Remove cycles from the dependency graph

Applies the strategy suggested by Strzyz et al., 2019 to attach the
leftmost token in a cycle to the first root token.

Author: danieldk

Cargo.lock

@@ -11,6 +11,7 @@ finalfusion = "0.5"
 itertools = "0.8"
 ndarray = "0.12"
 ordered-float = "1"
+petgraph = "0.4"
 protobuf = "1"
 serde = "1"
 serde_derive = "1"

sticker/Cargo.toml

@@ -1,5 +1,7 @@
 use conllx::graph::{DepTriple, Sentence};
 use ordered_float::OrderedFloat;
+use petgraph::algo::tarjan_scc;
+use petgraph::graph::DiGraph;
 
 use super::DependencyEncoding;
 use crate::EncodingProb;
@@ -29,6 +31,50 @@ where
     }
 }
 
+/// Break cycles in the graph.
+///
+/// Panics when a token does not have a head. To ensure that each
+/// token has a head, apply `attach_orphans` to the dependency graph
+/// before this function.
+pub fn break_cycles(sent: &mut Sentence, root_idx: usize) {
+    loop {
+        let components = {
+            let digraph: &DiGraph<_, _> = (&*sent).into();
+            tarjan_scc(digraph)
+                .into_iter()
+                .filter(|c| c.len() > 1)
+                .collect::<Vec<_>>()
+        };
+
+        // We are done if there are no more cycles.
+        if components.is_empty() {
+            break;
+        }
+
+        for cycle in components.into_iter() {
+            // Find the first token in the cycle, exclude the root
+            // token to avoid self-cycles.
+            let first_token = cycle
+                .into_iter()
+                .filter(|idx| idx.index() != root_idx)
+                .min()
+                .expect("Cannot get minimum, but iterator is non-empty")
+                .index();
+
+            // Reattach the token to the root.
+            let head_rel = sent
+                .dep_graph()
+                .head(first_token)
+                .expect("Token without a head")
+                .relation()
+                .map(ToOwned::to_owned);
+
+            sent.dep_graph_mut()
+                .add_deprel(DepTriple::new(root_idx, head_rel, first_token));
+        }
+    }
+}
+
 /// Find a candidate root token.
 ///
 /// The token which with the highest-probability encoding with the
@@ -113,7 +159,7 @@ mod tests {
     use conllx::graph::{DepTriple, Sentence};
     use conllx::token::TokenBuilder;
 
-    use super::{attach_orphans, find_or_create_root, first_root, ROOT_RELATION};
+    use super::{attach_orphans, break_cycles, find_or_create_root, first_root, ROOT_RELATION};
     use crate::depparse::{
         pos_position_table, DependencyEncoding, RelativePOS, RelativePOSEncoder,
     };
@@ -137,6 +183,24 @@ mod tests {
         sent
     }
 
+    fn test_graph_cycle() -> Sentence {
+        let mut sent = Sentence::new();
+        sent.push(TokenBuilder::new("Die").pos("det").into());
+        sent.push(TokenBuilder::new("AWO").pos("noun").into());
+        sent.push(TokenBuilder::new("veruntreute").pos("verb").into());
+        sent.push(TokenBuilder::new("Spendengeld").pos("noun").into());
+        sent.dep_graph_mut()
+            .add_deprel(DepTriple::new(2, Some("det"), 1));
+        sent.dep_graph_mut()
+            .add_deprel(DepTriple::new(1, Some("subj"), 2));
+        sent.dep_graph_mut()
+            .add_deprel(DepTriple::new(0, Some(ROOT_RELATION), 3));
+        sent.dep_graph_mut()
+            .add_deprel(DepTriple::new(3, Some("obj"), 4));
+
+        sent
+    }
+
     fn test_graph_no_root() -> Sentence {
         let mut sent = Sentence::new();
         sent.push(TokenBuilder::new("Die").pos("det").into());
@@ -230,4 +294,20 @@ mod tests {
 
         assert_eq!(sent, test_graph());
     }
+
+    #[test]
+    fn break_simple_cycle() {
+        let mut check = test_graph_cycle();
+        // Token 1 is the leftmost token in the cycle and
+        // should be reattached to the head.
+        check
+            .dep_graph_mut()
+            .add_deprel(DepTriple::new(3, Some("det"), 1));
+
+        // Detect cycle and break it.
+        let mut sent = test_graph_cycle();
+        break_cycles(&mut sent, 3);
+
+        assert_eq!(sent, check);
+    }
 }

sticker/src/depparse/post_processing.rs

@@ -4,7 +4,9 @@ use conllx::graph::{DepTriple, Node, Sentence};
 use failure::Error;
 use serde_derive::{Deserialize, Serialize};
 
-use super::{attach_orphans, find_or_create_root, DecodeError, DependencyEncoding, EncodeError};
+use super::{
+    attach_orphans, break_cycles, find_or_create_root, DecodeError, DependencyEncoding, EncodeError,
+};
 use crate::{EncodingProb, SentenceDecoder, SentenceEncoder};
 
 /// Relative head position by part-of-speech.
@@ -201,10 +203,11 @@ impl SentenceDecoder for RelativePOSEncoder {
         }
 
         // Fixup tree.
-        let root = find_or_create_root(labels, sentence, |idx, encoding| {
+        let root_idx = find_or_create_root(labels, sentence, |idx, encoding| {
             Self::decode_idx(&pos_table, idx, encoding).ok()
         });
-        attach_orphans(labels, sentence, root);
+        attach_orphans(labels, sentence, root_idx);
+        break_cycles(sentence, root_idx);
 
         Ok(())
     }

sticker/src/depparse/relative_pos.rs

@@ -2,7 +2,9 @@ use conllx::graph::{DepTriple, Sentence};
 use failure::Error;
 use serde_derive::{Deserialize, Serialize};
 
-use super::{attach_orphans, find_or_create_root, DecodeError, DependencyEncoding, EncodeError};
+use super::{
+    attach_orphans, break_cycles, find_or_create_root, DecodeError, DependencyEncoding, EncodeError,
+};
 use crate::{EncodingProb, SentenceDecoder, SentenceEncoder};
 
 /// Relative head position.
@@ -101,10 +103,11 @@ impl SentenceDecoder for RelativePositionEncoder {
 
         // Fixup tree.
         let sentence_len = sentence.len();
-        let root = find_or_create_root(labels, sentence, |idx, encoding| {
+        let root_idx = find_or_create_root(labels, sentence, |idx, encoding| {
             Self::decode_idx(idx, sentence_len, encoding).ok()
         });
-        attach_orphans(labels, sentence, root);
+        attach_orphans(labels, sentence, root_idx);
+        break_cycles(sentence, root_idx);
 
         Ok(())
     }