//----------------------------------------------------------------------
// File: bd_tree.cpp
// Programmer: David Mount
// Description: Basic methods for bd-trees.
// Last modified: 01/04/05 (Version 1.0)
//----------------------------------------------------------------------
// Copyright (c) 1997-2005 University of Maryland and Sunil Arya and
// David Mount. All Rights Reserved.
//
// This software and related documentation is part of the Approximate
// Nearest Neighbor Library (ANN). This software is provided under
// the provisions of the Lesser GNU Public License (LGPL). See the
// file ../ReadMe.txt for further information.
//
// The University of Maryland (U.M.) and the authors make no
// representations about the suitability or fitness of this software for
// any purpose. It is provided "as is" without express or implied
// warranty.
//----------------------------------------------------------------------
// History:
// Revision 0.1 03/04/98
// Initial release
// Revision l.0 04/01/05
// Fixed centroid shrink threshold condition to depend on the
// dimension.
// Moved dump routine to kd_dump.cpp.
//----------------------------------------------------------------------
#include "bd_tree.h" // bd-tree declarations
#include "kd_util.h" // kd-tree utilities
#include "kd_split.h" // kd-tree splitting rules
#include <ANN/ANNperf.h> // performance evaluation
//----------------------------------------------------------------------
// Printing a bd-tree
// These routines print a bd-tree. See the analogous procedure
// in kd_tree.cpp for more information.
//----------------------------------------------------------------------
void ANNbd_shrink::print( // print shrinking node
int level, // depth of node in tree
ostream &out) // output stream
{
child[ANN_OUT]->print(level+1, out); // print out-child
out << " ";
for (int i = 0; i < level; i++) // print indentation
out << "..";
out << "Shrink";
for (int j = 0; j < n_bnds; j++) { // print sides, 2 per line
if (j % 2 == 0) {
out << "\n"; // newline and indentation
for (int i = 0; i < level+2; i++) out << " ";
}
out << " ([" << bnds[j].cd << "]"
<< (bnds[j].sd > 0 ? ">=" : "< ")
<< bnds[j].cv << ")";
}
out << "\n";
child[ANN_IN]->print(level+1, out); // print in-child
}
//----------------------------------------------------------------------
// kd_tree statistics utility (for performance evaluation)
// This routine computes various statistics information for
// shrinking nodes. See file kd_tree.cpp for more information.
//----------------------------------------------------------------------
void ANNbd_shrink::getStats( // get subtree statistics
int dim, // dimension of space
ANNkdStats &st, // stats (modified)
ANNorthRect &bnd_box) // bounding box
{
ANNkdStats ch_stats; // stats for children
ANNorthRect inner_box(dim); // inner box of shrink
annBnds2Box(bnd_box, // enclosing box
dim, // dimension
n_bnds, // number of bounds
bnds, // bounds array
inner_box); // inner box (modified)
// get stats for inner child
ch_stats.reset(); // reset
child[ANN_IN]->getStats(dim, ch_stats, inner_box);
st.merge(ch_stats); // merge them
// get stats for outer child
ch_stats.reset(); // reset
child[ANN_OUT]->getStats(dim, ch_stats, bnd_box);
st.merge(ch_stats); // merge them
st.depth++; // increment depth
st.n_shr++; // increment number of shrinks
}
//----------------------------------------------------------------------
// bd-tree constructor
// This is the main constructor for bd-trees given a set of points.
// It first builds a skeleton kd-tree as a basis, then computes the
// bounding box of the data points, and then invokes rbd_tree() to
// actually build the tree, passing it the appropriate splitting
// and shrinking information.
//----------------------------------------------------------------------
ANNkd_ptr rbd_tree( // recursive construction of bd-tree
ANNpointArray pa, // point array
ANNidxArray pidx, // point indices to store in subtree
int n, // number of points
int dim, // dimension of space
int bsp, // bucket space
ANNorthRect &bnd_box, // bounding box for current node
ANNkd_splitter splitter, // splitting routine
ANNshrinkRule shrink); // shrinking rule
ANNbd_tree::ANNbd_tree( // construct from point array
ANNpointArray pa, // point array (with at least n pts)
int n, // number of points
int dd, // dimension
int bs, // bucket size
ANNsplitRule split, // splitting rule
ANNshrinkRule shrink) // shrinking rule
: ANNkd_tree(n, dd, bs) // build skeleton base tree
{
pts = pa; // where the points are
if (n == 0) return; // no points--no sweat
ANNorthRect bnd_box(dd); // bounding box for points
// construct bounding rectangle
annEnclRect(pa, pidx, n, dd, bnd_box);
// copy to tree structure
bnd_box_lo = annCopyPt(dd, bnd_box.lo);
bnd_box_hi = annCopyPt(dd, bnd_box.hi);
switch (split) { // build by rule
case ANN_KD_STD: // standard kd-splitting rule
root = rbd_tree(pa, pidx, n, dd, bs, bnd_box, kd_split, shrink);
break;
case ANN_KD_MIDPT: // midpoint split
root = rbd_tree(pa, pidx, n, dd, bs, bnd_box, midpt_split, shrink);
break;
case ANN_KD_SUGGEST: // best (in our opinion)
case ANN_KD_SL_MIDPT: // sliding midpoint split
root = rbd_tree(pa, pidx, n, dd, bs, bnd_box, sl_midpt_split, shrink);
break;
case ANN_KD_FAIR: // fair split
root = rbd_tree(pa, pidx, n, dd, bs, bnd_box, fair_split, shrink);
break;
case ANN_KD_SL_FAIR: // sliding fair split
root = rbd_tree(pa, pidx, n, dd, bs,
bnd_box, sl_fair_split, shrink);
break;
default:
annError("Illegal splitting method", ANNabort);
}
}
//----------------------------------------------------------------------
// Shrinking rules
//----------------------------------------------------------------------
enum ANNdecomp {SPLIT, SHRINK}; // decomposition methods
//----------------------------------------------------------------------
// trySimpleShrink - Attempt a simple shrink
//
// We compute the tight bounding box of the points, and compute
// the 2*dim ``gaps'' between the sides of the tight box and the
// bounding box. If any of the gaps is large enough relative to
// the longest side of the tight bounding box, then we shrink
// all sides whose gaps are large enough. (The reason for
// comparing against the tight bounding box, is that after
// shrinking the longest box size will decrease, and if we use
// the standard bounding box, we may decide to shrink twice in
// a row. Since the tight box is fixed, we cannot shrink twice
// consecutively.)
//----------------------------------------------------------------------
const float BD_GAP_THRESH = 0.5; // gap threshold (must be < 1)
const int BD_CT_THRESH = 2; // min number of shrink sides
ANNdecomp trySimpleShrink( // try a simple shrink
ANNpointArray pa, // point array
ANNidxArray pidx, // point indices to store in subtree
int n, // number of points
int dim, // dimension of space
const ANNorthRect &bnd_box, // current bounding box
ANNorthRect &inner_box) // inner box if shrinking (returned)
{
int i;
// compute tight bounding box
annEnclRect(pa, pidx, n, dim, inner_box);
ANNcoord max_length = 0; // find longest box side
for (i = 0; i < dim; i++) {
ANNcoord length = inner_box.hi[i] - inner_box.lo[i];
if (length > max_length) {
max_length = length;
}
}
int shrink_ct = 0; // number of sides we shrunk
for (i = 0; i < dim; i++) { // select which sides to shrink
// gap between boxes
ANNcoord gap_hi = bnd_box.hi[i] - inner_box.hi[i];
// big enough gap to shrink?
if (gap_hi < max_length*BD_GAP_THRESH)
inner_box.hi[i] = bnd_box.hi[i]; // no - expand
else shrink_ct++; // yes - shrink this side
// repeat for high side
ANNcoord gap_lo = inner_box.lo[i] - bnd_box.lo[i];
if (gap_lo < max_length*BD_GAP_THRESH)
inner_box.lo[i] = bnd_box.lo[i]; // no - expand
else shrink_ct++; // yes - shrink this side
}
if (shrink_ct >= BD_CT_THRESH) // did we shrink enough sides?
return SHRINK;
else return SPLIT;
}
//----------------------------------------------------------------------
// tryCentroidShrink - Attempt a centroid shrink
//
// We repeatedly apply the splitting rule, always to the larger subset
// of points, until the number of points decreases by the constant
// fraction BD_FRACTION. If this takes more than dim*BD_MAX_SPLIT_FAC
// splits for this to happen, then we shrink to the final inner box
// Otherwise we split.
//----------------------------------------------------------------------
const float BD_MAX_SPLIT_FAC = 0.5; // maximum number of splits allowed
const float BD_FRACTION = 0.5; // ...to reduce points by this fraction
// ...This must be < 1.
ANNdecomp tryCentroidShrink( // try a centroid shrink
ANNpointArray pa, // point array
ANNidxArray pidx, // point indices to store in subtree
int n, // number of points
int dim, // dimension of space
const ANNorthRect &bnd_box, // current bounding box
ANNkd_splitter splitter, // splitting procedure
ANNorthRect &inner_box) // inner box if shrinking (returned)
{
int n_sub = n; // number of points in subset
int n_goal = (int) (n*BD_FRACTION); // number of point in goal
int n_splits = 0; // number of splits needed
// initialize inner box to bounding box
annAssignRect(dim, inner_box, bnd_box);
while (n_sub > n_goal) { // keep splitting until goal reached
int cd; // cut dim from splitter (ignored)
ANNcoord cv; // cut value from splitter (ignored)
int n_lo; // number of points on low side
// invoke splitting procedure
(*splitter)(pa, pidx, inner_box, n_sub, dim, cd, cv, n_lo);
n_splits++; // increment split count
if (n_lo >= n_sub/2) { // most points on low side
inner_box.hi[cd] = cv; // collapse high side
n_sub = n_lo; // recurse on lower points
}
else { // most points on high side
inner_box.lo[cd] = cv; // collapse low side
pidx += n_lo; // recurse on higher points
n_sub -= n_lo;
}
}
if (n_splits > dim*BD_MAX_SPLIT_FAC)// took too many splits
return SHRINK; // shrink to final subset
else
return SPLIT;
}
//----------------------------------------------------------------------
// selectDecomp - select which decomposition to use
//----------------------------------------------------------------------
ANNdecomp selectDecomp( // select decomposition method
ANNpointArray pa, // point array
ANNidxArray pidx, // point indices to store in subtree
int n, // number of points
int dim, // dimension of space
const ANNorthRect &bnd_box, // current bounding box
ANNkd_splitter splitter, // splitting procedure
ANNshrinkRule shrink, // shrinking rule
ANNorthRect &inner_box) // inner box if shrinking (returned)
{
ANNdecomp decomp = SPLIT; // decomposition
switch (shrink) { // check shrinking rule
case ANN_BD_NONE: // no shrinking allowed
decomp = SPLIT;
break;
case ANN_BD_SUGGEST: // author's suggestion
case ANN_BD_SIMPLE: // simple shrink
decomp = trySimpleShrink(
pa, pidx, // points and indices
n, dim, // number of points and dimension
bnd_box, // current bounding box
inner_box); // inner box if shrinking (returned)
break;
case ANN_BD_CENTROID: // centroid shrink
decomp = tryCentroidShrink(
pa, pidx, // points and indices
n, dim, // number of points and dimension
bnd_box, // current bounding box
splitter, // splitting procedure
inner_box); // inner box if shrinking (returned)
break;
default:
annError("Illegal shrinking rule", ANNabort);
}
return decomp;
}
//----------------------------------------------------------------------
// rbd_tree - recursive procedure to build a bd-tree
//
// This is analogous to rkd_tree, but for bd-trees. See the
// procedure rkd_tree() in kd_split.cpp for more information.
//
// If the number of points falls below the bucket size, then a
// leaf node is created for the points. Otherwise we invoke the
// procedure selectDecomp() which determines whether we are to
// split or shrink. If splitting is chosen, then we essentially
// do exactly as rkd_tree() would, and invoke the specified
// splitting procedure to the points. Otherwise, the selection
// procedure returns a bounding box, from which we extract the
// appropriate shrinking bounds, and create a shrinking node.
// Finally the points are subdivided, and the procedure is
// invoked recursively on the two subsets to form the children.
//----------------------------------------------------------------------
ANNkd_ptr rbd_tree( // recursive construction of bd-tree
ANNpointArray pa, // point array
ANNidxArray pidx, // point indices to store in subtree
int n, // number of points
int dim, // dimension of space
int bsp, // bucket space
ANNorthRect &bnd_box, // bounding box for current node
ANNkd_splitter splitter, // splitting routine
ANNshrinkRule shrink) // shrinking rule
{
ANNdecomp decomp; // decomposition method
ANNorthRect inner_box(dim); // inner box (if shrinking)
if (n <= bsp) { // n small, make a leaf node
if (n == 0) // empty leaf node
return KD_TRIVIAL; // return (canonical) empty leaf
else // construct the node and return
return new ANNkd_leaf(n, pidx);
}
decomp = selectDecomp( // select decomposition method
pa, pidx, // points and indices
n, dim, // number of points and dimension
bnd_box, // current bounding box
splitter, shrink, // splitting/shrinking methods
inner_box); // inner box if shrinking (returned)
if (decomp == SPLIT) { // split selected
int cd; // cutting dimension
ANNcoord cv; // cutting value
int n_lo; // number on low side of cut
// invoke splitting procedure
(*splitter)(pa, pidx, bnd_box, n, dim, cd, cv, n_lo);
ANNcoord lv = bnd_box.lo[cd]; // save bounds for cutting dimension
ANNcoord hv = bnd_box.hi[cd];
bnd_box.hi[cd] = cv; // modify bounds for left subtree
ANNkd_ptr lo = rbd_tree( // build left subtree
pa, pidx, n_lo, // ...from pidx[0..n_lo-1]
dim, bsp, bnd_box, splitter, shrink);
bnd_box.hi[cd] = hv; // restore bounds
bnd_box.lo[cd] = cv; // modify bounds for right subtree
ANNkd_ptr hi = rbd_tree( // build right subtree
pa, pidx + n_lo, n-n_lo,// ...from pidx[n_lo..n-1]
dim, bsp, bnd_box, splitter, shrink);
bnd_box.lo[cd] = lv; // restore bounds
// create the splitting node
return new ANNkd_split(cd, cv, lv, hv, lo, hi);
}
else { // shrink selected
int n_in; // number of points in box
int n_bnds; // number of bounding sides
annBoxSplit( // split points around inner box
pa, // points to split
pidx, // point indices
n, // number of points
dim, // dimension
inner_box, // inner box
n_in); // number of points inside (returned)
ANNkd_ptr in = rbd_tree( // build inner subtree pidx[0..n_in-1]
pa, pidx, n_in, dim, bsp, inner_box, splitter, shrink);
ANNkd_ptr out = rbd_tree( // build outer subtree pidx[n_in..n]
pa, pidx+n_in, n - n_in, dim, bsp, bnd_box, splitter, shrink);
ANNorthHSArray bnds = NULL; // bounds (alloc in Box2Bnds and
// ...freed in bd_shrink destroyer)
annBox2Bnds( // convert inner box to bounds
inner_box, // inner box
bnd_box, // enclosing box
dim, // dimension
n_bnds, // number of bounds (returned)
bnds); // bounds array (modified)
// return shrinking node
return new ANNbd_shrink(n_bnds, bnds, in, out);
}
}