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/**
* @file
* @brief
* [transitive reduction](https://en.wikipedia.org/wiki/Transitive_reduction)
* filter for directed graphs, API: cgraph.h,
* implements @ref graphviz_tred,
* used in cmd/tools/tred.c
*
* @ingroup cgraph_app
*/
/*
* Copyright (c) 2011 AT&T Intellectual Property
* All rights reserved. This program and the accompanying materials
* are made available under the terms of the Eclipse Public License v1.0
* which accompanies this distribution, and is available at
* https://www.eclipse.org/legal/epl-v10.html
*
* Authors: Stephen North, Emden Gansner
* Contributors: Details at https://graphviz.org
*/
#include <cgraph/cghdr.h>
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>
#include <util/alloc.h>
#include <util/list.h>
typedef struct {
bool on_stack : 1;
unsigned char dist;
} nodeinfo_t;
#define ON_STACK(ninfo, n) (ninfo[AGSEQ(n)].on_stack)
#define DISTANCE(ninfo, n) (ninfo[AGSEQ(n)].dist)
#define agrootof(n) ((n)->root)
static unsigned char uchar_min(unsigned char a, unsigned char b) {
if (a < b)
return a;
return b;
}
typedef LIST(Agedge_t *) edge_stack_t;
static void push(edge_stack_t *sp, Agedge_t *ep, nodeinfo_t *ninfo) {
// mark this edge on the stack
ON_STACK(ninfo, aghead(ep)) = true;
// insert the new edge
LIST_PUSH_BACK(sp, ep);
}
static Agedge_t *pop(edge_stack_t *sp, nodeinfo_t *ninfo) {
if (LIST_IS_EMPTY(sp)) {
return NULL;
}
// remove the top
Agedge_t *e = LIST_POP_BACK(sp);
// mark it as no longer on the stack
ON_STACK(ninfo, aghead(e)) = false;
return e;
}
static Agedge_t *top(edge_stack_t *sp) {
if (LIST_IS_EMPTY(sp)) {
return NULL;
}
return *LIST_BACK(sp);
}
/* Main function for transitive reduction.
* This does a DFS starting at node n. Each node records the length of
* its largest simple path from n. We only care if the length is > 1. Node
* n will have distance 0; outneighbors of n will have distance 1 or 2; all
* others will have distance 2.
*
* During the DFS, we only push edges on the stack whose head has distance 0
* (i.e., hasn't been visited yet), setting its distance to the distance of the
* tail node plus one. If we find a head node with distance 1, we don't push the
* edge, since it has already been in a DFS, but we update its distance. We also
* check for back edges and report these.
*
* After the DFS, we check all outedges of n. Those edges whose head has
* distance 2 we delete. We also delete all but one copy of any edges with the
* same head.
*/
static int dfs(Agnode_t *n, nodeinfo_t *ninfo, int warn,
const graphviz_tred_options_t *opts) {
Agraph_t *g = agrootof(n);
Agedgepair_t dummy;
Agedge_t *link;
Agedge_t *next;
Agedge_t *prev;
Agedge_t *e;
Agedge_t *f;
Agnode_t *v;
Agnode_t *hd;
Agnode_t *oldhd;
int do_delete;
dummy.out.base.tag.objtype = AGOUTEDGE;
dummy.out.node = n;
dummy.in.base.tag.objtype = AGINEDGE;
dummy.in.node = NULL;
edge_stack_t estk = {0};
push(&estk, &dummy.out, ninfo);
prev = 0;
while ((link = top(&estk))) {
v = aghead(link);
if (prev)
next = agnxtout(g, prev);
else
next = agfstout(g, v);
for (; next; next = agnxtout(g, next)) {
hd = aghead(next);
if (hd == v)
continue; // Skip a loop
if (ON_STACK(ninfo, hd)) {
if (!warn) {
warn++;
if (opts->err != NULL) {
fprintf(
opts->err,
"warning: %s has cycle(s), transitive reduction not unique\n",
agnameof(g));
fprintf(opts->err, "cycle involves edge %s -> %s\n", agnameof(v),
agnameof(hd));
}
}
} else if (DISTANCE(ninfo, hd) == 0) {
DISTANCE(ninfo, hd) = uchar_min(1, DISTANCE(ninfo, v)) + 1;
break;
} else if (DISTANCE(ninfo, hd) == 1) {
DISTANCE(ninfo, hd) = uchar_min(1, DISTANCE(ninfo, v)) + 1;
}
}
if (next) {
push(&estk, next, ninfo);
prev = 0;
} else {
prev = pop(&estk, ninfo);
}
}
oldhd = NULL;
for (e = agfstout(g, n); e; e = f) {
do_delete = 0;
f = agnxtout(g, e);
hd = aghead(e);
if (oldhd == hd)
do_delete = 1;
else {
oldhd = hd;
if (DISTANCE(ninfo, hd) > 1)
do_delete = 1;
}
if (do_delete) {
if (opts->PrintRemovedEdges && opts->err != NULL)
fprintf(opts->err, "removed edge: %s: \"%s\" -> \"%s\"\n", agnameof(g),
agnameof(aghead(e)), agnameof(agtail(e)));
agdelete(g, e);
}
}
LIST_FREE(&estk);
return warn;
}
/* Do a DFS for each vertex in graph g, so the time
* complexity is O(|V||E|).
*/
void graphviz_tred(Agraph_t *g, const graphviz_tred_options_t *opts) {
Agnode_t *n;
int cnt = 0;
int warn = 0;
time_t secs;
time_t total_secs = 0;
nodeinfo_t *ninfo;
size_t infosize;
infosize = (agnnodes(g) + 1) * sizeof(nodeinfo_t);
ninfo = gv_alloc(infosize);
if (opts->Verbose && opts->err != NULL)
fprintf(stderr, "Processing graph %s\n", agnameof(g));
for (n = agfstnode(g); n; n = agnxtnode(g, n)) {
memset(ninfo, 0, infosize);
const time_t start = time(NULL);
warn = dfs(n, ninfo, warn, opts);
if (opts->Verbose) {
secs = time(NULL) - start;
total_secs += secs;
cnt++;
if (cnt % 1000 == 0 && opts->err != NULL) {
fprintf(opts->err, "[%d]\n", cnt);
}
}
}
if (opts->Verbose && opts->err != NULL)
fprintf(opts->err, "Finished graph %s: %lld.00 secs.\n", agnameof(g),
(long long)total_secs);
free(ninfo);
agwrite(g, opts->out);
fflush(opts->out);
}
/**
* @defgroup cgraph_app app
* @brief uncoupled application specific functions
* @ingroup cgraph
*/
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