Procedures for dynamic variable ordering of ZDDs. More...

#include "util.h"
#include "mtrInt.h"
#include "cuddInt.h"

Include dependency graph for cuddZddReord.c:

Macros
#define	DD_MAX_SUBTABLE_SPARSITY 8

Functions
int	Cudd_zddReduceHeap (DdManager *table, Cudd_ReorderingType heuristic, int minsize)
	Main dynamic reordering routine for ZDDs. More...

int	Cudd_zddShuffleHeap (DdManager table, int permutation)
	Reorders ZDD variables according to given permutation. More...

int	cuddZddAlignToBdd (DdManager *table)
	Reorders ZDD variables according to the order of the BDD variables. More...

int	cuddZddNextHigh (DdManager *table, int x)
	Finds the next subtable with a larger index. More...

int	cuddZddNextLow (DdManager *table, int x)
	Finds the next subtable with a smaller index. More...

int	cuddZddUniqueCompare (void const ptr_x, void const ptr_y)
	Comparison function used by qsort. More...

int	cuddZddSwapInPlace (DdManager *table, int x, int y)
	Swaps two adjacent variables. More...

int	cuddZddSwapping (DdManager *table, int lower, int upper, Cudd_ReorderingType heuristic)
	Reorders variables by a sequence of (non-adjacent) swaps. More...

int	cuddZddSifting (DdManager *table, int lower, int upper)
	Implementation of Rudell's sifting algorithm. More...

static Move *	zddSwapAny (DdManager *table, int x, int y)
	Swaps any two variables. More...

static int	cuddZddSiftingAux (DdManager *table, int x, int x_low, int x_high)
	Given xLow <= x <= xHigh moves x up and down between the boundaries. More...

static Move *	cuddZddSiftingUp (DdManager *table, int x, int x_low, int initial_size)
	Sifts a variable up. More...

static Move *	cuddZddSiftingDown (DdManager *table, int x, int x_high, int initial_size)
	Sifts a variable down. More...

static int	cuddZddSiftingBackward (DdManager table, Move moves, int size)
	Given a set of moves, returns the ZDD heap to the position giving the minimum size. More...

static void	zddReorderPreprocess (DdManager *table)
	Prepares the ZDD heap for dynamic reordering. More...

static int	zddReorderPostprocess (DdManager *table)
	Shrinks almost empty ZDD subtables at the end of reordering to guarantee that they have a reasonable load factor. More...

static int	zddShuffle (DdManager table, int permutation)
	Reorders ZDD variables according to a given permutation. More...

static int	zddSiftUp (DdManager *table, int x, int xLow)
	Moves one ZDD variable up. More...

static void	zddFixTree (DdManager table, MtrNode treenode)
	Fixes the ZDD variable group tree after a shuffle. More...

Detailed Description

Procedures for dynamic variable ordering of ZDDs.

Author: Hyong-Kyoon Shin, In-Ho Moon

Copyright

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

Neither the name of the University of Colorado nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

Function Documentation

◆ Cudd_zddReduceHeap()

int Cudd_zddReduceHeap	(	DdManager *	table,
		Cudd_ReorderingType	heuristic,
		int	minsize
	)

Main dynamic reordering routine for ZDDs.

Calls one of the possible reordering procedures:

Swapping
Sifting
Symmetric Sifting

For sifting and symmetric sifting it is possible to request reordering to convergence.

The core of all methods is the reordering procedure cuddZddSwapInPlace() which swaps two adjacent variables.

Returns: 1 in case of success; 0 otherwise. In the case of symmetric sifting (with and without convergence) returns 1 plus the number of symmetric variables, in case of success.

Side effects Changes the variable order for all ZDDs and clears: the cache.

Parameters

table	DD manager
heuristic	method used for reordering
minsize	bound below which no reordering occurs

◆ Cudd_zddShuffleHeap()

int Cudd_zddShuffleHeap	(	DdManager *	table,
		int *	permutation
	)

Reorders ZDD variables according to given permutation.

The i-th entry of the permutation array contains the index of the variable that should be brought to the i-th level. The size of the array should be equal or greater to the number of variables currently in use.

Returns: 1 in case of success; 0 otherwise.

Side effects Changes the ZDD variable order for all diagrams and clears: the cache.

See also: Cudd_zddReduceHeap

Parameters

table	DD manager
permutation	required variable permutation

◆ cuddZddAlignToBdd()

int cuddZddAlignToBdd ( DdManager * table )

Reorders ZDD variables according to the order of the BDD variables.

This function can be called at the end of BDD reordering to insure that the order of the ZDD variables is consistent with the order of the BDD variables. The number of ZDD variables must be a multiple of the number of BDD variables. Let M be the ratio of the two numbers. cuddZddAlignToBdd then considers the ZDD variables from M*i to (M+1)*i-1 as corresponding to BDD variable i. This function should be normally called from Cudd_ReduceHeap, which clears the cache.

Returns: 1 in case of success; 0 otherwise.

Side effects Changes the ZDD variable order for all diagrams and performs: garbage collection of the ZDD unique table.

See also: Cudd_zddShuffleHeap Cudd_ReduceHeap

Parameters

table DD manager

◆ cuddZddNextHigh()

int cuddZddNextHigh	(	DdManager *	table,
		int	x
	)

Finds the next subtable with a larger index.

Returns: the index.

Side effects None

◆ cuddZddNextLow()

int cuddZddNextLow	(	DdManager *	table,
		int	x
	)

Finds the next subtable with a smaller index.

Returns: the index.

Side effects None

◆ cuddZddSifting()

int cuddZddSifting	(	DdManager *	table,
		int	lower,
		int	upper
	)

Implementation of Rudell's sifting algorithm.

Assumes that no dead nodes are present.

Order all the variables according to the number of entries in each unique table.
Sift the variable up and down, remembering each time the total size of the DD heap.
Select the best permutation.
Repeat 3 and 4 for all variables.

Returns: 1 if successful; 0 otherwise.

Side effects None

◆ cuddZddSiftingAux()

static int cuddZddSiftingAux	(	DdManager *	table,
		int	x,
		int	x_low,
		int	x_high
	)

static

Given xLow <= x <= xHigh moves x up and down between the boundaries.

Finds the best position and does the required changes.

Returns: 1 if successful; 0 otherwise.

Side effects None

◆ cuddZddSiftingBackward()

static int cuddZddSiftingBackward	(	DdManager *	table,
		Move *	moves,
		int	size
	)

static

Given a set of moves, returns the ZDD heap to the position giving the minimum size.

In case of ties, returns to the closest position giving the minimum size.

Returns: 1 in case of success; 0 otherwise.

Side effects None

◆ cuddZddSiftingDown()

static Move* cuddZddSiftingDown	(	DdManager *	table,
		int	x,
		int	x_high,
		int	initial_size
	)

static

Sifts a variable down.

Moves x down until either it reaches the bound (x_high) or the size of the ZDD heap increases too much.

Returns: the set of moves in case of success; NULL if memory is full.

Side effects None

◆ cuddZddSiftingUp()

static Move* cuddZddSiftingUp	(	DdManager *	table,
		int	x,
		int	x_low,
		int	initial_size
	)

static

Sifts a variable up.

Moves y up until either it reaches the bound (x_low) or the size of the ZDD heap increases too much.

Returns: the set of moves in case of success; NULL if memory is full.

Side effects None

◆ cuddZddSwapInPlace()

int cuddZddSwapInPlace	(	DdManager *	table,
		int	x,
		int	y
	)

Swaps two adjacent variables.

It assumes that no dead nodes are present on entry to this procedure. The procedure then guarantees that no dead nodes will be present when it terminates. cuddZddSwapInPlace assumes that x < y.

Returns: the number of keys in the table if successful; 0 otherwise.

Side effects None

◆ cuddZddSwapping()

int cuddZddSwapping	(	DdManager *	table,
		int	lower,
		int	upper,
		Cudd_ReorderingType	heuristic
	)

Reorders variables by a sequence of (non-adjacent) swaps.

Implementation of Plessier's algorithm that reorders variables by a sequence of (non-adjacent) swaps.

Select two variables (RANDOM or HEURISTIC).
Permute these variables.
If the nodes have decreased accept the permutation.
Otherwise reconstruct the original heap.
Loop.

Returns: 1 in case of success; 0 otherwise.

Side effects None

◆ cuddZddUniqueCompare()

int cuddZddUniqueCompare	(	void const *	ptr_x,
		void const *	ptr_y
	)

Comparison function used by qsort.

Comparison function used by qsort to order the variables according to the number of keys in the subtables.

Returns: the difference in number of keys between the two variables being compared.

Side effects None

◆ zddFixTree()

static void zddFixTree	(	DdManager *	table,
		MtrNode *	treenode
	)

static

Fixes the ZDD variable group tree after a shuffle.

Assumes that the order of the variables in a terminal node has not been changed.

Side effects Changes the ZDD variable group tree.

◆ zddReorderPostprocess()

static int zddReorderPostprocess ( DdManager * table )

static

Shrinks almost empty ZDD subtables at the end of reordering to guarantee that they have a reasonable load factor.

However, if there many nodes are being reclaimed, then no resizing occurs.

Returns: 1 in case of success; 0 otherwise.

Side effects None

◆ zddReorderPreprocess()

static void zddReorderPreprocess ( DdManager * table )

static

Prepares the ZDD heap for dynamic reordering.

Does garbage collection, to guarantee that there are no dead nodes; and clears the cache, which is invalidated by dynamic reordering.

Side effects None

◆ zddShuffle()

static int zddShuffle	(	DdManager *	table,
		int *	permutation
	)

static

Reorders ZDD variables according to a given permutation.

The i-th permutation array contains the index of the variable that should be brought to the i-th level. zddShuffle assumes that no dead nodes are present. The reordering is achieved by a series of upward sifts.

Returns: 1 if successful; 0 otherwise.

Side effects None

◆ zddSiftUp()

static int zddSiftUp	(	DdManager *	table,
		int	x,
		int	xLow
	)

static

Moves one ZDD variable up.

Takes a ZDD variable from position x and sifts it up to position xLow; xLow should be less than or equal to x.

Returns: 1 if successful; 0 otherwise

Side effects None

◆ zddSwapAny()

static Move* zddSwapAny	(	DdManager *	table,
		int	x,
		int	y
	)

static

Swaps any two variables.

Returns: the set of moves.

Side effects None

Macros

Functions

Detailed Description

Function Documentation

◆ Cudd_zddReduceHeap()

◆ Cudd_zddShuffleHeap()

◆ cuddZddAlignToBdd()

◆ cuddZddNextHigh()

◆ cuddZddNextLow()

◆ cuddZddSifting()

◆ cuddZddSiftingAux()

◆ cuddZddSiftingBackward()

◆ cuddZddSiftingDown()

◆ cuddZddSiftingUp()

◆ cuddZddSwapInPlace()

◆ cuddZddSwapping()

◆ cuddZddUniqueCompare()

◆ zddFixTree()

◆ zddReorderPostprocess()

◆ zddReorderPreprocess()

◆ zddShuffle()

◆ zddSiftUp()

◆ zddSwapAny()