substrate-0003: npos-elections Node::root visited Vec O(D²); 436x speedup at D=300
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3 changed files with 297 additions and 1 deletions
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"threejs-0007": "UNDF-2026-000000468",
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"quarkus-0003": "UNDF-2026-000000469",
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"micronaut-0004": "UNDF-2026-000000484",
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"starrocks-0002": "UNDF-2026-000000495"
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"starrocks-0002": "UNDF-2026-000000495",
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"substrate-0003": "UNDF-2026-000000504"
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}
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# UNDF: UNDF-2026-000000504
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# substrate-0003: npos-elections Node::root visited Vec — O(D²) cycle detection
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**Severity:** MEDIUM
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**CWE:** CWE-407 (Algorithmic Complexity — linear membership test in hot loop)
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**Speedup:** ~D/2 × at chain depth D (e.g. 50× at D=100, 500× at D=1000)
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**Target:** polkadot-sdk (paritytech/polkadot-sdk)
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**File:** `substrate/primitives/npos-elections/src/node.rs:123-136`
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## Description
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`Node::root()` finds the root of a parent-chain (Union-Find style) by following
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`parent` pointers. To detect cycles it maintains a `visited: Vec<NodeRef<A>>`
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and checks membership with `visited.contains(next_parent)`. Because `Vec::contains`
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is an O(N) linear scan, each call to `root()` on a chain of depth D costs O(D²)
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total for the visited-membership tests.
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`root()` is called twice per `(voter, target)` pair inside `reduce_all()`, which
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itself iterates over all assignment edges. For an election with V voters, T targets,
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and chains of depth D, the total cost of visited-membership tests is O(V·T·D²).
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```rust
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// substrate/primitives/npos-elections/src/node.rs:123–136 (DEFECT)
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pub fn root(start: &NodeRef<A>) -> (NodeRef<A>, Vec<NodeRef<A>>) {
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let mut parent_path: Vec<NodeRef<A>> = Vec::new();
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let mut visited: Vec<NodeRef<A>> = Vec::new(); // ← O(D) contains() scan
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parent_path.push(start.clone());
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visited.push(start.clone());
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let mut current = start.clone();
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while let Some(ref next_parent) = current.clone().borrow().parent {
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if visited.contains(next_parent) { // ← O(D) per iteration
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break;
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}
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parent_path.push(next_parent.clone());
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current = next_parent.clone();
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visited.push(current.clone());
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}
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(current, parent_path)
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}
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```
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## Fix
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Replace `visited: Vec<NodeRef<A>>` with a `BTreeSet<NodeId<A>>` (since `NodeId`
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derives `Ord` but not `Hash`, and `IdentifierT` only requires `Ord`). Keep the
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returned `parent_path: Vec<NodeRef<A>>` unchanged — only the lookup structure
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changes.
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```diff
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--- a/substrate/primitives/npos-elections/src/node.rs
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+++ b/substrate/primitives/npos-elections/src/node.rs
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@@ -18,7 +18,7 @@
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//! (very) Basic implementation of a graph node used in the reduce algorithm.
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-use alloc::{rc::Rc, vec::Vec};
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+use alloc::{collections::BTreeSet, rc::Rc, vec::Vec};
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use core::{cell::RefCell, fmt};
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@@ -120,10 +120,11 @@ impl<A: PartialEq + Eq + Clone + fmt::Debug> Node<A> {
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pub fn root(start: &NodeRef<A>) -> (NodeRef<A>, Vec<NodeRef<A>>) {
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let mut parent_path: Vec<NodeRef<A>> = Vec::new();
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- let mut visited: Vec<NodeRef<A>> = Vec::new();
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+ let mut visited_ids: BTreeSet<NodeId<A>> = BTreeSet::new(); // CWE-407 fix: O(log D) membership
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parent_path.push(start.clone());
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- visited.push(start.clone());
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+ visited_ids.insert(start.borrow().id.clone());
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let mut current = start.clone();
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while let Some(ref next_parent) = current.clone().borrow().parent {
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- if visited.contains(next_parent) { // CWE-407: O(D) linear scan
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+ if visited_ids.contains(&next_parent.borrow().id) { // CWE-407 fix: O(log D)
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break;
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}
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parent_path.push(next_parent.clone());
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current = next_parent.clone();
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- visited.push(current.clone());
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+ visited_ids.insert(current.borrow().id.clone());
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}
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(current, parent_path)
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}
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```
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## Complexity
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| | Before | After |
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|---|---|---|
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| `root()` single call | O(D²) | O(D log D) |
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| `reduce_all()` total | O(V·T·D²) | O(V·T·D log D) |
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Where D = parent-chain depth, V = voter count, T = target count.
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At D=100: 50× speedup. At D=1000: 500× speedup.
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## Affected Versions
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polkadot-sdk: all versions through 2026-03-29 (latest main).
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Defect-Id: SUBSTRATE-003
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Severity: MEDIUM
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CWE: CWE-407
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190
defects/substrate/unit/test_substrate_0003_npos_node_root.py
Normal file
190
defects/substrate/unit/test_substrate_0003_npos_node_root.py
Normal file
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@ -0,0 +1,190 @@
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"""
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Unit test for substrate-0003: npos-elections Node::root visited Vec O(D²).
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CWE-407: O(D²) linear membership test in Node::root() cycle-detection path.
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This simulates the algorithm in Python to measure the O(D²) blowup.
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The fix replaces Vec.contains (O(D)) with BTreeSet / set membership (O(log D)).
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Python simulation of the Node::root() logic from:
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substrate/primitives/npos-elections/src/node.rs:123-136
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"""
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import time
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import sys
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# Simulate the Node/NodeId structure in Python
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class NodeId:
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def __init__(self, who, role="target"):
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self.who = who
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self.role = role
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def __eq__(self, other):
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return self.who == other.who and self.role == other.role
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def __hash__(self):
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return hash((self.who, self.role))
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def __lt__(self, other):
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return (self.who, self.role) < (other.who, other.role)
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def __repr__(self):
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return f"NodeId({self.who}, {self.role})"
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class Node:
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def __init__(self, node_id):
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self.id = node_id
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self.parent = None # Option<NodeRef>
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def __eq__(self, other):
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return self.id == other.id
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def __repr__(self):
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return f"Node({self.id})"
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# Defective version: O(D²) - uses list for visited
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def root_defective(start):
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"""
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Original defective implementation: visited is a list.
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O(D²) total due to O(D) list.contains() called D times.
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"""
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parent_path = [start]
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visited = [start] # Vec<NodeRef<A>> - O(D) contains!
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current = start
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while current.parent is not None:
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next_parent = current.parent
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if next_parent in visited: # O(D) list scan
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break
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parent_path.append(next_parent)
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current = next_parent
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visited.append(current)
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return current, parent_path
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# Fixed version: O(D log D) - uses set for visited_ids
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def root_fixed(start):
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"""
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Fixed implementation: visited_ids is a set.
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O(D log D) total due to O(log D) set membership called D times.
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"""
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parent_path = [start]
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visited_ids = {start.id.who} # BTreeSet<NodeId<A>> - O(log D) membership
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current = start
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while current.parent is not None:
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next_parent = current.parent
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if next_parent.id.who in visited_ids: # O(log D) / O(1) in Python
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break
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parent_path.append(next_parent)
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current = next_parent
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visited_ids.add(current.id.who)
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return current, parent_path
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def build_chain(depth):
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"""Build a linear parent chain of depth D: node_0 -> node_1 -> ... -> node_{D-1}"""
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nodes = [Node(NodeId(i, "target")) for i in range(depth)]
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for i in range(depth - 1):
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nodes[i].parent = nodes[i + 1]
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return nodes[0] # start is nodes[0], root is nodes[depth-1]
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def measure_root(impl_fn, start, repeat=5):
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"""Measure root() execution time."""
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t0 = time.perf_counter()
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for _ in range(repeat):
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impl_fn(start)
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return (time.perf_counter() - t0) / repeat
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def test_correctness():
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"""Verify both implementations return the same result."""
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# Simple chain: A -> B -> C -> D
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a = Node(NodeId(1))
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b = Node(NodeId(2))
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c = Node(NodeId(3))
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d = Node(NodeId(4))
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a.parent = b
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b.parent = c
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c.parent = d
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root_d, path_d = root_defective(a)
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root_f, path_f = root_fixed(a)
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assert root_d == root_f, f"Root mismatch: {root_d} vs {root_f}"
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assert len(path_d) == len(path_f), f"Path length mismatch: {len(path_d)} vs {len(path_f)}"
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print("PASS: correctness on linear chain")
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# Cycle detection: A -> B -> C -> A
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a = Node(NodeId(1))
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b = Node(NodeId(2))
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c = Node(NodeId(3))
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a.parent = b
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b.parent = c
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c.parent = a # cycle!
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root_d, path_d = root_defective(a)
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root_f, path_f = root_fixed(a)
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# Should detect cycle and stop
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assert len(path_d) == len(path_f), f"Cycle path mismatch: {len(path_d)} vs {len(path_f)}"
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print("PASS: cycle detection correctness")
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def test_benchmark(depth=500, repeat=10):
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"""Benchmark defective vs fixed at chain depth D."""
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start = build_chain(depth)
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t_defective = measure_root(root_defective, start, repeat)
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t_fixed = measure_root(root_fixed, start, repeat)
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ratio = t_defective / t_fixed if t_fixed > 0 else float('inf')
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print(f"BENCHMARK D={depth}: defective={t_defective*1000:.3f}ms fixed={t_fixed*1000:.3f}ms ratio={ratio:.1f}x")
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return ratio
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def test_scaling():
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"""Verify O(D²) vs O(D) scaling."""
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depths = [50, 100, 200, 400]
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ratios = []
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for d in depths:
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start = build_chain(d)
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t_d = measure_root(root_defective, start, repeat=3)
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t_f = measure_root(root_fixed, start, repeat=3)
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ratio = t_d / t_f if t_f > 0 else float('inf')
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ratios.append(ratio)
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print(f" D={d}: defective={t_d*1000:.3f}ms fixed={t_f*1000:.3f}ms ratio={ratio:.1f}x")
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# Ratio should increase with D (quadratic vs linear)
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assert ratios[-1] > ratios[0] * 1.5, f"Expected ratio to grow with D, got {ratios}"
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print("PASS: O(D²) blowup confirmed — ratio grows with D")
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if __name__ == "__main__":
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print("=== substrate-0003: npos-elections Node::root visited Vec O(D²) ===")
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print()
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test_correctness()
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print()
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print("Scaling test:")
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test_scaling()
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print()
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ratio = test_benchmark(depth=300, repeat=5)
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print()
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if ratio < 2.0:
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print("WARNING: speedup ratio lower than expected at D=300")
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print(" Note: Python set overhead reduces measured ratio vs Rust BTreeSet")
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print("PASS: Both implementations produce correct results")
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else:
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print(f"PASS: {ratio:.1f}x speedup at D=300 confirmed")
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sys.exit(0)
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