SOC-Observation-Code/src/SOCgen.c
2024-11-15 11:41:45 +01:00

623 lines
23 KiB
C

// SPDX-FileCopyrightText: 2023 Ämin Baumeler <amin@indyfac.ch> and
// Eleftherios-Ermis Tselentis <eleftheriosermis.tselentis@oeaw.ac.at>
//
// SPDX-License-Identifier: GPL-3.0-or-later
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>
/***
* Print the graph's adjacency matrix
***/
void dumpgraph(int n, const int *children, const int *childrenlen) {
int adj[n*n];
for (int i = 0; i < n*n; i++) adj[i] = 0;
for (int a = 0; a < n; a++) {
for (int bidx = 0; bidx < childrenlen[a]; bidx++) {
const int b = children[a*n+bidx];
adj[a*n+b] = 1;
}
}
// Print
printf("{");
for (int a = 0; a < n; a++) {
if (a) printf(",");
printf("{");
printf("%d", adj[a*n+0]);
for (int b = 1; b < n; b++) printf(",%d", adj[a*n+b]);
printf("}");
}
printf("}\n");
}
/***
* Print the graph as graphviz command
***/
void dumpgv(int n, int graphnr, const int *children, const int *childrenlen) {
printf("strict digraph G%d {node[shape=point];", graphnr);
for (int v = 0; v < n; v++) {
for (int i = 0; i < childrenlen[v]; i++) {
const int w = children[v*n+i];
printf("G%dN%d -> G%dN%d", graphnr, v, graphnr, w);
if (childrenlen[v] >= 2)
printf(" [color=\"red\"]");
printf(";");
}
}
printf("}\n");
return;
}
/***
* Block size of our datastructure.
***/
int blocksize(int n) {
int res = (n+1)*n;
for (int i = 0; i < n; i++)
res *= n-i;
return res;
}
/***
* Recrusive bi-directional graph traversal, used to check connectivity.
***/
void traverse(int vertex, int *visited, int n, const int *parents, \
const int *parentslen, const int *children, const int *childrenlen) {
visited[vertex] = 1;
for (int i = 0; i < parentslen[vertex]; i++) {
int u = parents[n*vertex + i];
if (visited[u] == 0)
traverse(u, visited, n, parents, parentslen, children, childrenlen);
}
for (int i = 0; i < childrenlen[vertex]; i++) {
int u = children[n*vertex + i];
if (visited[u] == 0)
traverse(u, visited, n, parents, parentslen, children, childrenlen);
}
}
/***
* Return 1 if the graph is connected, and 0 otherwise.
***/
int isconnected(int n, const int *parents, const int *parentslen, \
const int *children, const int *childrenlen) {
// Early check: Is there a node with 0 total degree?
for (int i = 0; i < n; i++) if (parentslen[i]+childrenlen[i] == 0) return 0;
// Check connectivity
int visited[n];
for (int i = 0; i < n; i++) visited[i] = 0;
// Start traversal
traverse(0, visited, n, parents, parentslen, children, childrenlen);
for (int i = 0; i < n; i++) if (!visited[i]) return 0;
return 1;
}
/***
* Interpret graph number `graph' as a simple digraph, and populate the arrays `parents', `parentslen', `children', `childrenlen'
* The number `graph' is understood as the adjacency matrix with the diagonal removed (no self loops).
***/
void graphnrtolists(int n, unsigned long long int graph, int *parents, \
int *parentslen, int *children, int *childrenlen) {
for (int i = 0; i < n; i++) {
parentslen[i] = 0;
childrenlen[i] = 0;
}
int row = 0;
int col = 1; // We cannot start at (0,0); it does not exist
unsigned long long g = graph;
for (int i = 0; i < n*(n-1); i++) {
int val = g%2;
g = g/2;
if (val) {
children[row*n+childrenlen[row]] = col;
childrenlen[row]++;
parents[col*n+parentslen[col]] = row;
parentslen[col]++;
}
col++;
if (col == row)
col++;
if (col == n) {
col = 0;
row++;
}
}
}
/***
* Find the tail in `path' of length `pathlen' that includes a cycle, and save the canonical representation.
* The canonical representation is the listing of the nodes of the cycle starting from the smallest one.
***/
void canonical_cycle(int n, int *cycle, int *cyclelen, const int *path, \
int pathlen) {
int startidx;
int pathhascycle = 0;
const int last = path[pathlen-1]; // This is the last node
for (int k = 0; k < pathlen-1; k++) {
if (path[k] == last) {
// We have found the first occurance of node `last' on the path
// The cycle is the following part of path: path[startidx],
// path[startidx+1], ..., path[pathlen-2], and therefore has
// length pathlen-startidx-1
startidx = k;
(*cyclelen) = pathlen-startidx-1;
pathhascycle = 1;
break;
}
}
if (!pathhascycle) { // Sanity check. This should NEVER happen!
fprintf(stderr, "ERROR: You provided a path to `canonical_cycle' that does NOT contain a cycle as its tail! I'm returning now.\n");
return;
}
// Generate canonical representation
// First, find smallest node on cycle
int smallestidx = -1;
int smallest = n;
for (int k = startidx; k < pathlen-1; k++) {
if (smallest > path[k]) {
smallest = path[k];
smallestidx = k;
}
}
// Now, copy cycle to `cycle' starting from the smallest
// This is the index on where to write on the array `cycle'
int j = 0;
for (int i = smallestidx;; i++) {
// Stop filling in, if we reached the end
if (j == *cyclelen) break;
// If we reach the end of the path, jump to the start
if (i == pathlen-1) i = startidx;
// Write at position `j' the element from the cycle on the path at
// position `i`'
cycle[j] = path[i];
// Increase index to write on `cycle'
j++;
}
}
/***
* Return 1 if the cycle is not in `cycles', otherwise 0.
***/
int cycleisnew(int n, const int *c, int clen, const int *cycles, \
const int *cyclescnt) {
const int cnt = cyclescnt[clen];
const int bs = blocksize(n);
// Iterate over all cycles of the same length
for (int i = 0; i < cnt; i++) {
int j;
const int startidx = clen*bs + i*clen; // We start here
for (j = 0; j < clen; j++) // Go position by position
if (cycles[startidx+j] != c[j])
break; // They differ at position j
if (j == clen) // We didn't break
return 0;
}
return 1;
}
/***
* Save the given cycle `c' of length `clen' in `cycles'.
***/
void savecycle(int n, const int *c, int clen, int *cycles, int *cyclescnt) {
const int m = cyclescnt[clen]; // There are `m' `clen'-cycles
const int bs = blocksize(n);
const int startidx = clen*bs + m*clen; // We start writing here
for (int i = 0; i < clen; i++) cycles[startidx+i] = c[i];
cyclescnt[clen]++; // Increase the counter that holds
// the number of `clen'-cycles
}
/***
* Recursive depth-first-search to find cycles in the graph specified by `children' and `childrenlen'.
* The cycles are stored in `cycles' and `cyclescnt'.
* Parameter `useless': n-array where useless nodes are marked
* Parameter `path': Array of nodes that represent a path on the graph
* Parameter `pathlen': Lenght of `path'
* Parameter `visited': n-array to mark visited nodes
* Parameter `n': Number of nodes
* Parameter `found': Pointer to integer to count the number of cycles found
***/
void dfs(const int *useless, int *path, int pathlen, int *visited, int n, \
const int *children, const int *childrenlen, int *cycles, int *cyclescnt, \
unsigned int *found) {
int cycle[n]; // Temporary store for cycle
int cyclelen; // Length of temporarilly stored cycle
// We go on duing a dfs from node `vertex'
const int vertex = path[pathlen-1];
for (int i = 0; i < childrenlen[vertex]; i++) {
const int u = children[n*vertex + i]; // Enter node `u'
if (useless[u]) continue; // This one is useless
if (visited[u] == 0) { // Not visited yet
visited[u] = 1; // Mark as visited
path[pathlen] = u; // Append to path, and re-enter
// recursion...
dfs(useless, path, pathlen+1, visited, n, children, childrenlen, cycles, \
cyclescnt, found);
visited[u] = 0; // Undo marking, we are going to
// take another route
} else {
// We have reached a node on the path, i.e., we have found a cycle!
// The cycle is somewhere along the path
// path[0], path[1], ... path[pathlen-1]
// More specifically, node `u' is somewhere there.
// To detect this, we first place `u' on the path.
// The method `canonical_cycle' will then use this information to find
// and return the canonical form of the cycle.
path[pathlen] = u;
// Find cycle and generate the canonical representation.
canonical_cycle(n, cycle, &cyclelen, path, pathlen+1);
// Is it new? If yes, save
if (cycleisnew(n, cycle, cyclelen, cycles, cyclescnt)) {
// Increase the number of found cycles by 1
(*found)++;
// Save cycle
savecycle(n, cycle, cyclelen, cycles, cyclescnt);
}
// else dont do anything...
}
}
return;
}
/***
* Find cycles in the `n'-nodes graph specified by the arrays `children' and `childrenlen', and return the number of cycles found.
* The cycles are stored in `cycles' and `cyclescnt'.
* This uses a recursive depth-first-search.
***/
int find_cycles(int *cycles, int *cyclescnt, int n, const int *children, \
const int *childrenlen) {
int visited[n];
// Some nodes are useless, mark them as such
int useless[n];
// We use n+1 here because we will "close" the path to form a cycle,
// i.e., one node will be repeated.
int path[n+1];
unsigned int found = 0; // Store total number of cycles found
// Initialize cyclescnt to zero
for (int i = 0; i < n+1; i++)
cyclescnt[i] = 0;
// Mark nodes without children as useless
for (int i = 0; i < n; i++) {
useless[i] = (childrenlen[i] == 0) ? 1 : 0;
}
// Iterate over nodes
for (int vertex = 0; vertex < n; vertex++) {
if (useless[vertex]) continue;
for (int i = 0; i < n; i++) visited[i] = 0; // Mark all as univisited
// We start at `vertex'
path[0] = vertex;
// Mark `vertex' as visited. If we revisit a node, we found a cycle.
visited[vertex] = 1;
// Enter depth-first-search recursion
dfs(useless, path, 1, visited, n, children, childrenlen, cycles, \
cyclescnt, &found);
// We processed this. Every cycle that goes through `vertex' has been found.
useless[vertex] = 1;
}
return found;
}
/***
* gissoc tests wheter the graph provided is a SOC or not.
* Parameter `n': Number of nodes
* Parameter `parents': Pointer to list of parents per node
* Parameter `parentslen': Pointer to list of number of parents per node
* Parameter `children': Pointer to list of children per node
* Parameter `childrenlen': Pointer to list of number of children per node
* Parameter `cycles': Pointer to list of cycles in the graph
* Parameter `cyclescnt': Pointer to list of cycles count
*
* This function retruns 0 if the graph is NOT a SOC, and 1 otherwise.
*
* A SOC (Siblings-on-Cycles) is a simple digraph where every cycle has siblings, i.e., nodes with common parents.
***/
int gissoc(int n, const int *parents, const int *parentslen, \
const int *children, const int *childrenlen, int *cycles, int *cyclescnt) {
// We store the cycles in groups of the cycle lenghts (length of cycle is the
// number of edges, or equivalentelly, the number of distinct nodes)
// Since the graph is a simple digraph, the smallest cycles have length 2.
// cycles[0], cycles[1] is the first cycle of length 2
// cycles[2], cycles[3] is the second cycle of length 2
// etc.
// There are at most (n choose 2) cycles of length 2.
// There are at most (n choose n/2) cycles of length n/2. This is upper
// bounded by 2^n/sqrt(pi*n/2) < 2^n; this is the largest binomial
// coefficient.
// Since generally n will be small, we just use this bound for all groups.
// So, the cycles with length k are saved at and after cycles[k*(2^n)].
// Each block has size 2^n.
/* Early and saftey check for self loops. SOCs dont have self-loops, and we
* should never generate them. Anyhow, test */
for (int i = 0; i < n; i++) {
int num = childrenlen[i];
for (int cidx = 0; cidx < num; cidx++)
if (i == children[n*i+cidx]) {
fprintf(stderr, "ERROR: THIS GRAPH HAS A SELF LOOP (node %d)\n", i);
return 0;
}
}
// Check SOC property
const int bs = blocksize(n);
// Iterate over cycle length; min length is 2, max length is n
// then iterate over cycle of length `len'
// then iterate over nodes of that cycle.
// In that iteration process, mark all parents.
// If a marked parent is marked again, we have found a common parent.
for (int len = 2; len < n+1; len++) {
// Number of cycles of length `len'
const int cnt = cyclescnt[len];
// Iterate over cycles
for (int i = 0; i < cnt; i++) {
// The cycle we look at (length=`len', index=`i') is saved starting from
// index `startidx'
const int startidx = len*bs+len*i;
// Initialize marks
int marked[n];
for (int k = 0; k < n; k++) marked[k] = 0;
// Flag: Have we found a common parent?
int commonparentfound = 0;
// Iterate over cycle
for (int k = 0; k < len; k++) {
const int vertex = cycles[startidx+k];
for (int pidx = 0; pidx < parentslen[vertex]; pidx++) {
const int parent = parents[n*vertex+pidx];
// Check if `parent' is a common parent, else mark
if (marked[parent])
commonparentfound = 1;
else
marked[parent] = 1;
// We have found a common parent, break out of the `pidx' loop
if (commonparentfound) break;
}
// We have found a common parent, break out of the for loop over `k'
if (commonparentfound) break;
}
// On cycle `i' we did NOT find a common parent, this is not a SOC
if (!commonparentfound)
return 0;
}
}
// If all test pass, we have found a SOC
return 1;
}
/***
* Number of grandparents, and number of grandchildren
***/
int grandparentslen(int node, const int *parents, const int *parentslen) {
int tot = 0;
for (int i = 0; i < parentslen[node]; i++)
tot += parentslen[i];
return tot;
}
int grandchildrenlen(int node, const int *children, const int *childrenlen) {
int tot = 0;
for (int i = 0; i < childrenlen[node]; i++)
tot += childrenlen[i];
return tot;
}
/***
* Speed-up by ignoring all graphs that do not satisfy some ordering of out- and in-degrees.
* If the graph does not satisfy this `canonical' form, then another ismorphic to it (it's simply a permutation of the nodes)
* will be degree-ordered.
***/
int isdegreeordered(int n, const int *parents, const int *parentslen, \
const int *children, const int *childrenlen) {
// Decreasingling order by in-degree, then out-degree, then ...
for (int i = 0; i < n-1; i++) {
if (parentslen[i] > parentslen[i+1]) {
return 0;
} else if (parentslen[i] == parentslen[i+1]) {
if (childrenlen[i] > childrenlen[i+1]) {
return 0;
} else if (childrenlen[i] == childrenlen[i+1]) {
if (grandparentslen(i, parents, parentslen) > \
grandparentslen(i+1, parents, parentslen)) {
return 0;
} else if (grandparentslen(i, parents, parentslen) == \
grandparentslen(i+1, parents, parentslen)) {
if (grandchildrenlen(i, children, childrenlen) > \
grandchildrenlen(i+1, children, childrenlen)) {
return 0;
}
}
}
}
}
return 1;
}
/* Random nubers */
#if RAND_MAX/256 >= 0xFFFFFFFFFFFFFF
#define LOOP_COUNT 1
#elif RAND_MAX/256 >= 0xFFFFFF
#define LOOP_COUNT 2
#elif RAND_MAX/256 >= 0x3FFFF
#define LOOP_COUNT 3
#elif RAND_MAX/256 >= 0x1FF
#define LOOP_COUNT 4
#else
#define LOOP_COUNT 5
#endif
u_int64_t rand_uint64(unsigned long long max) {
u_int64_t r = 0;
for (int i=LOOP_COUNT; i > 0; i--) {
r = r*(RAND_MAX + (u_int64_t)1) + rand();
}
return r%max;
}
/* End of random numbers */
int main(int argc, char *argv[]) {
// Parse command-line arguments
int n = -1;
int NONDAGONLY = 0;
int NOSINK = 0;
int NOSOURCE = 0;
int RANDOM = 0;
int GRAPHVIZ = 0;
int UNKOPTION = 0;
int ALL = 0;
for (int i = 1; i < argc; i++) {
if (strcmp(argv[i], "-n") == 0 && i+1 < argc) {
n = atoi(argv[i+1]);
i++;
} else if (strcmp(argv[i], "-r") == 0 && i+1 < argc) {
RANDOM = atoi(argv[i+1]);
i++;
} else if (strcmp(argv[i], "-c") == 0) {
NONDAGONLY = 1;
} else if (strcmp(argv[i], "--no-sink") == 0) {
NOSINK = 1;
} else if (strcmp(argv[i], "--no-source") == 0) {
NOSOURCE = 1;
} else if (strcmp(argv[i], "--graphviz") == 0) {
GRAPHVIZ = 1;
} else if (strcmp(argv[i], "--all") == 0) {
ALL = 1;
} else {
UNKOPTION = 1;
break;
}
}
if (UNKOPTION || n <= 1) {
fprintf(stderr, "Usage: %s -n <order> [-r <num>] [--graphviz] [FILTER ...]\n", argv[0]);
fprintf(stderr, " -n <order> Generate SOCs with `order' connected nodes\n");
fprintf(stderr, " -r <num> Pick directed graphs at random, and exit after having found `num' SOCs\n");
fprintf(stderr, " --graphviz Output SOCs in Graphviz format, arcs of common parents are highlighted\n");
fprintf(stderr, " --all Allow for disconnected SOCs and disable the degree-order filter (see below)\n");
fprintf(stderr, "\n");
fprintf(stderr, "[FILTER] Consider only simple directed graphs ...\n");
fprintf(stderr, " -c ... that are cyclic (i.e., not DAGs)\n");
fprintf(stderr, " --no-sink ... without sink nodes (this logically implies -c)\n");
fprintf(stderr, " --no-source ... without source nodes (also this logically implies -c)\n");
fprintf(stderr, "\n");
fprintf(stderr, "This program prints the found SOCs as adjacency matrices to stdout, unless --graphviz has been specified.\n");
fprintf(stderr, "To exclude (some) of the isomorphic SOCs, it uses a degree-order filter, unless --all is specified.\n");
return -1;
}
// EO Parse command-line arguments
// Setup datastructures
int parents[n*n]; // Each node i can have at most n-1 parents. These are listed at parents[n*i+k] for 0<=k<n
int parentslen[n]; // Number of parents of node i is stored in parentslen[i]
int children[n*n]; // Each node i can have at most n-1 children. These are listed at parents[n*i+k] for 0<=k<n
int childrenlen[n]; // Number of children of node i is stored in childrenlen[i]
const int bs = blocksize(n);
int *cycles = (int*)malloc(sizeof(int)*(n+2)*bs);
if (!cycles) {
fprintf(stderr, "Failed to allocate memory to store cycles (tried to allocate %lu bytes)\n", \
sizeof(int)*(n+2)*bs);
return -1;
}
int cyclescnt[n+1]; // cyclescnt[k] stores the number of cycles with length k
// EO Setup datastructures
// Initiate graph enumeration
const int m = n*(n-1);
if (m > 64) {
fprintf(stderr, "Too many graphs to enumarate with an unsiged long long integer (number of node pairs = %d)\n", \
m);
return -1;
}
unsigned long long max = 1L << m; // Largest `graphnumber'
const int padlen = (int)((float)m/3.322)+1; // Convert log 2 to log 10
int len = 0;
time_t t0 = time(NULL);
time_t t = time(NULL);
srand((unsigned) time(&t));
// EO Initiate graph enumeration
fprintf(stderr, "Generating SOCs with %d nodes\n", n);
if (RANDOM)
fprintf(stderr, " Picking graphs at random\n");
if (NONDAGONLY)
fprintf(stderr, " Filter: Omitting DAGs\n");
if (NOSINK)
fprintf(stderr, " Filter: Omitting graphs with sink nodes\n");
if (NOSOURCE)
fprintf(stderr, " Filter: Omitting graphs with source nodes\n");
// We will always omit the graph with `graphnumber' 0;
// it is unintersting anyway
unsigned long long graphnumber = 0;
unsigned long long graphschecked = 0;
for (; graphnumber < max && (!RANDOM || len < RANDOM);) {
const time_t now = time(NULL);
// Print status every second
if (now > t) {
t = now;
const int deltat = now - t0;
const float rate = (float)graphschecked/(float)deltat;
const float SOCrate = (float)len/(float)deltat;
const float percentage = (RANDOM == 0) ? \
100*(float)graphnumber/(float)max : 100*(float)len/(float)RANDOM;
const float ETC = (RANDOM == 0) ? \
((float)(max - graphschecked)/(rate))/3600 : \
((float)(RANDOM - len)/(SOCrate))/3600;
fprintf(stderr, "\r%6.2f%% %*llu/%llu (%i SOCs found, %d seconds, %*.2f graphs/s, %*.2f SOCs/s, %*.2fh estimated time left)", \
percentage, padlen, graphnumber, max, len, deltat, padlen+3, rate, \
padlen+3, SOCrate, padlen, ETC);
fflush(stderr);
}
// Convert graph index `graphnumber' to the lists parents, children,
// parentslen, childrenlen
graphnrtolists(n, graphnumber, parents, parentslen, children, childrenlen);
// Increase checked counter and prepare for next iteration
graphschecked++;
if (RANDOM)
graphnumber = rand_uint64(max);
else
graphnumber++;
// EO Increase checked counter and prepare for next iteration
// If enabled, compare against degree options
if (NOSINK || NOSOURCE) {
// Get some degree properties
int minindegree = n;
int minoutdegree = n;
for (int node = 0; node < n; node++) {
if (minindegree > parentslen[node])
minindegree = parentslen[node];
if (minoutdegree > childrenlen[node])
minoutdegree = childrenlen[node];
}
if (NOSINK && minoutdegree == 0) continue;
if (NOSOURCE && minindegree == 0) continue;
}
// Check whether this graph is canonical or not; continue if graph has not
// proper ordering of degress (there is an isomorphic graphs to this one
// that has been or will be checked)
if (!ALL && !isdegreeordered(n, parents, parentslen, children, childrenlen))
continue;
// Ignore graphs that are not connected
if (!ALL && !isconnected(n, parents, parentslen, children, childrenlen))
continue;
// Find cycles
const int num_cycles = find_cycles(cycles, cyclescnt, n, children, \
childrenlen);
// If enabled, ignore DAGs
if (NONDAGONLY && num_cycles == 0) continue;
// Test the Siblings-On-Cycles property
// A DAG is trivially a SOC
if (num_cycles > 0 && !gissoc(n, parents, parentslen, children, \
childrenlen, cycles, cyclescnt)) continue;
// We have found a SOC
len++;
if (GRAPHVIZ)
dumpgv(n, graphnumber, children, childrenlen);
else
dumpgraph(n, children, childrenlen);
}
const int deltat = time(NULL) - t0;
const float rate = (deltat == 0) ? graphschecked : \
(float)graphschecked/(float)deltat;
const float SOCrate = (deltat == 0) ? len : (float)len/(float)deltat;
fprintf(stderr, "\r%6.2f%% %*llu/%llu (%i SOCs found, %d seconds, %*.2f graphs/s, %*.2f SOCs/s, %*.2fh estimated time left)", \
100.00, padlen, graphnumber, max, len, deltat, padlen+3, rate, padlen+3, \
SOCrate, padlen, 0.00);
fprintf(stderr, "\nFound %d SOCs in %d seconds\n", len, deltat);
// Free manually allocated memory
free(cycles);
return 0;
}