Previously graph layout was done using the Kamada-Kawai layout algorithm

implemented in Boost.  I am replacing this with a custom implementation of
a constrained stress-majorization algorithm.

The stress-majorization algorithm is more robust and has better convergence
characteristics than Kamada-Kawai, and also simple constraints can be placed
on node position (for example, to enforce downward-pointing edges, non-overlap constraints, or cluster constraints).

Another big advantage is that we no longer need Boost.

I've tested the basic functionality, but I have yet to properly handle
disconnected graphs or to properly scale the resulting layout.

This commit also includes significant refactoring... the quadratic program solver - libvpsc (Variable Placement with Separation Constraints) has been moved to src/libvpsc and the actual graph layout algorithm is in libcola.

(bzr r1394)

1 files changed, 417 insertions, 0 deletions

diff --git a/src/libvpsc/solve_VPSC.cpp b/src/libvpsc/solve_VPSC.cpp
new file mode 100644
index 000000000..44918951d
--- /dev/null
+++ b/src/libvpsc/solve_VPSC.cpp
@@ -0,0 +1,417 @@
+/**
+ * \brief Solve an instance of the "Variable Placement with Separation
+ * Constraints" problem.
+ *
+ * Authors:
+ *   Tim Dwyer <tgdwyer@gmail.com>
+ *
+ * Copyright (C) 2005 Authors
+ *
+ * Released under GNU LGPL.  Read the file 'COPYING' for more information.
+ */
+
+#include <cassert>
+#include "constraint.h"
+#include "block.h"
+#include "blocks.h"
+#include "solve_VPSC.h"
+#include <math.h>
+#include <sstream>
+#ifdef RECTANGLE_OVERLAP_LOGGING
+#include <fstream>
+using std::ios;
+using std::ofstream;
+using std::endl;
+#endif
+
+using std::ostringstream;
+using std::list;
+using std::set;
+
+static const double ZERO_UPPERBOUND=-0.0000001;
+
+IncVPSC::IncVPSC(const unsigned n, Variable* const vs[], const unsigned m, Constraint *cs[]) 
+	: VPSC(n,vs,m,cs) {
+	inactive.assign(cs,cs+m);
+	for(ConstraintList::iterator i=inactive.begin();i!=inactive.end();++i) {
+		(*i)->active=false;
+	}
+}
+VPSC::VPSC(const unsigned n, Variable* const vs[], const unsigned m, Constraint *cs[]) : m(m), cs(cs), n(n), vs(vs) {
+	bs=new Blocks(n, vs);
+#ifdef RECTANGLE_OVERLAP_LOGGING
+	printBlocks();
+	assert(!constraintGraphIsCyclic(n,vs));
+#endif
+}
+VPSC::~VPSC() {
+	delete bs;
+}
+
+// useful in debugging
+void VPSC::printBlocks() {
+#ifdef RECTANGLE_OVERLAP_LOGGING
+	ofstream f(LOGFILE,ios::app);
+	for(set<Block*>::iterator i=bs->begin();i!=bs->end();++i) {
+		Block *b=*i;
+		f<<"  "<<*b<<endl;
+	}
+	for(unsigned i=0;i<m;i++) {
+		f<<"  "<<*cs[i]<<endl;
+	}
+#endif
+}
+/**
+* Produces a feasible - though not necessarily optimal - solution by
+* examining blocks in the partial order defined by the directed acyclic
+* graph of constraints. For each block (when processing left to right) we
+* maintain the invariant that all constraints to the left of the block
+* (incoming constraints) are satisfied. This is done by repeatedly merging
+* blocks into bigger blocks across violated constraints (most violated
+* first) fixing the position of variables inside blocks relative to one
+* another so that constraints internal to the block are satisfied.
+*/
+void VPSC::satisfy() {
+	list<Variable*> *vs=bs->totalOrder();
+	for(list<Variable*>::iterator i=vs->begin();i!=vs->end();++i) {
+		Variable *v=*i;
+		if(!v->block->deleted) {
+			bs->mergeLeft(v->block);
+		}
+	}
+	bs->cleanup();
+	for(unsigned i=0;i<m;i++) {
+		if(cs[i]->slack() < ZERO_UPPERBOUND) {
+#ifdef RECTANGLE_OVERLAP_LOGGING
+			ofstream f(LOGFILE,ios::app);
+			f<<"Error: Unsatisfied constraint: "<<*cs[i]<<endl;
+#endif
+			//assert(cs[i]->slack()>-0.0000001);
+			throw "Unsatisfied constraint";
+		}
+	}
+	delete vs;
+}
+
+void VPSC::refine() {
+	bool solved=false;
+	// Solve shouldn't loop indefinately
+	// ... but just to make sure we limit the number of iterations
+	unsigned maxtries=100;
+	while(!solved&&maxtries>=0) {
+		solved=true;
+		maxtries--;
+		for(set<Block*>::const_iterator i=bs->begin();i!=bs->end();++i) {
+			Block *b=*i;
+			b->setUpInConstraints();
+			b->setUpOutConstraints();
+		}
+		for(set<Block*>::const_iterator i=bs->begin();i!=bs->end();++i) {
+			Block *b=*i;
+			Constraint *c=b->findMinLM();
+			if(c!=NULL && c->lm<0) {
+#ifdef RECTANGLE_OVERLAP_LOGGING
+				ofstream f(LOGFILE,ios::app);
+				f<<"Split on constraint: "<<*c<<endl;
+#endif
+				// Split on c
+				Block *l=NULL, *r=NULL;
+				bs->split(b,l,r,c);
+				bs->cleanup();
+				// split alters the block set so we have to restart
+				solved=false;
+				break;
+			}
+		}
+	}
+	for(unsigned i=0;i<m;i++) {
+		if(cs[i]->slack() < ZERO_UPPERBOUND) {
+			assert(cs[i]->slack()>ZERO_UPPERBOUND);
+			throw "Unsatisfied constraint";
+		}
+	}
+}
+/**
+ * Calculate the optimal solution. After using satisfy() to produce a
+ * feasible solution, refine() examines each block to see if further
+ * refinement is possible by splitting the block. This is done repeatedly
+ * until no further improvement is possible.
+ */
+void VPSC::solve() {
+	satisfy();
+	refine();
+}
+
+void IncVPSC::solve() {
+#ifdef RECTANGLE_OVERLAP_LOGGING
+	ofstream f(LOGFILE,ios::app);
+	f<<"solve_inc()..."<<endl;
+#endif
+	double lastcost,cost = bs->cost();
+	do {
+		lastcost=cost;
+		satisfy();
+		splitBlocks();
+		cost = bs->cost();
+#ifdef RECTANGLE_OVERLAP_LOGGING
+	f<<"  cost="<<cost<<endl;
+#endif
+	} while(fabs(lastcost-cost)>0.0001);
+}
+/**
+ * incremental version of satisfy that allows refinement after blocks are
+ * moved.
+ *
+ *  - move blocks to new positions
+ *  - repeatedly merge across most violated constraint until no more
+ *    violated constraints exist
+ *
+ * Note: there is a special case to handle when the most violated constraint
+ * is between two variables in the same block.  Then, we must split the block
+ * over an active constraint between the two variables.  We choose the 
+ * constraint with the most negative lagrangian multiplier. 
+ */
+void IncVPSC::satisfy() {
+#ifdef RECTANGLE_OVERLAP_LOGGING
+	ofstream f(LOGFILE,ios::app);
+	f<<"satisfy_inc()..."<<endl;
+#endif
+	splitBlocks();
+	long splitCtr = 0;
+	Constraint* v = NULL;
+	while((v=mostViolated(inactive))&&(v->equality || v->slack() < ZERO_UPPERBOUND)) {
+		assert(!v->active);
+		Block *lb = v->left->block, *rb = v->right->block;
+		if(lb != rb) {
+			lb->merge(rb,v);
+		} else {
+			if(splitCtr++>10000) {
+				throw "Cycle Error!";
+			}
+			// constraint is within block, need to split first
+			inactive.push_back(lb->splitBetween(v->left,v->right,lb,rb));
+			lb->merge(rb,v);
+			bs->insert(lb);
+		}
+	}
+#ifdef RECTANGLE_OVERLAP_LOGGING
+	f<<"  finished merges."<<endl;
+#endif
+	bs->cleanup();
+	for(unsigned i=0;i<m;i++) {
+		v=cs[i];
+		if(v->slack() < ZERO_UPPERBOUND) {
+			ostringstream s;
+			s<<"Unsatisfied constraint: "<<*v;
+#ifdef RECTANGLE_OVERLAP_LOGGING
+			ofstream f(LOGFILE,ios::app);
+			f<<s.str()<<endl;
+#endif
+			throw s.str().c_str();
+		}
+	}
+#ifdef RECTANGLE_OVERLAP_LOGGING
+	f<<"  finished cleanup."<<endl;
+	printBlocks();
+#endif
+}
+void IncVPSC::moveBlocks() {
+#ifdef RECTANGLE_OVERLAP_LOGGING
+	ofstream f(LOGFILE,ios::app);
+	f<<"moveBlocks()..."<<endl;
+#endif
+	for(set<Block*>::const_iterator i(bs->begin());i!=bs->end();++i) {
+		Block *b = *i;
+		b->wposn = b->desiredWeightedPosition();
+		b->posn = b->wposn / b->weight;
+	}
+#ifdef RECTANGLE_OVERLAP_LOGGING
+	f<<"  moved blocks."<<endl;
+#endif
+}
+void IncVPSC::splitBlocks() {
+#ifdef RECTANGLE_OVERLAP_LOGGING
+	ofstream f(LOGFILE,ios::app);
+#endif
+	moveBlocks();
+	splitCnt=0;
+	// Split each block if necessary on min LM
+	for(set<Block*>::const_iterator i(bs->begin());i!=bs->end();++i) {
+		Block* b = *i;
+		Constraint* v=b->findMinLM();
+		if(v!=NULL && v->lm < ZERO_UPPERBOUND) {
+			assert(!v->equality);
+#ifdef RECTANGLE_OVERLAP_LOGGING
+			f<<"    found split point: "<<*v<<" lm="<<v->lm<<endl;
+#endif
+			splitCnt++;
+			Block *b = v->left->block, *l=NULL, *r=NULL;
+			assert(v->left->block == v->right->block);
+			double pos = b->posn;
+			b->split(l,r,v);
+			l->posn=r->posn=pos;
+			l->wposn = l->posn * l->weight;
+			r->wposn = r->posn * r->weight;
+			bs->insert(l);
+			bs->insert(r);
+			b->deleted=true;
+			inactive.push_back(v);
+#ifdef RECTANGLE_OVERLAP_LOGGING
+			f<<"  new blocks: "<<*l<<" and "<<*r<<endl;
+#endif
+		}
+	}
+#ifdef RECTANGLE_OVERLAP_LOGGING
+	f<<"  finished splits."<<endl;
+#endif
+	bs->cleanup();
+}
+
+/**
+ * Scan constraint list for the most violated constraint, or the first equality
+ * constraint
+ */
+Constraint* IncVPSC::mostViolated(ConstraintList &l) {
+	double minSlack = DBL_MAX;
+	Constraint* v=NULL;
+#ifdef RECTANGLE_OVERLAP_LOGGING
+	ofstream f(LOGFILE,ios::app);
+	f<<"Looking for most violated..."<<endl;
+#endif
+	ConstraintList::iterator end = l.end();
+	ConstraintList::iterator deletePoint = end;
+	for(ConstraintList::iterator i=l.begin();i!=end;++i) {
+		Constraint *c=*i;
+		double slack = c->slack();
+		if(c->equality || slack < minSlack) {
+			minSlack=slack;	
+			v=c;
+			deletePoint=i;
+			if(c->equality) break;
+		}
+	}
+	// Because the constraint list is not order dependent we just
+	// move the last element over the deletePoint and resize
+	// downwards.  There is always at least 1 element in the
+	// vector because of search.
+	if(deletePoint != end && (minSlack<ZERO_UPPERBOUND||v->equality)) {
+		*deletePoint = l[l.size()-1];
+		l.resize(l.size()-1);
+	}
+#ifdef RECTANGLE_OVERLAP_LOGGING
+	f<<"  most violated is: "<<*v<<endl;
+#endif
+	return v;
+}
+
+#include <map>
+using std::map;
+using std::vector;
+struct node {
+	set<node*> in;
+	set<node*> out;
+};
+// useful in debugging - cycles would be BAD
+bool VPSC::constraintGraphIsCyclic(const unsigned n, Variable *vs[]) {
+	map<Variable*, node*> varmap;
+	vector<node*> graph;
+	for(unsigned i=0;i<n;i++) {
+		node *u=new node;
+		graph.push_back(u);
+		varmap[vs[i]]=u;
+	}
+	for(unsigned i=0;i<n;i++) {
+		for(vector<Constraint*>::iterator c=vs[i]->in.begin();c!=vs[i]->in.end();++c) {
+			Variable *l=(*c)->left;
+			varmap[vs[i]]->in.insert(varmap[l]);
+		}
+
+		for(vector<Constraint*>::iterator c=vs[i]->out.begin();c!=vs[i]->out.end();++c) {
+			Variable *r=(*c)->right;
+			varmap[vs[i]]->out.insert(varmap[r]);
+		}
+	}
+	while(graph.size()>0) {
+		node *u=NULL;
+		vector<node*>::iterator i=graph.begin();
+		for(;i!=graph.end();++i) {
+			u=*i;
+			if(u->in.size()==0) {
+				break;
+			}
+		}
+		if(i==graph.end() && graph.size()>0) {
+			//cycle found!
+			return true;
+		} else {
+			graph.erase(i);
+			for(set<node*>::iterator j=u->out.begin();j!=u->out.end();++j) {
+				node *v=*j;
+				v->in.erase(u);
+			}
+			delete u;
+		}
+	}
+	for(unsigned i=0; i<graph.size(); ++i) {
+		delete graph[i];
+	}
+	return false;
+}
+
+// useful in debugging - cycles would be BAD
+bool VPSC::blockGraphIsCyclic() {
+	map<Block*, node*> bmap;
+	vector<node*> graph;
+	for(set<Block*>::const_iterator i=bs->begin();i!=bs->end();++i) {
+		Block *b=*i;
+		node *u=new node;
+		graph.push_back(u);
+		bmap[b]=u;
+	}
+	for(set<Block*>::const_iterator i=bs->begin();i!=bs->end();++i) {
+		Block *b=*i;
+		b->setUpInConstraints();
+		Constraint *c=b->findMinInConstraint();
+		while(c!=NULL) {
+			Block *l=c->left->block;
+			bmap[b]->in.insert(bmap[l]);
+			b->deleteMinInConstraint();
+			c=b->findMinInConstraint();
+		}
+
+		b->setUpOutConstraints();
+		c=b->findMinOutConstraint();
+		while(c!=NULL) {
+			Block *r=c->right->block;
+			bmap[b]->out.insert(bmap[r]);
+			b->deleteMinOutConstraint();
+			c=b->findMinOutConstraint();
+		}
+	}
+	while(graph.size()>0) {
+		node *u=NULL;
+		vector<node*>::iterator i=graph.begin();
+		for(;i!=graph.end();++i) {
+			u=*i;
+			if(u->in.size()==0) {
+				break;
+			}
+		}
+		if(i==graph.end() && graph.size()>0) {
+			//cycle found!
+			return true;
+		} else {
+			graph.erase(i);
+			for(set<node*>::iterator j=u->out.begin();j!=u->out.end();++j) {
+				node *v=*j;
+				v->in.erase(u);
+			}
+			delete u;
+		}
+	}
+	for(unsigned i=0; i<graph.size(); i++) {
+		delete graph[i];
+	}
+	return false;
+}
+