From 0f13269040594c5a3b14aa75df5740e568cdc77f Mon Sep 17 00:00:00 2001
From: NiccoloN <niccolo.nicolosi@gmail.com>
Date: Tue, 21 Apr 2026 18:36:16 +0200
Subject: [PATCH] faster DCPAnalysis on partial graph

---
 src/PIM/Compiler/PimCompilerOptions.cpp       |   6 +
 src/PIM/Compiler/PimCompilerOptions.hpp       |   1 +
 .../DCPGraph/DCPAnalysis.cpp                  | 402 +++++++++++++++++-
 .../MergeComputeNodes/DCPGraph/Graph.cpp      |   7 +-
 4 files changed, 406 insertions(+), 10 deletions(-)

diff --git a/src/PIM/Compiler/PimCompilerOptions.cpp b/src/PIM/Compiler/PimCompilerOptions.cpp
index e13af09..7f4b18c 100644
--- a/src/PIM/Compiler/PimCompilerOptions.cpp
+++ b/src/PIM/Compiler/PimCompilerOptions.cpp
@@ -47,6 +47,12 @@ llvm::cl::opt<long> coresCount("core-count",
                                llvm::cl::desc("Number of cores in the chip. `-1` to use the minimum amount of cores."),
                                llvm::cl::init(-1));
 
+llvm::cl::opt<size_t> dcpCriticalWindowSize(
+  "dcp-critical-window-size",
+  llvm::cl::desc("Number of lowest-slack virtual nodes considered by each DCP coarsening iteration. "
+                 "Use 0 to run the legacy full-graph DCP analysis."),
+  llvm::cl::init(1024));
+
 llvm::cl::opt<bool>
   ignoreConcatError("ignore-concat-error",
                     llvm::cl::desc("Ignore ConcatOp corner case: do not assert and do a simplification"),
diff --git a/src/PIM/Compiler/PimCompilerOptions.hpp b/src/PIM/Compiler/PimCompilerOptions.hpp
index ab79c1f..e1f6c6a 100644
--- a/src/PIM/Compiler/PimCompilerOptions.hpp
+++ b/src/PIM/Compiler/PimCompilerOptions.hpp
@@ -29,6 +29,7 @@ extern llvm::cl::opt<bool> useExperimentalConvImpl;
 extern llvm::cl::opt<size_t> crossbarSize;
 extern llvm::cl::opt<size_t> crossbarCountInCore;
 extern llvm::cl::opt<long> coresCount;
+extern llvm::cl::opt<size_t> dcpCriticalWindowSize;
 
 // This option, by default set to false, will ignore an error when resolving a
 // specific tiles of the operands of a concat. This specific case is when the
diff --git a/src/PIM/Dialect/Spatial/Transforms/MergeComputeNodes/DCPGraph/DCPAnalysis.cpp b/src/PIM/Dialect/Spatial/Transforms/MergeComputeNodes/DCPGraph/DCPAnalysis.cpp
index 0c0c5a7..bf03e56 100644
--- a/src/PIM/Dialect/Spatial/Transforms/MergeComputeNodes/DCPGraph/DCPAnalysis.cpp
+++ b/src/PIM/Dialect/Spatial/Transforms/MergeComputeNodes/DCPGraph/DCPAnalysis.cpp
@@ -6,10 +6,18 @@
 #include "llvm/ADT/STLExtras.h"
 #include "llvm/Support/Casting.h"
 
+#include <algorithm>
 #include <iterator>
+#include <map>
+#include <numeric>
+#include <optional>
+#include <set>
+#include <utility>
+#include <vector>
 
 #include "DCPAnalysis.hpp"
 #include "Graph.hpp"
+#include "src/Accelerators/PIM/Compiler/PimCompilerOptions.hpp"
 #include "src/Support/TypeUtilities.hpp"
 
 namespace onnx_mlir {
@@ -17,6 +25,361 @@ namespace spatial {
 
 using namespace mlir;
 
+namespace {
+
+struct VirtualNode {
+  llvm::SmallVector<size_t, 4> originalComputeIndices;
+  Weight weight = 0;
+  CrossbarUsage crossbarUsage = 0;
+};
+
+struct VirtualGraph {
+  std::vector<VirtualNode> nodes;
+  std::vector<IndexedEdge> edges;
+};
+
+struct TimingInfo {
+  std::vector<Time> aest;
+  std::vector<Time> alst;
+  std::vector<size_t> topologicalOrder;
+  bool valid = false;
+};
+
+struct WindowScheduleResult {
+  std::vector<std::vector<size_t>> mergeGroups;
+  bool usedAllAvailableCpus = false;
+};
+
+std::vector<IndexedEdge> aggregateEdges(llvm::ArrayRef<IndexedEdge> edges) {
+  std::map<std::pair<size_t, size_t>, Weight> edgeWeights;
+  for (auto [start, end, weight] : edges) {
+    size_t startIndex = static_cast<size_t>(start);
+    size_t endIndex = static_cast<size_t>(end);
+    if (startIndex == endIndex)
+      continue;
+    auto key = std::make_pair(startIndex, endIndex);
+    Weight edgeWeight = static_cast<Weight>(weight);
+    auto it = edgeWeights.find(key);
+    if (it == edgeWeights.end())
+      edgeWeights.insert({key, edgeWeight});
+    else
+      it->second = std::max(it->second, edgeWeight);
+  }
+
+  std::vector<IndexedEdge> aggregatedEdges;
+  aggregatedEdges.reserve(edgeWeights.size());
+  for (auto [key, weight] : edgeWeights)
+    aggregatedEdges.push_back(
+      {static_cast<int64_t>(key.first), static_cast<int64_t>(key.second), static_cast<int64_t>(weight)});
+  return aggregatedEdges;
+}
+
+VirtualGraph buildInitialVirtualGraph(llvm::ArrayRef<SpatWeightedCompute> spatWeightedComputes,
+                                      llvm::ArrayRef<IndexedEdge> edges) {
+  VirtualGraph graph;
+  graph.nodes.reserve(spatWeightedComputes.size());
+  for (auto [index, spatWeightedCompute] : llvm::enumerate(spatWeightedComputes)) {
+    VirtualNode node;
+    node.originalComputeIndices.push_back(index);
+    node.weight = getSpatComputeWeight(spatWeightedCompute);
+    node.crossbarUsage = getSpatComputeCrossbarUsage(spatWeightedCompute);
+    graph.nodes.push_back(std::move(node));
+  }
+  graph.edges = aggregateEdges(edges);
+  return graph;
+}
+
+TimingInfo computeTiming(const VirtualGraph& graph) {
+  TimingInfo timing;
+  size_t nodeCount = graph.nodes.size();
+  timing.aest.assign(nodeCount, 0);
+  timing.alst.assign(nodeCount, 0);
+  timing.topologicalOrder.reserve(nodeCount);
+
+  std::vector<std::vector<std::pair<size_t, Weight>>> parents(nodeCount);
+  std::vector<std::vector<std::pair<size_t, Weight>>> children(nodeCount);
+  std::vector<size_t> incomingEdgeCount(nodeCount, 0);
+
+  for (auto [start, end, weight] : graph.edges) {
+    size_t startIndex = static_cast<size_t>(start);
+    size_t endIndex = static_cast<size_t>(end);
+    Weight edgeWeight = static_cast<Weight>(weight);
+    assert(startIndex < nodeCount && endIndex < nodeCount && "virtual edge endpoint out of range");
+    children[startIndex].push_back({endIndex, edgeWeight});
+    parents[endIndex].push_back({startIndex, edgeWeight});
+    incomingEdgeCount[endIndex]++;
+  }
+
+  std::vector<size_t> readyNodes;
+  readyNodes.reserve(nodeCount);
+  for (size_t i = 0; i < nodeCount; ++i)
+    if (incomingEdgeCount[i] == 0)
+      readyNodes.push_back(i);
+
+  size_t readyIndex = 0;
+  while (readyIndex != readyNodes.size()) {
+    size_t current = readyNodes[readyIndex++];
+    timing.topologicalOrder.push_back(current);
+    for (auto [child, weight] : children[current]) {
+      (void) weight;
+      assert(incomingEdgeCount[child] > 0 && "incoming edge count underflow");
+      incomingEdgeCount[child]--;
+      if (incomingEdgeCount[child] == 0)
+        readyNodes.push_back(child);
+    }
+  }
+
+  if (timing.topologicalOrder.size() != nodeCount)
+    return timing;
+
+  Time dcpl = 0;
+  for (size_t nodeIndex : timing.topologicalOrder) {
+    Time maxParentAest = 0;
+    for (auto [parent, transferCost] : parents[nodeIndex]) {
+      maxParentAest =
+        std::max(maxParentAest, addOrMax(addOrMax(timing.aest[parent], graph.nodes[parent].weight), transferCost));
+    }
+    timing.aest[nodeIndex] = maxParentAest;
+    dcpl = std::max(dcpl, addOrMax(maxParentAest, graph.nodes[nodeIndex].weight));
+  }
+
+  for (size_t nodeIndex : llvm::reverse(timing.topologicalOrder)) {
+    Time minAlst = std::numeric_limits<Time>::max();
+    if (children[nodeIndex].empty())
+      minAlst = subtractOrZero(dcpl, graph.nodes[nodeIndex].weight);
+    for (auto [child, transferCost] : children[nodeIndex]) {
+      minAlst =
+        std::min(minAlst, subtractOrZero(timing.alst[child], addOrMax(graph.nodes[nodeIndex].weight, transferCost)));
+    }
+    timing.alst[nodeIndex] = minAlst;
+  }
+
+  timing.valid = true;
+  return timing;
+}
+
+std::vector<size_t> selectCriticalWindow(const TimingInfo& timing, size_t windowSize) {
+  std::vector<size_t> selected(timing.aest.size());
+  std::iota(selected.begin(), selected.end(), 0);
+  std::stable_sort(selected.begin(), selected.end(), [&](size_t lhs, size_t rhs) {
+    Time lhsSlack = slackOrZero(timing.aest[lhs], timing.alst[lhs]);
+    Time rhsSlack = slackOrZero(timing.aest[rhs], timing.alst[rhs]);
+    if (lhsSlack != rhsSlack)
+      return lhsSlack < rhsSlack;
+    if (timing.aest[lhs] != timing.aest[rhs])
+      return timing.aest[lhs] < timing.aest[rhs];
+    return lhs < rhs;
+  });
+  selected.resize(std::min(windowSize, selected.size()));
+  return selected;
+}
+
+std::vector<size_t> getOriginalSignature(const VirtualGraph& graph, llvm::ArrayRef<size_t> selectedNodes) {
+  std::vector<size_t> signature;
+  for (size_t nodeIndex : selectedNodes) {
+    const VirtualNode& node = graph.nodes[nodeIndex];
+    signature.insert(signature.end(), node.originalComputeIndices.begin(), node.originalComputeIndices.end());
+  }
+  std::sort(signature.begin(), signature.end());
+  return signature;
+}
+
+std::vector<IndexedEdge> buildWindowEdges(const VirtualGraph& graph, const std::vector<int64_t>& nodeToWindowIndex) {
+  std::vector<IndexedEdge> windowEdges;
+  windowEdges.reserve(graph.edges.size());
+  for (auto [start, end, weight] : graph.edges) {
+    int64_t mappedStart = nodeToWindowIndex[static_cast<size_t>(start)];
+    int64_t mappedEnd = nodeToWindowIndex[static_cast<size_t>(end)];
+    if (mappedStart == -1 || mappedEnd == -1)
+      continue;
+    windowEdges.push_back({mappedStart, mappedEnd, weight});
+  }
+  return aggregateEdges(windowEdges);
+}
+
+WindowScheduleResult
+scheduleWindow(const VirtualGraph& graph, llvm::ArrayRef<size_t> selectedNodes, MLIRContext* context) {
+  std::vector<Weight> windowWeights;
+  std::vector<CrossbarUsage> windowCrossbarUsage;
+  std::vector<int64_t> nodeToWindowIndex(graph.nodes.size(), -1);
+  windowWeights.reserve(selectedNodes.size());
+  windowCrossbarUsage.reserve(selectedNodes.size());
+
+  for (auto [windowIndex, nodeIndex] : llvm::enumerate(selectedNodes)) {
+    nodeToWindowIndex[nodeIndex] = static_cast<int64_t>(windowIndex);
+    windowWeights.push_back(graph.nodes[nodeIndex].weight);
+    windowCrossbarUsage.push_back(graph.nodes[nodeIndex].crossbarUsage);
+  }
+
+  GraphDCP windowGraph(windowWeights, buildWindowEdges(graph, nodeToWindowIndex), windowCrossbarUsage);
+  if (coresCount.getValue() > 0)
+    windowGraph.setMaxCpuCount(static_cast<int>(coresCount.getValue()));
+  windowGraph.setContext(context);
+  windowGraph.runDcp();
+
+  WindowScheduleResult result;
+  result.usedAllAvailableCpus = windowGraph.cpuCount() >= windowGraph.getMaxCpuCount();
+  for (CPU cpu = 0; cpu < windowGraph.cpuCount(); ++cpu) {
+    auto scheduledTasks = windowGraph.getScheduledTasks(cpu);
+    if (scheduledTasks.size() < 2)
+      continue;
+
+    std::vector<size_t> mergeGroup;
+    mergeGroup.reserve(scheduledTasks.size());
+    for (const auto& task : scheduledTasks)
+      mergeGroup.push_back(selectedNodes[task.nodeIndex]);
+    std::sort(mergeGroup.begin(), mergeGroup.end());
+    result.mergeGroups.push_back(std::move(mergeGroup));
+  }
+  return result;
+}
+
+bool coarsenGraph(const VirtualGraph& graph,
+                  llvm::ArrayRef<std::vector<size_t>> mergeGroups,
+                  VirtualGraph& coarsenedGraph) {
+  std::vector<int64_t> nodeToMergeGroup(graph.nodes.size(), -1);
+  for (auto [groupIndex, mergeGroup] : llvm::enumerate(mergeGroups)) {
+    if (mergeGroup.size() < 2)
+      continue;
+    for (size_t nodeIndex : mergeGroup) {
+      assert(nodeIndex < graph.nodes.size() && "merge group node out of range");
+      nodeToMergeGroup[nodeIndex] = static_cast<int64_t>(groupIndex);
+    }
+  }
+
+  std::vector<std::optional<size_t>> mergeGroupToNewNode(mergeGroups.size());
+  std::vector<size_t> oldToNewNode(graph.nodes.size(), 0);
+  bool mergedAny = false;
+  coarsenedGraph.nodes.clear();
+  coarsenedGraph.edges.clear();
+  coarsenedGraph.nodes.reserve(graph.nodes.size());
+
+  for (size_t nodeIndex = 0; nodeIndex < graph.nodes.size(); ++nodeIndex) {
+    int64_t mergeGroupIndex = nodeToMergeGroup[nodeIndex];
+    if (mergeGroupIndex == -1) {
+      oldToNewNode[nodeIndex] = coarsenedGraph.nodes.size();
+      coarsenedGraph.nodes.push_back(graph.nodes[nodeIndex]);
+      continue;
+    }
+
+    auto& newNodeIndex = mergeGroupToNewNode[static_cast<size_t>(mergeGroupIndex)];
+    if (newNodeIndex.has_value()) {
+      oldToNewNode[nodeIndex] = *newNodeIndex;
+      continue;
+    }
+
+    VirtualNode mergedNode;
+    for (size_t memberIndex : mergeGroups[static_cast<size_t>(mergeGroupIndex)]) {
+      const VirtualNode& memberNode = graph.nodes[memberIndex];
+      mergedNode.originalComputeIndices.append(memberNode.originalComputeIndices.begin(),
+                                               memberNode.originalComputeIndices.end());
+      mergedNode.weight = addOrMax(mergedNode.weight, memberNode.weight);
+      mergedNode.crossbarUsage = addOrMax(mergedNode.crossbarUsage, memberNode.crossbarUsage);
+    }
+    std::sort(mergedNode.originalComputeIndices.begin(), mergedNode.originalComputeIndices.end());
+
+    mergedAny = true;
+    newNodeIndex = coarsenedGraph.nodes.size();
+    for (size_t memberIndex : mergeGroups[static_cast<size_t>(mergeGroupIndex)])
+      oldToNewNode[memberIndex] = *newNodeIndex;
+    coarsenedGraph.nodes.push_back(std::move(mergedNode));
+  }
+
+  if (!mergedAny)
+    return false;
+
+  std::vector<IndexedEdge> remappedEdges;
+  remappedEdges.reserve(graph.edges.size());
+  for (auto [start, end, weight] : graph.edges) {
+    size_t newStart = oldToNewNode[static_cast<size_t>(start)];
+    size_t newEnd = oldToNewNode[static_cast<size_t>(end)];
+    if (newStart == newEnd)
+      continue;
+    remappedEdges.push_back({static_cast<int64_t>(newStart), static_cast<int64_t>(newEnd), weight});
+  }
+  coarsenedGraph.edges = aggregateEdges(remappedEdges);
+
+  return computeTiming(coarsenedGraph).valid;
+}
+
+bool coarsenGraphWithFallback(const VirtualGraph& graph,
+                              llvm::ArrayRef<std::vector<size_t>> mergeGroups,
+                              VirtualGraph& coarsenedGraph) {
+  if (coarsenGraph(graph, mergeGroups, coarsenedGraph))
+    return true;
+
+  std::vector<size_t> orderedGroupIndices(mergeGroups.size());
+  std::iota(orderedGroupIndices.begin(), orderedGroupIndices.end(), 0);
+  std::stable_sort(orderedGroupIndices.begin(), orderedGroupIndices.end(), [&](size_t lhs, size_t rhs) {
+    return mergeGroups[lhs].size() > mergeGroups[rhs].size();
+  });
+
+  std::vector<std::vector<size_t>> acceptedMergeGroups;
+  acceptedMergeGroups.reserve(mergeGroups.size());
+  for (size_t groupIndex : orderedGroupIndices) {
+    std::vector<std::vector<size_t>> candidateMergeGroups = acceptedMergeGroups;
+    candidateMergeGroups.push_back(mergeGroups[groupIndex]);
+
+    VirtualGraph candidateGraph;
+    if (!coarsenGraph(graph, candidateMergeGroups, candidateGraph))
+      continue;
+
+    acceptedMergeGroups = std::move(candidateMergeGroups);
+    coarsenedGraph = std::move(candidateGraph);
+  }
+  return !acceptedMergeGroups.empty();
+}
+
+std::vector<size_t> computeOriginalTopologicalOrder(size_t computeCount, llvm::ArrayRef<IndexedEdge> edges) {
+  VirtualGraph graph;
+  graph.nodes.resize(computeCount);
+  graph.edges = aggregateEdges(edges);
+  TimingInfo timing = computeTiming(graph);
+  if (timing.valid)
+    return timing.topologicalOrder;
+
+  std::vector<size_t> fallbackOrder(computeCount);
+  std::iota(fallbackOrder.begin(), fallbackOrder.end(), 0);
+  return fallbackOrder;
+}
+
+DCPAnalysisResult buildResultFromVirtualGraph(const VirtualGraph& graph,
+                                              llvm::ArrayRef<SpatWeightedCompute> spatWeightedComputes,
+                                              llvm::ArrayRef<IndexedEdge> originalEdges) {
+  DCPAnalysisResult result;
+  std::vector<size_t> originalToVirtualNode(spatWeightedComputes.size(), 0);
+  for (auto [virtualNodeIndex, virtualNode] : llvm::enumerate(graph.nodes))
+    for (size_t originalIndex : virtualNode.originalComputeIndices)
+      originalToVirtualNode[originalIndex] = virtualNodeIndex;
+
+  auto dominanceOrder = computeOriginalTopologicalOrder(spatWeightedComputes.size(), originalEdges);
+  result.dominanceOrderCompute.reserve(dominanceOrder.size());
+  for (size_t originalIndex : dominanceOrder) {
+    SpatWeightedCompute spatWeightedCompute = spatWeightedComputes[originalIndex];
+    size_t cpu = originalToVirtualNode[originalIndex];
+    result.dominanceOrderCompute.push_back(spatWeightedCompute);
+    result.computeToCpuMap[spatWeightedCompute] = cpu;
+    result.cpuToLastComputeMap[cpu] = spatWeightedCompute;
+  }
+
+  for (auto [cpu, lastCompute] : result.cpuToLastComputeMap)
+    result.isLastComputeOfCpu.insert(lastCompute);
+  return result;
+}
+
+DCPAnalysisResult runLegacyDcp(llvm::ArrayRef<SpatWeightedCompute> spatWeightedComputes,
+                               llvm::ArrayRef<IndexedEdge> edges,
+                               MLIRContext* context) {
+  GraphDCP graphDCP(spatWeightedComputes, edges);
+  if (coresCount.getValue() > 0)
+    graphDCP.setMaxCpuCount(static_cast<int>(coresCount.getValue()));
+  graphDCP.setContext(context);
+  graphDCP.runDcp();
+  return graphDCP.getResult();
+}
+
+} // namespace
+
 SpatWeightedCompute getOriginalSpatWeightedCompute(Operation* op) {
   if (!op)
     return {};
@@ -31,8 +394,8 @@ SpatWeightedCompute getOriginalSpatWeightedCompute(Operation* op) {
 }
 
 DCPAnalysisResult DCPAnalysis::run() {
-  llvm::SmallVector<SpatWeightedCompute, 10> spatWeightedComputes;
-  llvm::SmallVector<IndexedEdge, 10> edges;
+  SmallVector<SpatWeightedCompute, 10> spatWeightedComputes;
+  SmallVector<IndexedEdge, 10> edges;
   for (auto& region : entryOp->getRegions())
     for (SpatWeightedCompute spatWeightedCompute : region.getOps<SpatWeightedCompute>())
       spatWeightedComputes.push_back(spatWeightedCompute);
@@ -53,10 +416,37 @@ DCPAnalysisResult DCPAnalysis::run() {
       }
     }
   }
-  GraphDCP graphDCP(spatWeightedComputes, edges);
-  graphDCP.setContext(entryOp->getContext());
-  graphDCP.runDcp();
-  return graphDCP.getResult();
+
+  if (dcpCriticalWindowSize.getValue() == 0)
+    return runLegacyDcp(spatWeightedComputes, edges, entryOp->getContext());
+
+  VirtualGraph virtualGraph = buildInitialVirtualGraph(spatWeightedComputes, edges);
+  std::set<std::vector<size_t>> seenCriticalWindows;
+  while (virtualGraph.nodes.size() > 1) {
+    TimingInfo timing = computeTiming(virtualGraph);
+    if (!timing.valid)
+      break;
+
+    auto selectedNodes = selectCriticalWindow(timing, dcpCriticalWindowSize.getValue());
+    if (selectedNodes.size() < 2)
+      break;
+
+    if (!seenCriticalWindows.insert(getOriginalSignature(virtualGraph, selectedNodes)).second)
+      break;
+
+    WindowScheduleResult windowSchedule = scheduleWindow(virtualGraph, selectedNodes, entryOp->getContext());
+    if (windowSchedule.mergeGroups.empty())
+      break;
+
+    VirtualGraph coarsenedGraph;
+    if (!coarsenGraphWithFallback(virtualGraph, windowSchedule.mergeGroups, coarsenedGraph))
+      break;
+    virtualGraph = std::move(coarsenedGraph);
+    if (windowSchedule.usedAllAvailableCpus)
+      break;
+  }
+
+  return buildResultFromVirtualGraph(virtualGraph, spatWeightedComputes, edges);
 }
 
 } // namespace spatial
diff --git a/src/PIM/Dialect/Spatial/Transforms/MergeComputeNodes/DCPGraph/Graph.cpp b/src/PIM/Dialect/Spatial/Transforms/MergeComputeNodes/DCPGraph/Graph.cpp
index 0056071..dfbf6fd 100644
--- a/src/PIM/Dialect/Spatial/Transforms/MergeComputeNodes/DCPGraph/Graph.cpp
+++ b/src/PIM/Dialect/Spatial/Transforms/MergeComputeNodes/DCPGraph/Graph.cpp
@@ -6,7 +6,7 @@
 // consumer land on different CPUs.
 //
 // Output: an assignment of every task to a CPU and an order within that CPU,
-// aiming to minimise the overall critical-path length (DCPL).
+// aiming to minimize the overall critical-path length (DCPL).
 //
 // Every task keeps two timing estimates:
 //   AEST - earliest start time, driven by parent completions + transfers.
@@ -16,9 +16,9 @@
 // Main loop (runDcp):
 //   1. Build a topological order and seed AEST/ALST from the unscheduled DAG.
 //   2. While there are ready tasks (all dependency parents scheduled):
-//        a. Pick the candidate with tightest slack (earliest AEST breaks ties).
+//        a. Pick the candidate with the tightest slack (earliest AEST breaks ties).
 //        b. selectProcessor() tries every candidate CPU and picks the one that
-//           minimises a composite cost (own slot + smallest unscheduled child).
+//           minimizes a composite cost (own slot + the smallest unscheduled child).
 //        c. Commit the placement and refresh AEST/ALST.
 //        d. Release any child whose dependency parents are now all scheduled.
 //
@@ -43,7 +43,6 @@
 #include <cassert>
 #include <chrono>
 #include <cstdio>
-#include <cstdlib>
 #include <vector>
 
 #include "DCPAnalysis.hpp"