Special cases.

[saga.git] / PLAN

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-*  Minimum spanning trees
+*  Minimum Spanning Trees
 
+  o  The Problem
   o  Basic properties
   o  Red/Blue meta-algorithm
   o  Classical algorithms
-  o  Fredman-Tarjan algorithm
-  o  ?? Chazelle ??
-  o  ?? Pettie ??
-  o  Minor-closed classes
-  o  MST verification
-  o  Randomized algorithms
+  o  Contractive algorithms
 
-*  Integer data structures
+*  Fine Details of Computation
 
-  o  Models of computation
+  o  Models and machines
+  o  Radix-sorting
   o  Bit tricks
-  o  Ranking sets
-  o  Bitwise B-trees
   o  Q-Heaps
 
+*  Advanced MST Algorithms
+
+  o  Minor-closed classes
+  o  Fredman-Tarjan algorithm
+  .  MST verification
+  .  Randomized algorithms
+  .  ?? Chazelle ??
+  .  ?? Pettie ??
+  o  Special cases and related problems
+
 *  Ranking combinatorial objects
 
-  o  Ranking of permutations: history
-  o  Linear-time algorithm
-  o  k-permutations
-  o  Permutations with no fixed point
-  o  ?? other objects ??
+  o  Ranking and unranking
+  o  Ranking of permutations
+  o  Ranking of k-permutations
+  o  Restricted permutations
+  o  Hatcheck lady and other derangements
+  .  ?? other objects ??
+  .  ?? general perspective ??
 
 *  Dynamic MST algorithms
 
-  o  (Semi-)dynamic algorithms
-  o  Sleator-Tarjan trees
-  o  ET-trees
-  o  Fully dynamic connectivity
-  o  Semi-dynamic MST
-  o  Fully dynamic MST
+  .  (Semi-)dynamic algorithms
+  .  Sleator-Tarjan trees
+  .  ET-trees
+  .  Fully dynamic connectivity
+  .  Semi-dynamic MST
+  .  Fully dynamic MST
+
+TODO:
+
+Spanning trees:
+
+- cite Eisner's tutorial \cite{eisner:tutorial}
+- \cite{pettie:onlineverify} online lower bound
+- mention matroids
+- mention disconnected graphs
+- Some algorithms (most notably Fredman-Tarjan) do not need flattening
+- reference to mixed Boruvka-Jarnik
+- use the notation for contraction by a set
+- practical considerations: katriel:cycle, moret:practice (mention pairing heaps)
+- parallel algorithms: p243-cole (are there others?)
+- bounded expansion classes?
+- restricted cases and arborescences
+
+Models:
+
+- bit tricks: reference to HAKMEM
+- mention in-place radix-sorting?
+- consequences of Q-Heaps: Thorup's undirected SSSP etc.
+- add more context from thorup:aczero, also mention FP operations
+
+Ranking:
+
+- the general perspective: is it only a technical trick?
+- ranking of permutations on general sets, relationship with integer sorting
+- 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 vlstne za matice co splnuji 4.5.2
+- JN: bounded-degree restriction graphs; would it imply general speedup?
+
+Notation:
+
+- 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
+- use calligraphic letters from ams?
+- change the notation for contractions -- use double slash instead of the dot?