SOC-Observation-Code/SOCgen.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");
}

/***
 * 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 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
	int j=0;                                        // This is the index on where to write on the array `cycle'
	for(int i=smallestidx;; i++) {
		if(j==*cyclelen) break;                 // Stop filling in, if we reached the end
		if(i==pathlen-1) i = startidx;          // If we reach the end of the path, jump to the start
		cycle[j] = path[i];                     // Write at position `j' the element from the cycle on the path at position `i`'
		j++;                                    // Increase index to write on `cycle'
	}
}

/***
 * 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);
	for(int i=0; i<cnt; i++) {                      // Iterate over all cycles of the same length
		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 already `m' cycles of length `clen'
	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 cycles of length `clen'
}


/***
 * 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
	const int vertex = path[pathlen-1];     // We go on duing a dfs from node `vertex'
	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;
			canonical_cycle(n, cycle, &cyclelen, path, pathlen+1);          // Find cycle and generate the canonical representation.
			if(cycleisnew(n, cycle, cyclelen, cycles, cyclescnt)) {         // Is it new? If yes, save
				(*found)++;                                             // Increase the number of found cycles by 1
				savecycle(n, cycle, cyclelen, cycles, cyclescnt);       // Save cycle
			}
			// 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];
	int useless[n];                 // Some nodes are useless, mark them as such
	int path[n+1];                  // We use n+1 here because we will "close" the path to form a cycle, i.e., one node will be repeated.
	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
		path[0] = vertex;                       // We start at `vertex'
		visited[vertex] = 1;                    // Mark `vertex' as visited. If we revisit a node, we found a cycle.
		// 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++) {
		const int cnt = cyclescnt[len];             // Number of cycles of length `len'
		for(int i=0; i<cnt; i++) {                  // Iterate over cycles
			const int startidx = len*bs+len*i;  // The cycle we look at (length=`len', index=`i') is saved starting from index `startidx'
			// 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];
					if(marked[parent]) commonparentfound = 1;    // The node `parent' is a common parent
					else marked[parent] = 1;                     // Mark the parent node
					if(commonparentfound) break;                 // We have found a common parent, break out of the for loop over `pidx'
				}
				if(commonparentfound) break;                         // We have found a common parent, break out of the for loop over `k'
			}
			if(!commonparentfound)                          // On cycle `i' we did NOT find a common parent, this is not a SOC
				return 0;
		}
	}
	return 1;                                                       // If all test pass, we have found a SOC
}

/***
 * 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 UNKOPTION = 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 {
			UNKOPTION = 1;
			break;
		}
	}
	if(UNKOPTION || n<=1) {
		fprintf(stderr, "Usage: %s -n <order> [-r <num> ] [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, "\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.\n");
		fprintf(stderr, "To exclude (some) of the isomorphic SOCs, it uses a degree-order filter.\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;
	}
	const unsigned long long max = 1L << m;		// Largest `graphnumber'
	const int padlen = (int)((float)m/3.322)+1;
	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");
	unsigned long long graphnumber = 0;	// We will always omit the graph with `graphnumber' 0; it is unintersting anyway
	unsigned long long graphschecked = 0;
	for(;graphnumber < max && (!RANDOM || len < RANDOM);) {
		const time_t now = time(NULL);
		// Break if we exhaustively check all graphs or if we found enough SOCs at random
		//if(graphnumber >= max || (RANDOM && len >= RANDOM))
		//	break;
		// Print status every second
		if(now > t) {
			t = now;
			const int deltat = now - t0;
			const float rate = (float)graphschecked/(float)deltat;
			const float percentage = (RANDOM==0) ? 100*(float)graphnumber/(float)max : (float)len/(float)RANDOM;
			fprintf(stderr, "\r%6.2f%%    %*llu/%llu (found=%i at rate %*.2f graphs/s in %d seconds)",percentage,padlen,graphnumber,max,len,padlen+3,rate,deltat);
			fflush(stderr);
		}
		// Convert graph index `grpahnumber' 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(!isdegreeordered(n, parents, parentslen, children, childrenlen)) continue;
		// Ignore graphs that are not connected
		if(!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++;
		dumpgraph(n, children, childrenlen);
	}
	const int deltat = time(NULL) - t0;
	const float rate = (deltat == 0) ? graphschecked : (float)graphschecked/(float)deltat;
	//fprintf(stderr, "\r100%%    %llu/%llu                                                                                                       ", max,max);
	fprintf(stderr, "\r%6.2f%%    %*llu/%llu (found=%i at rate %*.2f graphs/s in %d seconds)",100.00,padlen,graphnumber,max,len,padlen+3,rate,deltat);
	fprintf(stderr, "\nFound %d SOCs at rate %.2f graphs/s in %d seconds\n", len,rate,deltat);
	// Free manually allocated memory
	free(cycles);
	return 0;
}