X-Git-Url: http://mj.ucw.cz/gitweb/?a=blobdiff_plain;f=PLAN;h=51732fb331fc7803759ef613346fbaae697aedb1;hb=501e0109a4b9bbcb68d49965528459ccf34c30c8;hp=ff4dd14e1c27c9e738e527a097c96f3633ffc9ca;hpb=1d0d0f02919c3e54c7559087945c7e9cf2adbef5;p=saga.git diff --git a/PLAN b/PLAN index ff4dd14..51732fb 100644 --- a/PLAN +++ b/PLAN @@ -10,67 +10,56 @@ o Models and machines o Radix-sorting - . Bit tricks - . Ranking sets - . Bitwise B-trees - . Q-Heaps + o Bit tricks + 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 - . Ranking of permutations: history - . Linear-time algorithm - . k-permutations - . Permutations with no fixed point - . ?? other objects ?? + o Soft heaps + o Robust contractions + o Decision trees + o An optimal algorithm * Dynamic MST algorithms - . (Semi-)dynamic algorithms - . Sleator-Tarjan trees - . ET-trees - . Fully dynamic connectivity - . Semi-dynamic MST - . Fully dynamic MST + o (Semi-)dynamic algorithms + o ET-trees + o Fully dynamic connectivity + o Dynamic MST + o Almost minimum trees -TODO: +* Ranking Combinatorial Objects -Spanning trees: + o Ranking and unranking + o Ranking of permutations + o Ranking of k-permutations + o Restricted permutations + o Hatcheck lady and other derangements -- 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 +TODO: -Models: +Applications: -- bit tricks: reference to HAKMEM -- mention in-place radix-sorting? +- degree-restricted cases and arborescences +- bounded expansion classes? 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 +- 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: +Typography: -- \O(...) as a set? -- 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 +- formatting of multi-line \algin, \algout