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
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 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
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
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
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
use super::*;
use std::collections::BTreeMap;

/// Find all minimal quorums in the FBAS...
pub fn find_minimal_quorums(fbas: &Fbas) -> Vec<NodeIdSet> {
    info!("Starting to look for minimal quorums...");
    let quorums = find_quorums(fbas, minimal_quorums_finder);
    info!("Found {} (not necessarily minimal) quorums.", quorums.len());
    let minimal_quorums = remove_non_minimal_quorums(quorums, fbas);
    info!("Reduced to {} minimal quorums.", minimal_quorums.len());
    minimal_quorums
}

/// Find at least two non-intersecting quorums. Use this function if it is very likely that
/// the FBAS lacks quorum intersection and you want to stop early in such cases.
pub fn find_nonintersecting_quorums(fbas: &Fbas) -> Option<Vec<NodeIdSet>> {
    info!("Starting to look for potentially non-intersecting quorums...");
    let quorums = find_quorums(fbas, nonintersecting_quorums_finder);
    if quorums.len() < 2 {
        info!("Found no non-intersecting quorums.");
        None
    } else {
        warn!(
            "Found {} non-intersecting quorums (there could more).",
            quorums.len()
        );
        Some(quorums)
    }
}

/// Finds groups of nodes (represented as quorum sets) such that all members of the same group have
/// the exact identical quorum set, and the nodes contained in this quorum set are exactly the
/// group of nodes (a symmetric cluster). Once no more such clusters are found, returns the maximum
/// quorum of the remaining nodes. (So, getting a result with more than 1 entry implies that we
/// don't have quorum intersection.)
pub fn find_symmetric_clusters(fbas: &Fbas) -> Vec<QuorumSet> {
    info!("Starting to look for symmetric quorum clusters...");
    let quorums = find_quorums(fbas, symmetric_clusters_finder);
    info!("Found {} different quorum clusters.", quorums.len());
    quorums
}

/// Does preprocessing common to all finders
fn find_quorums<F, R>(fbas: &Fbas, finder: F) -> Vec<R>
where
    F: Fn(Vec<NodeIdSet>, &Fbas) -> Vec<R>,
{
    let all_nodes: NodeIdSet = (0..fbas.nodes.len()).collect();

    debug!("Removing nodes not part of any quorum...");
    let (satisfiable, unsatisfiable) = find_unsatisfiable_nodes(&all_nodes, fbas);
    if !unsatisfiable.is_empty() {
        warn!(
            "The quorum sets of {} nodes are not satisfiable at all in the given FBAS!",
            unsatisfiable.len()
        );
        info!(
            "Ignoring {} unsatisfiable nodes ({} nodes left).",
            unsatisfiable.len(),
            satisfiable.len()
        );
    } else {
        debug!("All nodes are satisfiable");
    }

    debug!("Partitioning into strongly connected components...");
    let sccs = partition_into_strongly_connected_components(&satisfiable, fbas);

    debug!("Reducing to strongly connected components that contain quorums...");
    let consensus_clusters: Vec<NodeIdSet> = sccs
        .into_iter()
        .filter(|node_set| contains_quorum(&node_set, fbas))
        .collect();
    if consensus_clusters.len() > 1 {
        warn!(
            "{} connected components contain quorums => the FBAS lacks quorum intersection!",
            consensus_clusters.len()
        );
    }
    finder(consensus_clusters, fbas)
}

fn minimal_quorums_finder(consensus_clusters: Vec<NodeIdSet>, fbas: &Fbas) -> Vec<NodeIdSet> {
    let mut found_quorums_in_all_clusters = vec![];
    for (i, nodes) in consensus_clusters.into_iter().enumerate() {
        debug!("Finding minimal quorums in cluster {}...", i);
        let mut found_quorums: Vec<NodeIdSet> = vec![];

        let quorum_clusters = find_symmetric_clusters_in_node_set(&nodes, fbas);
        if !quorum_clusters.is_empty() {
            assert!(quorum_clusters.len() == 1);
            debug!("Cluster contains a symmetric quorum cluster! Extracting quorums...");
            let quorum_cluster = quorum_clusters.into_iter().next().unwrap();
            {
                let mut remaining_nodes = nodes.clone();
                remaining_nodes.difference_with(&quorum_cluster.contained_nodes());
                assert!(!contains_quorum(&remaining_nodes, fbas));
            }
            found_quorums.extend_from_slice(&quorum_cluster.to_quorum_slices());
        } else {
            debug!("Sorting nodes by rank...");
            let sorted_nodes = sort_by_rank(nodes.into_iter().collect(), fbas);
            debug!("Sorted.");

            let unprocessed = sorted_nodes;
            let mut selection = NodeIdSet::with_capacity(fbas.nodes.len());
            let mut available = unprocessed.iter().cloned().collect();

            debug!("Collecting quorums...");
            minimal_quorums_finder_step(
                &mut unprocessed.into(),
                &mut selection,
                &mut available,
                &mut found_quorums,
                fbas,
                true,
            );
        }
        found_quorums_in_all_clusters.append(&mut found_quorums);
    }
    found_quorums_in_all_clusters
}
fn minimal_quorums_finder_step(
    unprocessed: &mut NodeIdDeque,
    selection: &mut NodeIdSet,
    available: &mut NodeIdSet,
    found_quorums: &mut Vec<NodeIdSet>,
    fbas: &Fbas,
    selection_changed: bool,
) {
    if selection_changed && fbas.is_quorum(selection) {
        found_quorums.push(selection.clone());
        if found_quorums.len() % 100_000 == 0 {
            debug!("...{} quorums found", found_quorums.len());
        }
    } else if let Some(current_candidate) = unprocessed.pop_front() {
        selection.insert(current_candidate);

        minimal_quorums_finder_step(unprocessed, selection, available, found_quorums, fbas, true);

        selection.remove(current_candidate);
        available.remove(current_candidate);

        if selection_satisfiable(selection, available, fbas) {
            minimal_quorums_finder_step(
                unprocessed,
                selection,
                available,
                found_quorums,
                fbas,
                false,
            );
        }
        unprocessed.push_front(current_candidate);
        available.insert(current_candidate);
    }
}

fn nonintersecting_quorums_finder(
    consensus_clusters: Vec<NodeIdSet>,
    fbas: &Fbas,
) -> Vec<NodeIdSet> {
    if consensus_clusters.len() > 1 {
        debug!("More than one consensus clusters - reducing to maximal quorums.");
        consensus_clusters
            .into_iter()
            .map(|node_set| find_unsatisfiable_nodes(&node_set, fbas).0)
            .collect()
    } else {
        warn!("There is only one consensus cluster - there might be no non-intersecting quorums and the subsequent search might be slow.");
        let nodes = consensus_clusters.into_iter().next().unwrap_or_default();
        debug!("Sorting nodes by rank...");
        let sorted_nodes = sort_by_rank(nodes.into_iter().collect(), fbas);
        debug!("Sorted.");

        let unprocessed = sorted_nodes;
        let mut selection = NodeIdSet::with_capacity(fbas.nodes.len());
        let mut available: NodeIdSet = unprocessed.iter().cloned().collect();
        let mut antiselection = available.clone();
        if let Some(intersecting_quorums) = nonintersecting_quorums_finder_step(
            &mut unprocessed.into(),
            &mut selection,
            &mut available,
            &mut antiselection,
            fbas,
        ) {
            assert!(intersecting_quorums.iter().all(|x| fbas.is_quorum(x)));
            assert!(intersecting_quorums[0].is_disjoint(&intersecting_quorums[1]));
            intersecting_quorums.to_vec()
        } else {
            assert!(fbas.is_quorum(&available));
            vec![available.clone()]
        }
    }
}
fn nonintersecting_quorums_finder_step(
    unprocessed: &mut NodeIdDeque,
    selection: &mut NodeIdSet,
    available: &mut NodeIdSet,
    antiselection: &mut NodeIdSet,
    fbas: &Fbas,
) -> Option<[NodeIdSet; 2]> {
    debug_assert!(selection.is_disjoint(&antiselection));
    if fbas.is_quorum(selection) {
        let (potential_complement, _) = find_unsatisfiable_nodes(&antiselection, fbas);

        if !potential_complement.is_empty() {
            return Some([selection.clone(), potential_complement]);
        }
    } else if let Some(current_candidate) = unprocessed.pop_front() {
        selection.insert(current_candidate);
        antiselection.remove(current_candidate);
        if let Some(intersecting_quorums) = nonintersecting_quorums_finder_step(
            unprocessed,
            selection,
            available,
            antiselection,
            fbas,
        ) {
            return Some(intersecting_quorums);
        }
        selection.remove(current_candidate);
        antiselection.insert(current_candidate);
        available.remove(current_candidate);

        if selection_satisfiable(selection, available, fbas) {
            if let Some(intersecting_quorums) = nonintersecting_quorums_finder_step(
                unprocessed,
                selection,
                available,
                antiselection,
                fbas,
            ) {
                return Some(intersecting_quorums);
            }
        }
        unprocessed.push_front(current_candidate);
        available.insert(current_candidate);
    }
    None
}

fn symmetric_clusters_finder(consensus_clusters: Vec<NodeIdSet>, fbas: &Fbas) -> Vec<QuorumSet> {
    let mut found_clusters_in_all_clusters = vec![];
    for (i, nodes) in consensus_clusters.into_iter().enumerate() {
        debug!("Finding symmetric quorum cluster in cluster {}...", i);
        found_clusters_in_all_clusters
            .append(&mut find_symmetric_clusters_in_node_set(&nodes, fbas));
    }
    found_clusters_in_all_clusters
}
fn find_symmetric_clusters_in_node_set(nodes: &NodeIdSet, fbas: &Fbas) -> Vec<QuorumSet> {
    // qset -> (#occurances, goal #occurances)
    let mut qset_occurances: BTreeMap<QuorumSet, (usize, usize)> = BTreeMap::new();
    let mut found_clusters = vec![];

    for node_id in nodes.iter() {
        let qset = &fbas.nodes[node_id].quorum_set;
        let (count, goal) = if let Some((counter, goal)) = qset_occurances.get_mut(qset) {
            *counter += 1;
            (*counter, *goal)
        } else {
            let goal = qset.contained_nodes().len();
            qset_occurances.insert(qset.clone(), (1, goal));
            (1, goal)
        };
        if count == goal {
            found_clusters.push(qset.clone());
        }
    }
    found_clusters
}

fn selection_satisfiable(selection: &NodeIdSet, available: &NodeIdSet, fbas: &Fbas) -> bool {
    selection
        .iter()
        .all(|x| fbas.nodes[x].is_quorum_slice(available))
}

fn contains_quorum(node_set: &NodeIdSet, fbas: &Fbas) -> bool {
    let mut satisfiable = node_set.clone();

    while let Some(unsatisfiable_node) = satisfiable
        .iter()
        .find(|&x| !fbas.nodes[x].is_quorum_slice(&satisfiable))
    {
        satisfiable.remove(unsatisfiable_node);
    }
    !satisfiable.is_empty()
}

fn remove_non_minimal_quorums(quorums: Vec<NodeIdSet>, fbas: &Fbas) -> Vec<NodeIdSet> {
    let mut minimal_quorums = vec![];
    let mut tester: NodeIdSet;
    let mut is_minimal;

    debug!("Filtering non-minimal quorums...");
    for (i, quorum) in quorums.into_iter().enumerate() {
        if i % 100_000 == 0 {
            debug!(
                "...at quorum {}; {} minimal quorums",
                i,
                minimal_quorums.len()
            );
        }
        is_minimal = true;
        // whyever, using clone() here seems to be faster than clone_from()
        tester = quorum.clone();

        for node_id in quorum.iter() {
            tester.remove(node_id);
            if contains_quorum(&tester, fbas) {
                is_minimal = false;
                break;
            }
            tester.insert(node_id);
        }
        if is_minimal {
            minimal_quorums.push(quorum);
        }
    }
    debug!("Filtering done.");
    debug_assert!(contains_only_minimal_node_sets(&minimal_quorums));
    minimal_quorums.sort();
    minimal_quorums.sort_by_key(|x| x.len());
    minimal_quorums
}

#[cfg(test)]
mod tests {
    use super::*;
    use std::path::Path;

    #[test]
    fn find_minimal_quorums_in_correct_trivial() {
        let fbas = Fbas::from_json_file(Path::new("test_data/correct_trivial.json"));

        let expected = vec![bitset![0, 1], bitset![0, 2], bitset![1, 2]];
        let actual = find_minimal_quorums(&fbas);

        assert_eq!(expected, actual);
    }

    #[test]
    fn find_minimal_quorums_in_broken_trivial() {
        let fbas = Fbas::from_json_file(Path::new("test_data/broken_trivial.json"));

        let expected = vec![bitset![0], bitset![1, 2]];
        let actual = find_minimal_quorums(&fbas);

        assert_eq!(expected, actual);
    }

    #[test]
    fn find_minimal_quorums_in_broken_trivial_reversed_node_ids() {
        let mut fbas = Fbas::from_json_file(Path::new("test_data/broken_trivial.json"));
        fbas.nodes.reverse();

        let expected = vec![bitset![2], bitset![0, 1]];
        let actual = find_minimal_quorums(&fbas);

        assert_eq!(expected, actual);
    }

    #[test]
    fn find_minimal_quorums_when_naive_remove_non_minimal_optimization_doesnt_work() {
        let fbas = Fbas::from_json_str(
            r#"[
            {
                "publicKey": "n0",
                "quorumSet": { "threshold": 2, "validators": ["n0", "n3"] }
            },
            {
                "publicKey": "n1",
                "quorumSet": { "threshold": 2, "validators": ["n1", "n2"] }
            },
            {
                "publicKey": "n2",
                "quorumSet": { "threshold": 2, "validators": ["n1", "n2"] }
            },
            {
                "publicKey": "n3",
                "quorumSet": { "threshold": 2, "validators": ["n0", "n3"] }
            }
        ]"#,
        );
        let expected = vec![bitset![0, 3], bitset![1, 2]];
        let actual = find_minimal_quorums(&fbas);
        assert_eq!(expected, actual);
    }

    #[test]
    fn find_nonintersecting_quorums_in_broken() {
        let fbas = Fbas::from_json_file(Path::new("test_data/broken.json"));

        let expected = Some(vec![bitset![3, 10], bitset![4, 6]]);
        let actual = find_nonintersecting_quorums(&fbas);

        assert_eq!(expected, actual);
    }

    #[test]
    fn find_symmetric_cluster_in_correct_trivial() {
        let fbas = Fbas::from_json_file(Path::new("test_data/correct_trivial.json"));

        let expected = vec![QuorumSet {
            validators: vec![0, 1, 2],
            threshold: 2,
            inner_quorum_sets: vec![],
        }];
        let actual = find_symmetric_clusters(&fbas);

        assert_eq!(expected, actual);
    }

    #[test]
    fn find_unsatisfiable_nodes_in_unconfigured_fbas() {
        let fbas = Fbas::new_generic_unconfigured(10);
        let all_nodes: NodeIdSet = (0..10).collect();

        let actual = find_unsatisfiable_nodes(&all_nodes, &fbas);
        let expected = (bitset![], all_nodes);

        assert_eq!(expected, actual);
    }

    #[test]
    fn find_transitively_unsatisfiable_nodes() {
        let mut fbas = Fbas::from_json_file(Path::new("test_data/correct_trivial.json"));

        let directly_unsatisfiable = fbas.add_generic_node(QuorumSet::new());
        let transitively_unsatisfiable = fbas.add_generic_node(QuorumSet {
            threshold: 1,
            validators: vec![directly_unsatisfiable],
            inner_quorum_sets: vec![],
        });

        fbas.nodes[0]
            .quorum_set
            .validators
            .push(directly_unsatisfiable);
        fbas.nodes[1]
            .quorum_set
            .validators
            .push(transitively_unsatisfiable);

        let all_nodes: NodeIdSet = (0..fbas.nodes.len()).collect();
        let (_, unsatisfiable) = find_unsatisfiable_nodes(&all_nodes, &fbas);

        assert!(unsatisfiable.contains(directly_unsatisfiable));
        assert!(unsatisfiable.contains(transitively_unsatisfiable));
    }

    #[test]
    fn unsatisfiable_nodes_not_returned_as_strongly_connected() {
        let mut fbas = Fbas::from_json_file(Path::new("test_data/correct_trivial.json"));

        let directly_unsatisfiable = fbas.add_generic_node(QuorumSet::new());
        let transitively_unsatisfiable = fbas.add_generic_node(QuorumSet {
            threshold: 1,
            validators: vec![directly_unsatisfiable],
            inner_quorum_sets: vec![],
        });

        fbas.nodes[0]
            .quorum_set
            .validators
            .push(directly_unsatisfiable);
        fbas.nodes[1]
            .quorum_set
            .validators
            .push(transitively_unsatisfiable);

        let all_nodes: NodeIdSet = (0..fbas.nodes.len()).collect();
        let (satisfiable, _) = find_unsatisfiable_nodes(&all_nodes, &fbas);
        let (strongly_connected, _) = reduce_to_strongly_connected_nodes(satisfiable, &fbas);

        assert!(strongly_connected.contains(0));
        assert!(strongly_connected.contains(1));
        assert!(!strongly_connected.contains(directly_unsatisfiable));
        assert!(!strongly_connected.contains(transitively_unsatisfiable));
    }

    #[test]
    fn reduce_to_strongly_connected_nodes_ignores_self_links() {
        let mut fbas = Fbas::new();
        let interconnected_qset = QuorumSet {
            validators: vec![0, 1],
            inner_quorum_sets: vec![],
            threshold: 2,
        };
        let self_connected_qset = QuorumSet {
            validators: vec![2],
            inner_quorum_sets: vec![],
            threshold: 1,
        };
        fbas.add_generic_node(interconnected_qset.clone());
        fbas.add_generic_node(interconnected_qset);
        fbas.add_generic_node(self_connected_qset);
        let (strongly_connected, not_strongly_connected) =
            reduce_to_strongly_connected_nodes(bitset![0, 1, 2], &fbas);
        assert_eq!(bitset![0, 1], strongly_connected);
        assert_eq!(bitset![2], not_strongly_connected);
    }
}