diff --git a/milli/src/search/new/ranking_rule_graph/build.rs b/milli/src/search/new/ranking_rule_graph/build.rs
new file mode 100644
index 000000000..605fe82d1
--- /dev/null
+++ b/milli/src/search/new/ranking_rule_graph/build.rs
@@ -0,0 +1,43 @@
+use std::collections::{BTreeSet, HashMap, HashSet};
+
+use heed::RoTxn;
+
+use super::{Edge, RankingRuleGraph, RankingRuleGraphTrait};
+use crate::new::db_cache::DatabaseCache;
+use crate::new::QueryGraph;
+use crate::{Index, Result};
+
+impl<G: RankingRuleGraphTrait> RankingRuleGraph<G> {
+    pub fn build<'db_cache, 'transaction: 'db_cache>(
+        index: &Index,
+        txn: &'transaction RoTxn,
+        db_cache: &mut DatabaseCache<'transaction>,
+        query_graph: QueryGraph,
+    ) -> Result<Self> {
+        let mut ranking_rule_graph = Self { query_graph, all_edges: vec![], node_edges: vec![] };
+
+        for (node_idx, node) in ranking_rule_graph.query_graph.nodes.iter().enumerate() {
+            ranking_rule_graph.node_edges.push(BTreeSet::new());
+            let new_edges = ranking_rule_graph.node_edges.last_mut().unwrap();
+
+            let Some(from_node_data) = G::build_visit_from_node(index, txn, db_cache, node)? else { continue };
+
+            for &successor_idx in ranking_rule_graph.query_graph.edges[node_idx].outgoing.iter() {
+                let to_node = &ranking_rule_graph.query_graph.nodes[successor_idx];
+                let Some(edges) = G::build_visit_to_node(index, txn, db_cache, to_node, &from_node_data)? else { continue };
+                for (cost, details) in edges {
+                    ranking_rule_graph.all_edges.push(Some(Edge {
+                        from_node: node_idx,
+                        to_node: successor_idx,
+                        cost,
+                        details,
+                    }));
+                    new_edges.insert(ranking_rule_graph.all_edges.len() - 1);
+                }
+            }
+        }
+        ranking_rule_graph.simplify();
+
+        Ok(ranking_rule_graph)
+    }
+}
diff --git a/milli/src/search/new/ranking_rule_graph/mod.rs b/milli/src/search/new/ranking_rule_graph/mod.rs
new file mode 100644
index 000000000..12f397df3
--- /dev/null
+++ b/milli/src/search/new/ranking_rule_graph/mod.rs
@@ -0,0 +1,207 @@
+pub mod build;
+pub mod cheapest_paths;
+pub mod edge_docids_cache;
+pub mod empty_paths_cache;
+pub mod paths_map;
+pub mod proximity;
+pub mod resolve_paths;
+
+use std::collections::{BTreeSet, HashMap, HashSet};
+use std::ops::ControlFlow;
+
+use heed::RoTxn;
+use roaring::RoaringBitmap;
+
+use super::db_cache::DatabaseCache;
+use super::{QueryGraph, QueryNode};
+use crate::{Index, Result};
+
+#[derive(Debug, Clone)]
+pub enum EdgeDetails<E> {
+    Unconditional,
+    Data(E),
+}
+
+#[derive(Debug, Clone)]
+pub struct Edge<E> {
+    from_node: usize,
+    to_node: usize,
+    cost: u8,
+    details: EdgeDetails<E>,
+}
+
+#[derive(Debug, Clone)]
+pub struct EdgePointer<'graph, E> {
+    pub index: EdgeIndex,
+    pub edge: &'graph Edge<E>,
+}
+
+#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
+pub struct EdgeIndex(pub usize);
+//  {
+//     // TODO: they could all be u16 instead
+//     // There may be a way to store all the edge indices in a u32 as well,
+//     // if the edges are in a vector
+//     // then we can store sets of edges in a bitmap efficiently
+//     pub from: usize,
+//     pub to: usize,
+//     pub edge_idx: usize,
+// }
+
+pub trait RankingRuleGraphTrait {
+    type EdgeDetails: Sized;
+    type BuildVisitedFromNode;
+
+    fn edge_details_dot_label(edge: &Self::EdgeDetails) -> String;
+
+    fn compute_docids<'transaction>(
+        index: &Index,
+        txn: &'transaction RoTxn,
+        db_cache: &mut DatabaseCache<'transaction>,
+        edge_details: &Self::EdgeDetails,
+    ) -> Result<RoaringBitmap>;
+
+    fn build_visit_from_node<'transaction>(
+        index: &Index,
+        txn: &'transaction RoTxn,
+        db_cache: &mut DatabaseCache<'transaction>,
+        from_node: &QueryNode,
+    ) -> Result<Option<Self::BuildVisitedFromNode>>;
+
+    fn build_visit_to_node<'from_data, 'transaction: 'from_data>(
+        index: &Index,
+        txn: &'transaction RoTxn,
+        db_cache: &mut DatabaseCache<'transaction>,
+        to_node: &QueryNode,
+        from_node_data: &'from_data Self::BuildVisitedFromNode,
+    ) -> Result<Option<Vec<(u8, EdgeDetails<Self::EdgeDetails>)>>>;
+}
+
+pub struct RankingRuleGraph<G: RankingRuleGraphTrait> {
+    pub query_graph: QueryGraph,
+    // pub edges: Vec<HashMap<usize, Vec<Edge<G::EdgeDetails>>>>,
+    pub all_edges: Vec<Option<Edge<G::EdgeDetails>>>,
+    pub node_edges: Vec<BTreeSet<usize>>,
+    // pub removed_edges: HashSet<EdgeIndex>,
+    // pub tmp_removed_edges: HashSet<EdgeIndex>,
+}
+impl<G: RankingRuleGraphTrait> RankingRuleGraph<G> {
+    // NOTE: returns the edge even if it was removed
+    pub fn get_edge(&self, edge_index: EdgeIndex) -> &Option<Edge<G::EdgeDetails>> {
+        &self.all_edges[edge_index.0]
+    }
+    pub fn visit_edges<'graph, O>(
+        &'graph self,
+        from: usize,
+        to: usize,
+        mut visit: impl FnMut(EdgeIndex, &'graph Edge<G::EdgeDetails>) -> ControlFlow<O>,
+    ) -> Option<O> {
+        let from_edges = &self.node_edges[from];
+        for &edge_idx in from_edges {
+            let edge = self.all_edges[edge_idx].as_ref().unwrap();
+            if edge.to_node == to {
+                let cf = visit(EdgeIndex(edge_idx), edge);
+                match cf {
+                    ControlFlow::Continue(_) => continue,
+                    ControlFlow::Break(o) => return Some(o),
+                }
+            }
+        }
+
+        None
+    }
+
+    fn remove_edge(&mut self, edge_index: EdgeIndex) {
+        let edge_opt = &mut self.all_edges[edge_index.0];
+        let Some(Edge { from_node, to_node, cost, details }) = &edge_opt else { return };
+
+        let node_edges = &mut self.node_edges[*from_node];
+        node_edges.remove(&edge_index.0);
+
+        *edge_opt = None;
+    }
+    pub fn remove_nodes(&mut self, nodes: &[usize]) {
+        for &node in nodes {
+            let edge_indices = &mut self.node_edges[node];
+            for edge_index in edge_indices.iter() {
+                self.all_edges[*edge_index] = None;
+            }
+            edge_indices.clear();
+
+            let preds = &self.query_graph.edges[node].incoming;
+            for pred in preds {
+                let edge_indices = &mut self.node_edges[*pred];
+                for edge_index in edge_indices.iter() {
+                    let edge_opt = &mut self.all_edges[*edge_index];
+                    let Some(edge) = edge_opt else { continue; };
+                    if edge.to_node == node {
+                        *edge_opt = None;
+                    }
+                }
+                panic!("remove nodes is incorrect at the moment");
+                edge_indices.clear();
+            }
+        }
+        self.query_graph.remove_nodes(nodes);
+    }
+    pub fn simplify(&mut self) {
+        loop {
+            let mut nodes_to_remove = vec![];
+            for (node_idx, node) in self.query_graph.nodes.iter().enumerate() {
+                if !matches!(node, QueryNode::End | QueryNode::Deleted)
+                    && self.node_edges[node_idx].is_empty()
+                {
+                    nodes_to_remove.push(node_idx);
+                }
+            }
+            if nodes_to_remove.is_empty() {
+                break;
+            } else {
+                self.remove_nodes(&nodes_to_remove);
+            }
+        }
+    }
+    // fn is_removed_edge(&self, edge: EdgeIndex) -> bool {
+    //     self.removed_edges.contains(&edge) || self.tmp_removed_edges.contains(&edge)
+    // }
+
+    pub fn graphviz(&self) -> String {
+        let mut desc = String::new();
+        desc.push_str("digraph G {\nrankdir = LR;\nnode [shape = \"record\"]\n");
+
+        for (node_idx, node) in self.query_graph.nodes.iter().enumerate() {
+            if matches!(node, QueryNode::Deleted) {
+                continue;
+            }
+            desc.push_str(&format!("{node_idx} [label = {:?}]", node));
+            if node_idx == self.query_graph.root_node {
+                desc.push_str("[color = blue]");
+            } else if node_idx == self.query_graph.end_node {
+                desc.push_str("[color = red]");
+            }
+            desc.push_str(";\n");
+        }
+        for edge in self.all_edges.iter().flatten() {
+            let Edge { from_node, to_node, cost, details } = edge;
+
+            match &details {
+                EdgeDetails::Unconditional => {
+                    desc.push_str(&format!(
+                        "{from_node} -> {to_node} [label = \"always cost {cost}\"];\n",
+                        cost = edge.cost,
+                    ));
+                }
+                EdgeDetails::Data(details) => {
+                    desc.push_str(&format!(
+                        "{from_node} -> {to_node} [label = \"cost {cost} {edge_label}\"];\n",
+                        cost = edge.cost,
+                        edge_label = G::edge_details_dot_label(details)
+                    ));
+                }
+            }
+        }
+
+        desc.push('}');
+        desc
+    }
+}