valhalla-0001: linkclassification.cc — IsSlipLane() nested linear scan O(F×R)

File

src/mjolnir/linkclassification.cc

Severity

MEDIUM

Lines Affected

Lines 658–662: std::find(forward_nodes.begin(), forward_nodes.end(), node) inside for (auto node : reverse_nodes) loop

Defective Code

// IsSlipLane() — lines 648–673
bool IsSlipLane(Data& data, SlipLaneInput input, double traverse_threshold) {
  auto forward_nodes =
      GoTowardsIntersection(input.first_node, input.fork_edge, true, traverse_threshold, data);
  auto reverse_nodes =
      GoTowardsIntersection(input.last_node, input.merge_edge, false, traverse_threshold, data);

  // O(R × F) — for each of R reverse nodes, linear scan over F forward nodes
  std::optional<uint32_t> intersection_node;
  for (auto node : reverse_nodes) {
    if (std::find(forward_nodes.begin(), forward_nodes.end(), node) != forward_nodes.end()) {
      intersection_node = node;
      break;
    }
  }
  return intersection_node != std::nullopt;
}

forward_nodes and reverse_nodes are std::vector<uint32_t>. For each node in reverse_nodes (up to R nodes), std::find does a linear scan over forward_nodes (up to F nodes). Total work: O(R × F).

Note: GoTowardsIntersection already uses an std::unordered_set<size_t> for its own visited tracking, so visited tracking is O(1) there — but the intersection check reverts to O(N²).

IsSlipLane is called during graph tile building (mjolnir) for every candidate link edge in the OSM road network. Dense urban areas may have thousands of slip lane candidates, and the traverse threshold controls path lengths. At high thresholds both vectors can reach hundreds of nodes.

Complexity Analysis

Path	Per intersection check	Call frequency	Overall
Slow (std::find on vector)	O(F × R)	per link edge	O(L × F × R)
Fast (unordered_set lookup)	O(R)	per link edge	O(L × R)

Where L = number of link edges, F = forward path length, R = reverse path length. At traverse_threshold = 200m and urban density, F and R can each reach ~50 nodes, giving 2500× overhead per link check vs O(R).

Fixed Code

bool IsSlipLane(Data& data, SlipLaneInput input, double traverse_threshold) {
  auto forward_nodes =
      GoTowardsIntersection(input.first_node, input.fork_edge, true, traverse_threshold, data);
  auto reverse_nodes =
      GoTowardsIntersection(input.last_node, input.merge_edge, false, traverse_threshold, data);

  // Build O(1) lookup set from forward_nodes
  std::unordered_set<uint32_t> forward_set(forward_nodes.begin(), forward_nodes.end());

  std::optional<uint32_t> intersection_node;
  for (auto node : reverse_nodes) {
    if (forward_set.count(node)) {   // O(1) instead of O(F)
      intersection_node = node;
      break;
    }
  }
  return intersection_node != std::nullopt;
}

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