[Haskell-cafe] Suggestion for Data Structure regarding Timetabling and Time Intervals

[Olaf Klinke]

Dear Michael,

if you can be sure your intervals will never overlap, why not use a binary search tree, such as Data.Set from containers? You could make a data structure distinguishing major and minor intervals such as:

type Time = -- your favourite totally ordered time type
data Major = Major {
  fromTime :: Time,
  untilTime :: Time} deriving (Eq)
data Minor = Minor {
  after :: Time
  before :: Time} deriving (Eq)
type TimeInterval = Either Minor Major

instance Ord (Either Minor Major) where
   Left  a <= Left  b = before a <= after b
   Right a <= Right b = untilTime a <= fromTime b
   Left  a <= Right b = before a <= fromTime b
   Right a <= Left  b = untilTime a <= after b

If I understood your intentions correctly, inserting a minor interval between a :: Major and b :: Major where a < b would mean to insert 

Minor {after = untilTime a, before = fromTime b}

It might also be handy to define a new type (isomorphic to the product (a,b))

Anno a b = Anno a b

whose Ord instance uses the Ord instance of b only, so that 

Anno "Some annotation" (Major t0 t1)

is an interval bearing some annotation that can be ordered just like the Major type.

If your intervals _do_ overlap, then two intervals can be in six different configurations (instead of LT, GT and EQ), and several tree structures exist that support some operations more or less efficiently. Bioinformatics and geometry has developed good data structures and algorithms to deal with efficient overlap searches. 

Olaf