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// Calculate rank-width and rank-decompositions of graphs.
// Philipp Klaus Krause, philipp@informatik.uni-frankfurt.de, pkk@spth.de, 2009 - 2016
// Copyright (c) 2009-2016 Philipp Klaus Krause
// Copyright (c) 2009-2015 Goethe-Universität Frankfurt
// This program is free software; you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation; either version 2 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License along
// with this program; if not, write to the Free Software Foundation, Inc.,
// 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
#include <stdlib.h>
#include "rw.h"
static uint_fast8_t subset_size;
static uint_fast8_t num_vertices;
subset_t *adjacency_matrix;
// This array is meant to contain max{f(Y), w(f, Y)} at the position corresponding to Y.
static uint_fast8_t *slots;
subset_t *cslots;
uint_fast8_t cut_rank(const subset_t s)
{
subset_t am[num_vertices];
subset_t x, y;
uint_fast8_t i, j;
uint_fast8_t rank = 0;
for(i = 0; i < num_vertices; i++)
am[i] = (s & (1ul << i)) ? 0 : (adjacency_matrix[i] & s);
for(i = 0; i < num_vertices; i++)
{
y = 0;
for(j = rank; j < num_vertices; j++)
{
x = am[j];
if(x & 1)
{
if(!y)
{
y = x;
am[j] = am[rank++];
continue;
}
x ^= y;
}
am[j] = x >> 1;
}
}
return(rank);
}
// Compute the binomial coefficient C(n, k).
// Time complexity: O(n) * complexity of integer division.
// Could be replaced by a lookup table of size O(n^2), but since this is not the bopttleneck, it doesn't matter.
subset_t binomial_coefficient(uint_fast8_t n, uint_fast8_t k)
{
uint_fast8_t i, delta, max;
subset_t c;
if(n < k)
return(0);
if(n == k)
return(1);
if(k < n - k)
{
delta = n - k;
max = k;
}
else
{
delta = k;
max = n - k;
}
c = delta + 1;
for(i = 2; i <= max; i++)
c = (c * (delta + i)) / i;
return(c);
}
// Convert unsigned integer from combinadic to machine representation.
subset_t comb_to_int(subset_t c)
{
uint_fast8_t k, n;
subset_t i;
i = 0;
for(k = 0, n = 1; k < num_vertices; k++, c >>= 1)
if(c & 1)
i += binomial_coefficient(k, n++);
return(i);
}
// Return largest value v where v < a and Choose(v,b) <= x.
static uint_fast8_t largest_v(uint_fast8_t a, uint_fast8_t b, subset_t x)
{
uint_fast8_t v = a - 1;
while(binomial_coefficient(v,b) > x)
v--;
return(v);
}
// Convert unsigned integer from machine representation to combinadic.
static subset_t int_to_comb(subset_t i)
{
uint_fast8_t j, v;
uint_fast8_t a = num_vertices;
uint_fast8_t b = subset_size;
subset_t c = 0;
for(j = 0; j < subset_size; j++, b--)
{
v = largest_v(a, b, i);
i = i - binomial_coefficient(v, b);
a = v;
c |= (1ul << v);
}
return(c);
}
// Masked increment.
static subset_t subset_inc(subset_t v, subset_t mask)
{
return((v - mask) & mask);
}
// Returns rank-width for a subset of size at least 2 given that slots already contains correct values for all nonempty subsets of sizes less than the size of s.
// This is where most of the time is spent.
uint_fast8_t width(subset_t s)
{
uint_fast8_t w = UINT_FAST8_MAX, v, v1, v2;
subset_t ss;
subset_t cs;
for(ss = subset_inc(0, s); ss != s; ss = subset_inc(ss, s))
{
v1 = slots[ss];
v2 = slots[s & ~ss];
v = v1 > v2 ? v1 : v2;
if(v < w)
{
w = v;
cs = ss;
}
}
cslots[s] = cs;
return(w);
}
void fill_slot(subset_t i)
{
uint_fast8_t v, w;
subset_t s = int_to_comb(i);
v = cut_rank(s);
w = width(s);
slots[s] = v > w ? v : w;
}
void calculate_level(uint_fast8_t ss)
{
uint_fast8_t i;
subset_size = ss;
if(subset_size == 0)
slots[0] = 0;
else if(subset_size == 1)
for(i = 0; i < num_vertices; i++)
{
slots[1ul << i] = cut_rank(1ul << i);
cslots[1ul << i] = 0x0;
}
else
{
subset_t i;
const subset_t end = binomial_coefficient(num_vertices, subset_size);
for(i = 0; i < end; i++)
fill_slot(i);
}
}
void calculate_all(void)
{
uint_fast8_t i;
for(i = 0; i < num_vertices; i++)
{
slots[1ul << i] = cut_rank(1ul << i);
cslots[1ul << i] = 0x0;
}
for(subset_size = 2; subset_size <= num_vertices; subset_size++)
{
subset_t i;
const subset_t end = binomial_coefficient(num_vertices, subset_size);
for(i = 0; i < end; i++)
fill_slot(i);
}
}
int init_rw(uint_fast8_t n)
{
// If sizeof(uint_fast8_t) * (1ul << n) overflows, it wraps around to 0, since size_t and unsigned long are unsigned integer types.
if(n > MAX_VERTICES || n && !(sizeof(uint_fast8_t) * (1ul << n)))
return(-1);
num_vertices = n;
adjacency_matrix = malloc(sizeof(subset_t) * n);
slots = malloc(sizeof(uint_fast8_t) * (1ul << n));
cslots = 0;
return((adjacency_matrix && slots) ? 0 : -1);
}
int init_rw_dec(uint_fast8_t n)
{
// If sizeof(subset_t) * (1ul << n) overflows, it wraps around to 0, since size_t and unsigned long are unsigned integer types.
if(n && !(sizeof(subset_t) * (1ul << n)))
return(-1);
if(init_rw(n))
return(-1);
cslots = malloc(sizeof(subset_t) * (1ul << n));
return(cslots ? 0 : -1);
}
void destroy_rw(void)
{
free(cslots);
free(slots);
free(adjacency_matrix);
}
uint_fast8_t get_rw(void)
{
return(slots[0xfffffffful >> (32 - num_vertices)]);
}
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