graph_generation.cc 17.8 KB
Newer Older
Tiago Peixoto's avatar
Tiago Peixoto committed
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
// graph-tool -- a general graph modification and manipulation thingy
//
// Copyright (C) 2006  Tiago de Paula Peixoto <tiago@forked.de>
//
// This program is free software; you can redistribute it and/or
// modify it under the terms of the GNU General Public License
// as published by the Free Software Foundation; either version 2
// of the License, or (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program; if not, write to the Free Software
// Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.

#include <algorithm>
#include <tr1/unordered_set>
#include <boost/lambda/lambda.hpp>
#include <boost/lambda/bind.hpp>
#include <boost/random.hpp>
#include <boost/multi_index_container.hpp>
#include <boost/multi_index/ordered_index.hpp>
#include <boost/multi_index/member.hpp>
#include <boost/multi_index/mem_fun.hpp>
#include <iomanip>
#include <map>

#include "graph.hh"
#include "histogram.hh"

using namespace std;
using namespace boost;
using namespace boost::lambda;
using namespace multi_index;
using namespace graph_tool;

typedef boost::mt19937 rng_t;

//==============================================================================
// sample_from_distribution
// this will sample a (j,k) pair from a pjk distribution given a ceil function
// and its inverse
//==============================================================================

template <class Distribution, class Ceil, class InvCeil>
struct sample_from_distribution
{
    sample_from_distribution(Distribution &dist, Ceil& ceil, InvCeil &inv_ceil, double bound, rng_t& rng)
52
        : _dist(dist), _ceil(ceil), _inv_ceil(inv_ceil), _bound(bound), _rng(rng), _uniform_p(0.0, 1.0) {}
Tiago Peixoto's avatar
Tiago Peixoto committed
53
54
55
    
    pair<size_t, size_t> operator()()
    {
56
57
58
59
60
61
62
63
64
65
        // sample j,k from ceil
        size_t j,k;
        double u;
        do
        {
            tie(j,k) = _inv_ceil(_uniform_p(_rng), _uniform_p(_rng));
            u = _uniform_p(_rng);
        }
        while (u > _dist(j,k)/(_bound*_ceil(j,k)));
        return make_pair(j,k);
Tiago Peixoto's avatar
Tiago Peixoto committed
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
    }

    Distribution& _dist;
    Ceil& _ceil;
    InvCeil& _inv_ceil;
    double _bound;
    rng_t &_rng;
    boost::uniform_real<double> _uniform_p;
};

// vertex type, with desired j,k values and the index in the real graph

struct vertex_t 
{
    vertex_t() {}
    vertex_t(size_t in, size_t out): in_degree(in), out_degree(out) {}
    vertex_t(const pair<size_t,size_t>& deg): in_degree(deg.first), out_degree(deg.second) {}
    size_t index, in_degree, out_degree;
    bool operator==(const vertex_t& other) const {return other.index == index;}
};

inline std::size_t hash_value(const vertex_t& v)
{
    size_t h = hash_value(v.in_degree);
    hash_combine(h, v.out_degree);
    return h;
}

inline size_t dist(const vertex_t& a, const vertex_t& b)
{
    return int(a.in_degree-b.in_degree)*int(a.in_degree-b.in_degree) + 
97
        int(a.out_degree-b.out_degree)*int(a.out_degree-b.out_degree);
Tiago Peixoto's avatar
Tiago Peixoto committed
98
99
100
101
102
103
}

struct total_deg_comp
{
    bool operator()(const pair<size_t,size_t>& a, const pair<size_t,size_t>& b)
    {
104
        return a.first + a.second < b.first + b.second;
Tiago Peixoto's avatar
Tiago Peixoto committed
105
106
107
108
109
110
111
112
113
    }
};

//==============================================================================
// degree_matrix_t
// this structure will keep the existing (j,k) pairs in the graph in a matrix,
// so that the nearest (j,k) to a given target can be found easily.
//==============================================================================

114
class degree_matrix_t
Tiago Peixoto's avatar
Tiago Peixoto committed
115
{
116
117
public:    
    degree_matrix_t(size_t N, size_t minj, size_t mink, size_t maxj, size_t maxk)
Tiago Peixoto's avatar
Tiago Peixoto committed
118
    {
119
120
121
122
123
124
125
126
127
        _L = max(size_t(pow(2,ceil(log2(sqrt(N))))),size_t(2));
        _minj = minj;
        _mink = mink;
        _maxj = max(maxj,_L);
        _maxk = max(maxk,_L);
        _bins.resize(_L, vector<vector<pair<size_t,size_t> > >(_L));
        _high_bins.resize(size_t(log2(_L)));
        for(size_t i = 0; i < _high_bins.size(); ++i)
            _high_bins[i].resize(_L/(1<<(i+1)), vector<size_t>(_L/(1<<(i+1))));
Tiago Peixoto's avatar
Tiago Peixoto committed
128
    }
129

Tiago Peixoto's avatar
Tiago Peixoto committed
130
131
    void insert(const pair<size_t, size_t>& v)
    {
132
133
134
135
136
137
138
139
140
        size_t j_bin, k_bin;
        tie(j_bin, k_bin) = get_bin(v.first, v.second, 0);
        _bins[j_bin][k_bin].push_back(v);
        for (size_t i = 0; i < _high_bins.size(); ++i)
        {
            size_t hj,hk;
            tie(hj,hk) = get_bin(j_bin,k_bin, i+1);
            _high_bins[i][hj][hk]++;
        }
Tiago Peixoto's avatar
Tiago Peixoto committed
141
    }
142
    
Tiago Peixoto's avatar
Tiago Peixoto committed
143
144
    void erase(const pair<size_t,size_t>& v)
    {
145
146
147
148
149
150
        size_t j_bin, k_bin;
        tie(j_bin, k_bin) = get_bin(v.first, v.second, 0);
        for(size_t i = 0; i < _bins[j_bin][k_bin].size(); ++i)
        {
            if (_bins[j_bin][k_bin][i] == v)
            {
151
152
                _bins[j_bin][k_bin].erase(_bins[j_bin][k_bin].begin()+i);
                break;
153
154
155
156
157
158
159
160
161
162
            }
        }
        
        for (size_t i = 0; i < _high_bins.size(); ++i)
        {
            size_t hj,hk;
            tie(hj,hk) = get_bin(j_bin,k_bin, i+1);
            _high_bins[i][hj][hk]--;
        }
        
Tiago Peixoto's avatar
Tiago Peixoto committed
163
164
    }

165
    pair<size_t,size_t> find_closest(size_t j, size_t k, rng_t& rng)
Tiago Peixoto's avatar
Tiago Peixoto committed
166
    {
167
168
169
170
171
172
173
174
175
176
177
        vector<pair<size_t,size_t> > candidates;

        size_t level;

        // find the appropriate level on which to operate
        for (level = _high_bins.size(); level <= 0; --level)
        {
            size_t hj, hk;
            tie(hj,hk) = get_bin(j,k,level);
            if (get_bin_count(hj,hk,level) == 0)
            {
178
179
180
                if (level < _high_bins.size())
                    level++;
                break;
181
182
183
184
185
186
187
188
            }
        }

        size_t j_bin, k_bin;
        tie(j_bin, k_bin) = get_bin(j, k, level);

        for (size_t hj = ((j_bin>0)?j_bin-1:j_bin); hj < j_bin + 1 && hj <= get_bin(_maxj, _maxk, level).first; ++hj)
            for (size_t hk = ((k_bin>0)?k_bin-1:k_bin); hk < k_bin + 1 && hk <= get_bin(_maxj, _maxk, level).second; ++hk)
189
                search_bin(hj,hk,j,k,level,candidates);
190
191
192
        
        uniform_int<size_t> sample(0, candidates.size() - 1);
        return candidates[sample(rng)];
Tiago Peixoto's avatar
Tiago Peixoto committed
193
194
195
    }

private:
196
197
    
    pair<size_t,size_t> get_bin(size_t j, size_t k, size_t level) 
Tiago Peixoto's avatar
Tiago Peixoto committed
198
    {
199
200
        if (level == 0)
            return make_pair(((j-_minj)*(_L-1))/_maxj, ((k-_mink)*(_L-1))/_maxk);
201

202
203
204
205
        pair<size_t, size_t> bin = get_bin(j,k,0);
        bin.first /=  1 << level;
        bin.second /= 1 << level;
        return bin;
206
207
208
209
    }

    size_t get_bin_count(size_t bin_j, size_t bin_k, size_t level)
    {
210
211
212
213
        if (level == 0)
            return _bins[bin_j][bin_k].size();
        else
            return _high_bins[level-1][bin_j][bin_k];
Tiago Peixoto's avatar
Tiago Peixoto committed
214
    }
215
216

    void search_bin(size_t hj, size_t hk, size_t j, size_t k, size_t level, vector<pair<size_t,size_t> >& candidates)
Tiago Peixoto's avatar
Tiago Peixoto committed
217
    {
218
219
220
221
        size_t w = 1 << level;
        for (size_t j_bin = hj*w; j_bin < (hj+1)*w; ++j_bin)
            for (size_t k_bin = hk*w; k_bin < (hk+1)*w; ++k_bin)
            {
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
                for (size_t i = 0; i < _bins[j_bin][k_bin].size(); ++i)
                {
                    pair<size_t, size_t>& v = _bins[j_bin][k_bin][i];
                    if (candidates.empty())
                    {
                        candidates.push_back(v);
                        continue;
                    }
                    if (dist(vertex_t(v), vertex_t(j,k)) < dist(vertex_t(candidates.front()),vertex_t(j,k)))
                    {
                        candidates.clear();
                        candidates.push_back(v);
                    }
                    else if (dist(vertex_t(v), vertex_t(j,k)) == dist(vertex_t(candidates.front()),vertex_t(j,k)))
                    {
                        candidates.push_back(v);
                    }
                }
240
            }
Tiago Peixoto's avatar
Tiago Peixoto committed
241
242
243
    }

    size_t _L;
244
245
246
247
248
249
    vector<vector<vector<pair<size_t,size_t> > > > _bins;
    vector<vector<vector<size_t> > > _high_bins;
    size_t _minj;
    size_t _mink;
    size_t _maxj;
    size_t _maxk;
Tiago Peixoto's avatar
Tiago Peixoto committed
250
251
252
253
254
255
256
};

//==============================================================================
// GenerateCorrelatedConfigurationalModel
// generates a directed graph with given pjk and degree correlation
//==============================================================================
void GraphInterface::GenerateCorrelatedConfigurationalModel(size_t N, pjk_t pjk, pjk_t ceil_pjk, inv_ceil_t inv_ceil_pjk, double ceil_pjk_bound,
257
258
                                                            corr_t corr, corr_t ceil_corr, inv_corr_t inv_ceil_corr, double ceil_corr_bound, 
                                                            bool undirected_corr, size_t seed, bool verbose)
Tiago Peixoto's avatar
Tiago Peixoto committed
259
260
261
{
    _mg.clear();
    _properties = dynamic_properties();
262
    rng_t rng(static_cast<rng_t::result_type>(seed));
Tiago Peixoto's avatar
Tiago Peixoto committed
263
264
265
266
267

    // sample the N (j,k) pairs

    sample_from_distribution<pjk_t, pjk_t, inv_ceil_t> pjk_sample(pjk, ceil_pjk, inv_ceil_pjk, ceil_pjk_bound, rng);
    vector<vertex_t> vertices(N);
268
    size_t sum_j=0, sum_k=0, min_j=0, min_k=0, max_j=0, max_k=0;
Tiago Peixoto's avatar
Tiago Peixoto committed
269
270
    if (verbose)
    {
271
        cout << "adding vertices: " << flush;
Tiago Peixoto's avatar
Tiago Peixoto committed
272
273
274
    }
    for(size_t i = 0; i < N; ++i)
    {
275
276
277
278
        if (verbose)
        {
            static stringstream str;
            for (size_t j = 0; j < str.str().length(); ++j)
279
                cout << "\b";
280
281
282
283
284
285
286
287
288
289
290
291
292
            str.str("");
            str << i+1 << " of " << N << " (" << (i+1)*100/N << "%)";
            cout << str.str() << flush;
        }
        vertex_t& v = vertices[i];
        v.index = _vertex_index[add_vertex(_mg)];
        tie(v.in_degree, v.out_degree) = pjk_sample();
        sum_j += v.in_degree;
        sum_k += v.out_degree;
        min_j = min(v.in_degree,min_j);
        min_k = min(v.out_degree,min_k);
        max_j = max(v.in_degree,max_j);
        max_k = max(v.out_degree,max_k); 
Tiago Peixoto's avatar
Tiago Peixoto committed
293
294
295
    }

    if (verbose)
296
        cout << "\nfixing average degrees: " << flush;
Tiago Peixoto's avatar
Tiago Peixoto committed
297
298
299
300
301

    // <j> and <k> must be the same. Resample random pairs until this holds.
    uniform_int<size_t> vertex_sample(0, N-1);
    while (sum_j != sum_k)
    {
302
303
304
305
306
        vertex_t& v = vertices[vertex_sample(rng)];
        sum_j -= v.in_degree;
        sum_k -= v.out_degree;
        tie(v.in_degree, v.out_degree) = pjk_sample();
        sum_j += v.in_degree;
Tiago Peixoto's avatar
Tiago Peixoto committed
307
        sum_k +=  v.out_degree;
308
309
310
311
312
313
        max_j = max(v.in_degree,max_j);
        max_k = max(v.out_degree,max_k);
        if (verbose)
        {
            static stringstream str;
            for (size_t j = 0; j < str.str().length(); ++j)
314
                cout << "\b";
315
            for (size_t j = 0; j < str.str().length(); ++j)
316
                cout << " ";
317
            for (size_t j = 0; j < str.str().length(); ++j)
318
                cout << "\b";
319
320
321
322
            str.str("");
            str << min(sum_j-sum_k, sum_k-sum_j);
            cout << str.str() << flush;
        }
Tiago Peixoto's avatar
Tiago Peixoto committed
323
324
325
326
327
328
329
330
331
332
333
334
335
336
    }

    size_t E = sum_k;
 
    vector<vertex_t> sources; // sources of edges
    typedef tr1::unordered_multimap<pair<size_t,size_t>, vertex_t, hash<pair<size_t,size_t> > > targets_t;
    targets_t targets; // vertices with j > 0
    typedef tr1::unordered_set<pair<size_t,size_t>, hash<pair<size_t,size_t> > > target_degrees_t;
    target_degrees_t target_degrees; // existing (j,k) pairs
    
    // fill up sources, targets and target_degrees
    sources.reserve(E);
    for(size_t i = 0; i < N; ++i)
    {
337
338
339
340
341
342
343
        for(size_t k = 0; k < vertices[i].out_degree; ++k)
            sources.push_back(vertices[i]);
        if (vertices[i].in_degree > 0)
        {
            targets.insert(make_pair(make_pair(vertices[i].in_degree, vertices[i].out_degree), vertices[i]));
            target_degrees.insert(make_pair(vertices[i].in_degree, vertices[i].out_degree));
        }
Tiago Peixoto's avatar
Tiago Peixoto committed
344
345
346
347
    }

    typedef multiset<pair<size_t,size_t>, total_deg_comp> ordered_degrees_t;
    ordered_degrees_t ordered_degrees; // (j,k) pairs ordered by (j+k), i.e, total degree
348
    degree_matrix_t degree_matrix(target_degrees.size(), min_j, min_k, max_j, max_k); // (j,k) pairs layed out in a 2 dimensional matrix
Tiago Peixoto's avatar
Tiago Peixoto committed
349
    for(typeof(target_degrees.begin()) iter = target_degrees.begin(); iter != target_degrees.end(); ++iter)
350
351
352
353
        if (undirected_corr)
            ordered_degrees.insert(*iter);
        else
            degree_matrix.insert(*iter);
Tiago Peixoto's avatar
Tiago Peixoto committed
354
355
356
357
    
    // shuffle sources 
    for (size_t i = 0; i < sources.size(); ++i)
    {
358
359
        uniform_int<size_t> source_sample(i, sources.size()-1);
        swap(sources[i], sources[source_sample(rng)]);
Tiago Peixoto's avatar
Tiago Peixoto committed
360
361
362
    }

    if (verbose)
363
        cout << "\nadding edges: " << flush;
Tiago Peixoto's avatar
Tiago Peixoto committed
364
365
366
367
368

    // connect the sources to targets
    uniform_real<double> sample_probability(0.0, 1.0); 
    for (size_t i = 0; i < sources.size(); ++i)
    {
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
        vertex_t source = sources[i], target;
        size_t j = source.in_degree;
        size_t k = source.out_degree;
        
        //choose the target vertex according to correlation
            
        pjk_t prob_func = lambda::bind(corr,lambda::_1,lambda::_2,j,k);
        pjk_t ceil = lambda::bind(ceil_corr,lambda::_1,lambda::_2,j,k);
        inv_ceil_t inv_ceil = lambda::bind(inv_ceil_corr,lambda::_1,lambda::_2,j,k);
        sample_from_distribution<pjk_t, pjk_t, inv_ceil_t> corr_sample(prob_func, ceil, inv_ceil, ceil_corr_bound, rng);
        
        size_t jl,kl;
        tie(jl,kl) = corr_sample(); // target (j,k)
        
        target_degrees_t::iterator iter = target_degrees.find(make_pair(jl,kl));
        if (iter != target_degrees.end())
        {
            target = targets.find(*iter)->second; // if an (jl,kl) pair exists, just use that
        }
        else
389
        {        
390
391
392
            pair<size_t, size_t> deg;
            if (undirected_corr)
            {
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
                // select the (j,k) pair with the closest total degree (j+k)
                ordered_degrees_t::iterator upper;
                upper = ordered_degrees.upper_bound(make_pair(jl,kl));
                if (upper == ordered_degrees.end())
                {
                    --upper;
                    deg = *upper;
                }
                else if (upper == ordered_degrees.begin())
                {
                    deg = *upper;
                }
                else
                {
                    ordered_degrees_t::iterator lower = upper;
                    --lower;
                    if (jl + kl - (lower->first + lower->second) < upper->first + upper->second - (jl + kl))
                        deg = *lower;
                    else if (jl + kl - (lower->first + lower->second) != upper->first + upper->second - (jl + kl))
                        deg = *upper;
                    else
                    {
                        // if equal, choose randomly with equal probability
                        uniform_int<size_t> sample(0, 1);
                        if (sample(rng))
                            deg = *lower;
                        else
                            deg = *upper;
                    }
                }
                target = targets.find(deg)->second;
424
425
426
            }
            else
            {   
427
428
429
430
431
                // select the (j,k) which is the closest in the j,k plane.
                deg = degree_matrix.find_closest(jl, kl, rng);
                target = targets.find(deg)->second;
//                cerr << "wanted: " << jl << ", " << kl
//                     << " got: " << deg.first << ", " << deg.second << "\n";
432
               
433
            }            
434
435
436
437
438
439
440
441
442
443
444
445
        }

        //add edge
        graph_traits<multigraph_t>::edge_descriptor e;
        e = add_edge(vertex(source.index, _mg), vertex(target.index, _mg), _mg).first;
        _edge_index[e] = i;

        // if target received all the edges it should, remove it from target
        if (in_degree(vertex(target.index, _mg), _mg) == target.in_degree)
        {
            targets_t::iterator iter,end;
            for(tie(iter,end) = targets.equal_range(make_pair(target.in_degree, target.out_degree)); iter != end; ++iter)
446
447
448
449
450
                if (iter->second == target)
                {
                    targets.erase(iter);
                    break;
                }
451
452
453
454

            // if there are no more targets with (jl,kl), remove pair from target_degrees, etc.
            if (targets.find(make_pair(target.in_degree, target.out_degree)) == targets.end())
            {
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
                target_degrees.erase(target_degrees.find(make_pair(target.in_degree, target.out_degree)));
                if (target_degrees.bucket_count() > 2*target_degrees.size())
                {
                    target_degrees_t temp;
                    for(target_degrees_t::iterator iter = target_degrees.begin(); iter != target_degrees.end(); ++iter)
                        temp.insert(*iter);
                    target_degrees = temp;
                }
                if (undirected_corr)
                {
                    for(ordered_degrees_t::iterator iter = ordered_degrees.find(make_pair(target.in_degree, target.out_degree)); 
                        iter != ordered_degrees.end(); ++iter)
                        if (*iter == make_pair(target.in_degree, target.out_degree))
                        {
                            ordered_degrees.erase(iter);
                            break;
                        }
                }
                else
                {
                    degree_matrix.erase(make_pair(target.in_degree, target.out_degree));
                }
477
478
479
480
481
482
            }
            
        }

        if (verbose)
        {
483
            static stringstream str;            
484
            for (size_t j = 0; j < str.str().length(); ++j)
485
                cout << "\b";
486
            for (size_t j = 0; j < str.str().length(); ++j)
487
                cout << " ";
488
            for (size_t j = 0; j < str.str().length(); ++j)
489
                cout << "\b";
490
491
492
493
494
            str.str("");
            str << (i+1) << " of " << E << " (" << (i+1)*100/E << "%)";
            cout << str.str() << flush;
        }
        
Tiago Peixoto's avatar
Tiago Peixoto committed
495
496
497
    }
    
    if (verbose)
498
        cout << "\n";
Tiago Peixoto's avatar
Tiago Peixoto committed
499
}