de.sciss.lucre.data

A transactional deterministic skip octree as outlined in the paper by Eppstein et al. It is constructed from a given space (dimensions) and a skip-gap parameter which determines the kind of skip list which is used to govern the level decimation.

The tree is a mutable data structure which supports lookup, insertion and removal in O(log n), as well as efficient range queries and nearest neighbour search.

The current implementation, backed by impl.SkipOctreeImpl, uses the types of the geom package, assuming that coordinates are integers, with the maximum root hyper-cube given by a span from 0 to 0x7FFFFFFF (e.g. in Space.IntTwoDim, this is IntSquare( 0x40000000, 0x40000000, 0x40000000 ).

A transactional version of the deterministic k-(2k+1) top-down operated skip list as described in T. Papadakis, Skip Lists and Probabilistic Analysis of Algorithms. Ch. 4 (Deterministic Skip Lists), pp. 55--78. Waterloo (CA) 1993

It uses the horizontal array technique with a parameter for k (minimum gap size). It uses a modified top-down removal algorithm that avoids the need for a second pass as in the original algorithm, and is careful about object creations, so that it will be able to persist the data structure without any unnecessary reads or writes to the store.

Three implementation notes: (1) We treat the nodes as immutable at the moment, storing them directly in the S#Val child pointers of their parents. While this currently seems to have a performance advantage (?), we could try to avoid this by using S#Refs for the child pointers, making the nodes become mutable. We could avoid copying the arrays for each insertion or deletion, at the cost of more space, but maybe better performance.

(2) The special treatment of isRight kind of sucks. Since now that information is also persisted, we might just have two types of branches and leaves, and avoid passing around this flag.

(3) Since there is a bug with the top-down one-pass removal, we might end up removing the creation of instances of virtual branches altogether again when replacing the current algorithm by a two-pass one.

TODO: nodes or at least leaves should be horizontally connected for a faster iterator and fast pair (interval) search

A SkipOctree is a multi-dimensional data structure that maps coordinates to values. It extends the interface of Scala's mutable Map and adds further operations such as range requires and nearest neighbour search.

A transactional data structure to maintain an ordered sequence of elements such that two random elements can be compared in O(1).

This uses an algorithm from the paper Bender, M. and Cole, R. and Demaine, E. and Farach-Colton, M. and Zito, J., Two simplified algorithms for maintaining order in a list, Algorithms—ESA 2002, pp. 219--223, 2002.

The relabel method is based on the Python implementation by David Eppstein, as published at http://www.ics.uci.edu/~eppstein/PADS/OrderedSequence.py however a bug resulting in a relabel size of 1 was fixed.

Original note: "Due to rebalancing on the integer tags used to maintain order, the amortized time per insertion in an n-item list is O(log n)."