranking combinatorial objects
+* Approaching Optimality
+
+ o Soft heaps
+ o Robust contractions
+ o Decision trees
+ o An optimal algorithm
+
+* Dynamic MST algorithms
+
+ o (Semi-)dynamic algorithms
+ o ET-trees
+ o Fully dynamic connectivity
+ o Dynamic MST
+
+* Ranking Combinatorial Objects
o Ranking and unranking
o Ranking of permutations
o Ranking of k-permutations
- . Permutations with no fixed point
+ o Restricted permutations
+ o Hatcheck lady and other derangements
. ?? other objects ??
+ . ?? general perspective ??
-* Dynamic MST algorithms
+TODO:
- . (Semi-)dynamic algorithms
- . Sleator-Tarjan trees
- . ET-trees
- . Fully dynamic connectivity
- . Semi-dynamic MST
- . Fully dynamic MST
+Preface:
-TODO:
+- move TOC to the beginning of the book
+- mention notation
+- cite GA booklet
Spanning trees:
- cite Eisner's tutorial \cite{eisner:tutorial}
-- \cite{pettie:onlineverify} online lower bound
-- mention Steiner trees
-- mention matroids
-- sorted weights
-- mention disconnected graphs
-- Euclidean MST
- Some algorithms (most notably Fredman-Tarjan) do not need flattening
-- reference to mixed Boruvka-Jarnik
- use the notation for contraction by a set
-
-Models:
-
-- bit tricks: reference to HAKMEM
-- mention in-place radix-sorting?
+- mention bugs in Valeria's verification paper
+- more references on decision trees
+- Lemma: deletion of a non-MST edge does not alter the MST
+- mention that there are only a few algorithms based on the Red rule
+
+Related:
+- practical considerations: katriel:cycle, moret:practice (mention pairing heaps)
+- parallel algorithms: p243-cole (see also remarks in Karger and pettie:minirand), pettie:parallel
+- K best trees
+- degree-restricted cases and arborescences
+- bounded expansion classes?
+- finding all MST's
Ranking:
- the general perspective: is it only a technical trick?
-- move description of the ranking set to the chapter on models?
- ranking of permutations on general sets, relationship with integer sorting
-- mention approximation of permanent
-- mention \pi[x...y]
+- JN: explain approx scheme
+- JN: 4.5.1: neslo by preci isolovat nejaky vlstnosti restriction matrices
+ tak aby byl speedup? Staci napr predpokladat 4.5.2 (jako to postulovat)
+ co je to vlastne za matice co splnuji 4.5.2
+- JN: bounded-degree restriction graphs; would it imply general speedup?
Notation:
-- use X+e, X-e for general sets?
-- \O(...) as a set?
+- sort the table
- G has to be connected, so m=O(n)
- impedance mismatch in terminology: contraction of G along e vs. contraction of e.
- use \delta(X) notation
- unify use of n(G) vs. n
+- change the notation for contractions -- use double slash instead of the dot?
+- introduce \widehat\O early
+
+Typography:
+
+- formatting of multi-line \algin, \algout
- use calligraphic letters from ams?
+
+Global:
+
+- each chapter should make clear in which model we work
+- clean up bibliography
+
+Pictures:
+
+- structure of a Q-heap
projects / saga.git / blobdiff