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cs2.c
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/* min-cost flow */
/* successive approximation algorithm */
/* Copyright C IG Systems, igsys@eclipse.com */
/* any use except for evaluation purposes requires a licence */
/************************************** constants & parameters ********/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
#include <assert.h>
//#include <values.h>
/* for measuring time */
/* definitions of types: node & arc */
#include "types_cs2.h"
/* function 'timer()' for measuring processor time */
#ifdef WINDOWS_TIMER
#include "winTimer.c"
#else
#include "timer.c"
#endif
#define N_NODE( i ) ( ( (i) == NULL ) ? -1 : ( (i) - ndp + nmin ) )
#define N_ARC( a ) ( ( (a) == NULL )? -1 : (a) - arp )
#define UNFEASIBLE 2
#define ALLOCATION_FAULT 5
#define PRICE_OFL 6
/* parameters */
#define UPDT_FREQ 0.4
#define UPDT_FREQ_S 30
#define SCALE_DEFAULT 12.0
/* PRICE_OUT_START may not be less than 1 */
#define PRICE_OUT_START 1
#define CUT_OFF_POWER 0.44
#define CUT_OFF_COEF 1.5
#define CUT_OFF_POWER2 0.75
#define CUT_OFF_COEF2 1
#define CUT_OFF_GAP 0.8
#define CUT_OFF_MIN 12
#define CUT_OFF_INCREASE 4
/*
#define TIME_FOR_PRICE_IN 5
*/
#define TIME_FOR_PRICE_IN1 2
#define TIME_FOR_PRICE_IN2 4
#define TIME_FOR_PRICE_IN3 6
//#define EMPTY_PUSH_COEF 1.0
/*
#define MAX_CYCLES_CANCELLED 10
#define START_CYCLE_CANCEL 3
*/
#define MAX_CYCLES_CANCELLED 0
#define START_CYCLE_CANCEL 100
/************************************************ shared macros *******/
#define MAX( x, y ) ( ( (x) > (y) ) ? x : y )
#define MIN( x, y ) ( ( (x) < (y) ) ? x : y )
#define OPEN( a ) ( a -> r_cap > 0 )
#define CLOSED( a ) ( a -> r_cap <= 0 )
#define REDUCED_COST( i, j, a ) ( (i->price) + (a->cost) - (j->price) )
#define FEASIBLE( i, j, a ) ( (i->price) + (a->cost) < (j->price) )
#define ADMISSIBLE( i, j, a ) ( OPEN(a) && FEASIBLE( i, j, a ) )
#define INCREASE_FLOW( i, j, a, df )\
{\
(i) -> excess -= df;\
(j) -> excess += df;\
(a) -> r_cap -= df;\
((a) -> sister) -> r_cap += df;\
}\
/*---------------------------------- macros for excess queue */
#define RESET_EXCESS_Q \
{\
for ( ; excq_first != NULL; excq_first = excq_last )\
{\
excq_last = excq_first -> q_next;\
excq_first -> q_next = sentinel_node;\
}\
}
#define OUT_OF_EXCESS_Q( i ) ( i -> q_next == sentinel_node )
#define EMPTY_EXCESS_Q ( excq_first == NULL )
#define NONEMPTY_EXCESS_Q ( excq_first != NULL )
#define INSERT_TO_EXCESS_Q( i )\
{\
if ( NONEMPTY_EXCESS_Q )\
excq_last -> q_next = i;\
else\
excq_first = i;\
\
i -> q_next = NULL;\
excq_last = i;\
}
#define INSERT_TO_FRONT_EXCESS_Q( i )\
{\
if ( EMPTY_EXCESS_Q )\
excq_last = i;\
\
i -> q_next = excq_first;\
excq_first = i;\
}
#define REMOVE_FROM_EXCESS_Q( i )\
{\
i = excq_first;\
excq_first = i -> q_next;\
i -> q_next = sentinel_node;\
}
/*---------------------------------- excess queue as a stack */
#define EMPTY_STACKQ EMPTY_EXCESS_Q
#define NONEMPTY_STACKQ NONEMPTY_EXCESS_Q
#define RESET_STACKQ RESET_EXCESS_Q
#define STACKQ_PUSH( i )\
{\
i -> q_next = excq_first;\
excq_first = i;\
}
#define STACKQ_POP( i ) REMOVE_FROM_EXCESS_Q( i )
/*------------------------------------ macros for buckets */
node dnd, *dnode;
#define RESET_BUCKET( b ) ( b -> p_first ) = dnode;
#define INSERT_TO_BUCKET( i, b )\
{\
i -> b_next = ( b -> p_first );\
( b -> p_first ) -> b_prev = i;\
( b -> p_first ) = i;\
}
#define NONEMPTY_BUCKET( b ) ( ( b -> p_first ) != dnode )
#define GET_FROM_BUCKET( i, b )\
{\
i = ( b -> p_first );\
( b -> p_first ) = i -> b_next;\
}
#define REMOVE_FROM_BUCKET( i, b )\
{\
if ( i == ( b -> p_first ) )\
( b -> p_first ) = i -> b_next;\
else\
{\
( i -> b_prev ) -> b_next = i -> b_next;\
( i -> b_next ) -> b_prev = i -> b_prev;\
}\
}
/*------------------------------------------- misc macros */
#define UPDATE_CUT_OFF \
{\
if (n_bad_pricein + n_bad_relabel == 0) \
{\
cut_off_factor = CUT_OFF_COEF2 * pow ( (double)n, CUT_OFF_POWER2 );\
cut_off_factor = MAX ( cut_off_factor, CUT_OFF_MIN );\
cut_off = cut_off_factor * epsilon;\
cut_on = cut_off * CUT_OFF_GAP;\
}\
else\
{\
cut_off_factor *= CUT_OFF_INCREASE;\
cut_off = cut_off_factor * epsilon;\
cut_on = cut_off * CUT_OFF_GAP;\
}\
}
#define TIME_FOR_UPDATE \
( n_rel > n * UPDT_FREQ + n_src * UPDT_FREQ_S )
#define FOR_ALL_NODES_i for ( i = nodes; i != sentinel_node; i ++ )
#define FOR_CURRENT_ARCS_a_FROM_i \
for ( a = i -> current, a_stop = ( i + 1 ) -> suspended; a != a_stop; a ++ )
#define FOR_ALL_ARCS_a_FROM_i \
for ( a = i -> suspended, a_stop = ( i + 1 ) -> suspended; a != a_stop; a ++ )
#define FOR_ACTIVE_ARCS_a_FROM_i \
for ( a = i -> first, a_stop = ( i + 1 ) -> suspended; a != a_stop; a ++ )
#define WHITE 0
#define GREY 1
#define BLACK 2
arc *sa, *sb;
long d_cap;
#define EXCHANGE( a, b )\
{\
if ( a != b )\
{\
sa = a -> sister;\
sb = b -> sister;\
\
d_arc.r_cap = a -> r_cap;\
d_arc.cost = a -> cost;\
d_arc.head = a -> head;\
\
a -> r_cap = b -> r_cap;\
a -> cost = b -> cost;\
a -> head = b -> head;\
\
b -> r_cap = d_arc.r_cap;\
b -> cost = d_arc.cost;\
b -> head = d_arc.head;\
\
if ( a != sb )\
{\
b -> sister = sa;\
a -> sister = sb;\
sa -> sister = b;\
sb -> sister = a;\
}\
\
d_cap = cap[a-arcs];\
cap[a-arcs] = cap[b-arcs];\
cap[b-arcs] = d_cap;\
}\
}
#define SUSPENDED( i, a ) ( a < i -> first )
long n_push =0,
n_relabel =0,
n_discharge =0,
n_refine =0,
n_update =0,
n_scan =0,
n_prscan =0,
n_prscan1 =0,
n_prscan2 =0,
n_bad_pricein = 0,
n_bad_relabel = 0,
n_prefine =0;
long n, /* number of nodes */
m; /* number of arcs */
long *cap; /* array containig capacities */
node *nodes, /* array of nodes */
*sentinel_node, /* next after last */
*excq_first, /* first node in push-queue */
*excq_last; /* last node in push-queue */
arc *arcs, /* array of arcs */
*sentinel_arc; /* next after last */
bucket *buckets, /* array of buckets */
*l_bucket; /* last bucket */
long linf; /* number of l_bucket + 1 */
int time_for_price_in;
price_t epsilon, /* quality measure */
dn; /* cost multiplier - number of nodes + 1 */
price_t price_min, /* lowest bound for prices */
mmc; /* multiplied maximal cost */
double f_scale, /* scale factor */
cut_off_factor, /* multiplier to produce cut_on and cut_off
from n and epsilon */
cut_on, /* the bound for returning suspended arcs */
cut_off; /* the bound for suspending arcs */
excess_t total_excess; /* total excess */
long n_rel, /* number of relabels from last price update */
n_ref, /* current number of refines */
n_src; /* current number of nodes with excess */
int flag_price = 0, /* if = 1 - signal to start price-in ASAP -
maybe there is infeasibility because of
susoended arcs */
flag_updt = 0; /* if = 1 - update failed some sources are
unreachable: either the problem is
unfeasible or you have to return
suspended arcs */
//long empty_push_bound; /* maximal possible number of zero pushes
// during one discharge */
int snc_max; /* maximal number of cycles cancelled
during price refine */
arc d_arc; /* dummy arc - for technical reasons */
node d_node, /* dummy node - for technical reasons */
*dummy_node; /* the address of d_node */
#ifdef CHECK_SOLUTION
long long int *node_balance;
#endif
/* parser for getting DIMACS format input and transforming the
data to the internal representation */
#include "parser_cs2.c"
/************************************************ abnormal finish **********/
void err_end ( int cc )
{
fprintf ( stderr, "\nError %d\n", cc );
/*
2 - problem is unfeasible
5 - allocation fault
6 - price overflow
*/
exit ( cc );
}
/************************************************* initialization **********/
void cs_init (long n_p, long m_p, node *nodes_p, arc *arcs_p,
long f_sc, price_t max_c, long *cap_p )
{
node *i; /* current node */
arc *a; /* current arc */
arc *a_stop;
long df;
bucket *b; /* current bucket */
n = n_p;
nodes = nodes_p;
sentinel_node = nodes + n;
m = m_p;
arcs = arcs_p;
sentinel_arc = arcs + m;
cap = cap_p;
FOR_ALL_NODES_i
{
i -> price = 0;
i -> suspended = i -> first;
i -> q_next = sentinel_node;
}
sentinel_node -> first = sentinel_node -> suspended = sentinel_arc;
/* saturate negative arcs, e.g. in the circulation problem case */
FOR_ALL_NODES_i
{
FOR_ACTIVE_ARCS_a_FROM_i
{
if (a -> cost < 0)
{
if ( ( df = a -> r_cap ) > 0 )
{
INCREASE_FLOW ( i, a -> head, a, df )
}
}
}
}
f_scale = f_sc;
dn = n+1;
#ifdef NO_ZERO_CYCLES
dn = 2*dn;
#endif
for ( a = arcs ; a != sentinel_arc ; a ++ )
a -> cost *= dn;
#ifdef NO_ZERO_CYCLES
for ( a = arcs ; a != sentinel_arc ; a ++ )
if ((a->cost == 0) && (a->sister->cost == 0)) {
a->cost = 1;
a->sister->cost = -1;
}
#endif
if ((double) max_c * (double) dn > MAX_64)
fprintf(stdin, "Warning: arc lengths too large, overflow possible\n");
mmc = max_c * dn;
linf = (long) (dn * ceil(f_scale) + 2);
buckets = (bucket*) calloc ( linf, sizeof (bucket) );
if ( buckets == NULL )
err_end ( ALLOCATION_FAULT );
l_bucket = buckets + linf;
dnode = &dnd;
for ( b = buckets; b != l_bucket; b ++ )
RESET_BUCKET ( b );
epsilon = mmc;
if ( epsilon < 1 )
epsilon = 1;
price_min = -PRICE_MAX;
cut_off_factor = CUT_OFF_COEF * pow ( (double)n, CUT_OFF_POWER );
cut_off_factor = MAX ( cut_off_factor, CUT_OFF_MIN );
n_ref = 0;
flag_price = 0;
dummy_node = &d_node;
excq_first = NULL;
//empty_push_bound = n * EMPTY_PUSH_COEF;
} /* end of initialization */
/********************************************** up_node_scan *************/
void up_node_scan ( node *i )
{
node *j; /* opposite node */
arc *a, /* ( i, j ) */
*a_stop, /* first arc from the next node */
*ra; /* ( j, i ) */
bucket *b_old, /* old bucket contained j */
*b_new; /* new bucket for j */
long i_rank,
j_rank, /* ranks of nodes */
j_new_rank;
price_t rc, /* reduced cost of (j,i) */
dr; /* rank difference */
n_scan ++;
i_rank = i -> rank;
FOR_ACTIVE_ARCS_a_FROM_i
{
ra = a -> sister;
if ( OPEN ( ra ) )
{
j = a -> head;
j_rank = j -> rank;
if ( j_rank > i_rank )
{
if ( ( rc = REDUCED_COST ( j, i, ra ) ) < 0 )
j_new_rank = i_rank;
else
{
dr = rc / epsilon;
j_new_rank = ( dr < linf ) ? i_rank + (long)dr + 1
: linf;
}
if ( j_rank > j_new_rank )
{
j -> rank = j_new_rank;
j -> current = ra;
if ( j_rank < linf )
{
b_old = buckets + j_rank;
REMOVE_FROM_BUCKET ( j, b_old )
}
b_new = buckets + j_new_rank;
INSERT_TO_BUCKET ( j, b_new )
}
}
}
} /* end of scanning arcs */
i -> price -= i_rank * epsilon;
i -> rank = -1;
}
/*************************************************** price_update *******/
void price_update ()
{
register node *i;
excess_t remain; /* total excess of unscanned nodes with
positive excess */
bucket *b; /* current bucket */
price_t dp; /* amount to be subtracted from prices */
n_update ++;
FOR_ALL_NODES_i
{
if ( i -> excess < 0 )
{
INSERT_TO_BUCKET ( i, buckets );
i -> rank = 0;
}
else
{
i -> rank = linf;
}
}
remain = total_excess;
if ( remain < 0.5 ) return;
/* main loop */
for ( b = buckets; b != l_bucket; b ++ )
{
while ( NONEMPTY_BUCKET ( b ) )
{
GET_FROM_BUCKET ( i, b )
up_node_scan ( i );
if ( i -> excess > 0 )
{
remain -= (i -> excess);
if ( remain <= 0 ) break;
}
} /* end of scanning the bucket */
if ( remain <= 0 ) break;
} /* end of scanning buckets */
if ( remain > 0.5 ) flag_updt = 1;
/* finishup */
/* changing prices for nodes which were not scanned during main loop */
dp = ( b - buckets ) * epsilon;
FOR_ALL_NODES_i
{
if ( i -> rank >= 0 )
{
if ( i -> rank < linf )
REMOVE_FROM_BUCKET ( i, (buckets + i -> rank) );
if ( i -> price > price_min )
i -> price -= dp;
}
}
} /* end of price_update */
/****************************************************** relabel *********/
int relabel ( node *i )
{
register arc *a, /* current arc from i */
*a_stop, /* first arc from the next node */
*a_max; /* arc which provides maximum price */
register price_t p_max, /* current maximal price */
i_price, /* price of node i */
dp; /* current arc partial residual cost */
p_max = price_min;
i_price = i -> price;
a_max = NULL;
for (
a = i -> current + 1, a_stop = ( i + 1 ) -> suspended;
a != a_stop;
a ++
)
{
if ( OPEN ( a )
&&
( ( dp = ( ( a -> head ) -> price ) - ( a -> cost ) ) > p_max )
)
{
if ( i_price < dp )
{
i -> current = a;
return ( 1 );
}
p_max = dp;
a_max = a;
}
} /* 1/2 arcs are scanned */
for (
a = i -> first, a_stop = ( i -> current ) + 1;
a != a_stop;
a ++
)
{
if ( OPEN ( a )
&&
( ( dp = ( ( a -> head ) -> price ) - ( a -> cost ) ) > p_max )
)
{
if ( i_price < dp )
{
i -> current = a;
return ( 1 );
}
p_max = dp;
a_max = a;
}
} /* 2/2 arcs are scanned */
/* finishup */
if ( p_max != price_min )
{
i -> price = p_max - epsilon;
i -> current = a_max;
}
else
{ /* node can't be relabelled */
if ( i -> suspended == i -> first )
{
if ( i -> excess == 0 )
{
i -> price = price_min;
}
else
{
if ( n_ref == 1 )
{
err_end ( UNFEASIBLE );
}
else
{
err_end ( PRICE_OFL );
}
}
}
else /* node can't be relabelled because of suspended arcs */
{
flag_price = 1;
}
}
n_relabel ++;
n_rel ++;
return ( 0 );
} /* end of relabel */
/***************************************************** discharge *********/
void discharge ( node *i )
{
register arc *a; /* an arc from i */
register node *j; /* head of a */
register long df; /* amoumt of flow to be pushed through a */
excess_t j_exc; /* former excess of j */
n_discharge ++;
a = i -> current;
j = a -> head;
if ( !ADMISSIBLE ( i, j, a ) )
{
relabel ( i );
a = i -> current;
j = a -> head;
}
while ( 1 )
{
j_exc = j -> excess;
if ( j_exc >= 0 )
{
df = MIN( i -> excess, a -> r_cap );
if (j_exc == 0) n_src++;
INCREASE_FLOW ( i, j, a, df );
n_push ++;
if ( OUT_OF_EXCESS_Q ( j ) )
{
INSERT_TO_EXCESS_Q ( j );
}
}
else /* j_exc < 0 */
{
df = MIN( i -> excess, a -> r_cap );
INCREASE_FLOW ( i, j, a, df );
n_push ++;
if ( j -> excess >= 0 )
{
if ( j -> excess > 0 )
{
n_src++;
relabel ( j );
INSERT_TO_EXCESS_Q ( j );
}
total_excess += j_exc;
}
else
total_excess -= df;
}
if (i -> excess <= 0)
n_src--;
if ( i -> excess <= 0 || flag_price ) break;
relabel ( i );
a = i -> current;
j = a -> head;
}
i -> current = a;
} /* end of discharge */
/***************************************************** price_in *******/
int price_in ()
{
node *i, /* current node */
*j;
arc *a, /* current arc from i */
*a_stop, /* first arc from the next node */
*b, /* arc to be exchanged with suspended */
*ra, /* opposite to a */
*rb; /* opposite to b */
price_t rc; /* reduced cost */
int n_in_bad, /* number of priced_in arcs with
negative reduced cost */
bad_found; /* if 1 we are at the second scan
if 0 we are at the first scan */
excess_t i_exc, /* excess of i */
df; /* an amount to increase flow */
bad_found = 0;
n_in_bad = 0;
restart:
FOR_ALL_NODES_i
{
for ( a = ( i -> first ) - 1, a_stop = ( i -> suspended ) - 1;
a != a_stop; a -- )
{
rc = REDUCED_COST ( i, a -> head, a );
if ( (rc < 0) && ( a -> r_cap > 0) )
{ /* bad case */
if ( bad_found == 0 )
{
bad_found = 1;
UPDATE_CUT_OFF;
goto restart;
}
df = a -> r_cap;
INCREASE_FLOW ( i, a -> head, a, df );
ra = a -> sister;
j = a -> head;
b = -- ( i -> first );
EXCHANGE ( a, b );
if ( SUSPENDED ( j, ra ) )
{
rb = -- ( j -> first );
EXCHANGE ( ra, rb );
}
n_in_bad ++;
}
else
if ( ( rc < cut_on ) && ( rc > -cut_on ) )
{
i->first--;
b = i -> first;
EXCHANGE ( a, b );
}
}
}
if ( n_in_bad != 0 )
{
n_bad_pricein ++;
/* recalculating excess queue */
total_excess = 0;
n_src=0;
RESET_EXCESS_Q;
FOR_ALL_NODES_i
{
i -> current = i -> first;
i_exc = i -> excess;
if ( i_exc > 0 )
{ /* i is a source */
total_excess += i_exc;
n_src++;
INSERT_TO_EXCESS_Q ( i );
}
}
INSERT_TO_EXCESS_Q ( dummy_node );
}
if (time_for_price_in == TIME_FOR_PRICE_IN2)
time_for_price_in = TIME_FOR_PRICE_IN3;
if (time_for_price_in == TIME_FOR_PRICE_IN1)
time_for_price_in = TIME_FOR_PRICE_IN2;
return ( n_in_bad );
} /* end of price_in */
/************************************************** refine **************/
void refine ()
{
node *i; /* current node */
excess_t i_exc; /* excess of i */
long np, nr, ns; /* variables for additional print */
int pr_in_int; /* current number of updates between price_in */
np = n_push;
nr = n_relabel;
ns = n_scan;
n_refine ++;
n_ref ++;
n_rel = 0;
pr_in_int = 0;
/* initialize */
total_excess = 0;
n_src=0;
RESET_EXCESS_Q
time_for_price_in = TIME_FOR_PRICE_IN1;
FOR_ALL_NODES_i
{
i -> current = i -> first;
i_exc = i -> excess;
if ( i_exc > 0 )
{ /* i is a source */
total_excess += i_exc;
n_src++;
INSERT_TO_EXCESS_Q ( i )
}
}
if ( total_excess <= 0 ) return;
/* main loop */
while ( 1 )
{
if ( EMPTY_EXCESS_Q )
{
if ( n_ref > PRICE_OUT_START )
{
pr_in_int = 0;
price_in ();
}
if ( EMPTY_EXCESS_Q ) break;
}
REMOVE_FROM_EXCESS_Q ( i );
/* push all excess out of i */
if ( i -> excess > 0 )
{
discharge ( i );
if ( TIME_FOR_UPDATE || flag_price )
{
if ( i -> excess > 0 )
{
INSERT_TO_EXCESS_Q ( i );
}
if ( flag_price && ( n_ref > PRICE_OUT_START ) )
{
pr_in_int = 0;
price_in ();
flag_price = 0;
}
price_update();
while ( flag_updt )
{
if ( n_ref == 1 )
{
err_end ( UNFEASIBLE );
}
else
{
flag_updt = 0;
UPDATE_CUT_OFF;
n_bad_relabel++;
pr_in_int = 0;
price_in ();
price_update ();
}
}
n_rel = 0;
if ( n_ref > PRICE_OUT_START &&
(pr_in_int ++ > time_for_price_in)
)
{
pr_in_int = 0;
price_in ();
}
} /* time for update */
}
} /* end of main loop */
return;
} /*----- end of refine */