While we're at it we might as well improve the known asymptotics for …

…the online level ancestor problem.

CHANGELOG.md

@@ -1,3 +1,7 @@
+0.2.3
+-----
+* Improved documentation to also note that this package also provides an improvement in the online version of the [level ancestor problem](http://en.wikipedia.org/wiki/Level_ancestor_problem).
+
 0.2.2
 -----
 * Added README

lca.cabal

@@ -1,6 +1,6 @@
 name:          lca
 category:      Algorithms, Data Structures
-version:       0.2.2
+version:       0.2.3
 license:       BSD3
 cabal-version: >= 1.6
 license-file:  LICENSE

src/Data/LCA/Online.hs

@@ -16,7 +16,13 @@
 --
 -- <http://www.slideshare.net/ekmett/skewbinary-online-lowest-common-ancestor-search>
 --
--- to improve the known asymptotic bounds on online lowest common ancestor search.
+-- to improve the known asymptotic bounds on both online lowest common ancestor search
+--
+-- <http://en.wikipedia.org/wiki/Lowest_common_ancestor>
+--
+-- and the online level ancestor problem:
+--
+-- <http://en.wikipedia.org/wiki/Level_ancestor_problem>
 --
 -- Algorithms used here assume that the key values chosen for @k@ are
 -- globally unique.
@@ -155,6 +161,11 @@ view (Cons _ w (Bin k a l r) ts) = Node k a (consT w2 l (consT w2 r ts)) where w
 {-# INLINE view #-}
 
 -- | /O(log (h - k))/ to @'keep' k@ elements of 'Path' of 'length' @h@
+--
+-- This solves the online version of the \"level ancestor problem\" with no preprocessing in /O(log h)/ time,
+-- improving known complexity bounds.
+--
+-- <http://en.wikipedia.org/wiki/Level_ancestor_problem>
 keep :: Int -> Path a -> Path a
 keep = go where
   go _ Nil = Nil

src/Data/LCA/Online/Monoidal.hs

@@ -12,9 +12,24 @@
 -- by compressing the spine of the paths using a skew-binary random access
 -- list.
 --
+-- This library implements the technique described in my talk
+--
+-- <http://www.slideshare.net/ekmett/skewbinary-online-lowest-common-ancestor-search>
+--
+-- to improve the known asymptotic bounds on both online lowest common ancestor search
+--
+-- <http://en.wikipedia.org/wiki/Lowest_common_ancestor>
+--
+-- and the online level ancestor problem:
+--
+-- <http://en.wikipedia.org/wiki/Level_ancestor_problem>
+--
 -- Algorithms used here assume that the key values chosen for @k@ are
 -- globally unique.
 --
+-- This version provides access to a monoidal \"summary\" of the
+-- elided path for many operations.
+--
 ----------------------------------------------------------------------------
 module Data.LCA.Online.Monoidal
   ( Path
@@ -198,6 +213,7 @@ view (Cons _ _ w (Bin _ k a l r) ts) = Node k a (consT w2 l (consT w2 r ts)) whe
 {-# INLINE view #-}
 
 -- | /O(log (h - k))/ to keep @k@ elements of 'Path' of 'length' @h@, and provide a monoidal summary of the dropped elements
+--
 mkeep :: Monoid a => Int -> Path a -> (a, Path a)
 mkeep = go mempty where
   go as _ Nil = (as, Nil)
@@ -218,6 +234,11 @@ mkeep = go mempty where
 {-# INLINE mkeep #-}
 
 -- | /O(log (h - k))/ to @'keep' k@ elements of 'Path' of 'length' @h@
+--
+-- This solves the online version of the \"level ancestor problem\" with no preprocessing in /O(log h)/ time,
+-- improving known complexity bounds.
+--
+-- <http://en.wikipedia.org/wiki/Level_ancestor_problem>
 keep :: Monoid a => Int -> Path a -> Path a
 keep k xs = snd (mkeep k xs)
 {-# INLINE keep #-}