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Graph traversal optimization

apache/mxnet
Based on 4 comments
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When working with graph structures, avoid performing redundant depth-first search (DFS) traversals as each traversal incurs an O(V+E) complexity cost. Instead, consider:

Algorithms Other

Reviewer Prompt

When working with graph structures, avoid performing redundant depth-first search (DFS) traversals as each traversal incurs an O(V+E) complexity cost. Instead, consider:

  1. Label nodes during initial traversal to maintain state information for subsequent operations
  2. Cache traversal order to avoid repeating the same path exploration
  3. Batch related operations that can be performed in a single pass
  4. Create graph copies when modifications might affect future traversals

For example, instead of:

// Multiple independent DFS calls on the same graph structure
for (auto pattern : patterns) {
  DFSVisit(sym.outputs, [&](const nnvm::ObjectPtr &node) {
    if (node->is_variable()) return;
    // Find nodes matching pattern
  });
}

Consider:

// Single traversal with collected state
std::vector<nnvm::ObjectPtr> traversal_order;
std::unordered_map<nnvm::ObjectPtr, int> node_labels;

DFSVisit(sym.outputs, [&](const nnvm::ObjectPtr &node) {
  if (node->is_variable()) return;
  traversal_order.push_back(node);
  // Label nodes as needed
});

// Now use cached traversal for pattern matching without repeating DFS
for (auto pattern : patterns) {
  for (const auto& node : traversal_order) {
    // Match against patterns
  }
}

This approach significantly reduces computational complexity when multiple operations or pattern matching need to be performed on the same graph structure.

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