diff --git a/gtsam/discrete/DiscreteLookupDAG.cpp b/gtsam/discrete/DiscreteLookupDAG.cpp
new file mode 100644
index 000000000..37e45de80
--- /dev/null
+++ b/gtsam/discrete/DiscreteLookupDAG.cpp
@@ -0,0 +1,153 @@
+/* ----------------------------------------------------------------------------
+
+ * GTSAM Copyright 2010, Georgia Tech Research Corporation,
+ * Atlanta, Georgia 30332-0415
+ * All Rights Reserved
+ * Authors: Frank Dellaert, et al. (see THANKS for the full author list)
+
+ * See LICENSE for the license information
+
+ * -------------------------------------------------------------------------- */
+
+/**
+ *  @file DiscreteLookupTable.cpp
+ *  @date Feb 14, 2011
+ *  @author Duy-Nguyen Ta
+ *  @author Frank Dellaert
+ */
+
+#include <gtsam/discrete/DiscreteLookupDAG.h>
+#include <gtsam/discrete/DiscreteValues.h>
+
+#include <string>
+#include <utility>
+
+using std::pair;
+using std::vector;
+
+namespace gtsam {
+
+// Instantiate base class
+template class GTSAM_EXPORT
+    Conditional<DecisionTreeFactor, DiscreteLookupTable>;
+
+/* ************************************************************************** */
+// TODO(dellaert): copy/paste from DiscreteConditional.cpp :-(
+void DiscreteLookupTable::print(const std::string& s,
+                                const KeyFormatter& formatter) const {
+  using std::cout;
+  using std::endl;
+
+  cout << s << " g( ";
+  for (const_iterator it = beginFrontals(); it != endFrontals(); ++it) {
+    cout << formatter(*it) << " ";
+  }
+  if (nrParents()) {
+    cout << "; ";
+    for (const_iterator it = beginParents(); it != endParents(); ++it) {
+      cout << formatter(*it) << " ";
+    }
+  }
+  cout << "):\n";
+  ADT::print("", formatter);
+  cout << endl;
+}
+
+/* ************************************************************************* */
+// TODO(dellaert): copy/paste from DiscreteConditional.cpp :-(
+vector<DiscreteValues> DiscreteLookupTable::frontalAssignments() const {
+  vector<pair<Key, size_t>> pairs;
+  for (Key key : frontals()) pairs.emplace_back(key, cardinalities_.at(key));
+  vector<pair<Key, size_t>> rpairs(pairs.rbegin(), pairs.rend());
+  return DiscreteValues::CartesianProduct(rpairs);
+}
+
+/* ************************************************************************** */
+// TODO(dellaert): copy/paste from DiscreteConditional.cpp :-(
+static DiscreteLookupTable::ADT Choose(const DiscreteLookupTable& conditional,
+                                       const DiscreteValues& given,
+                                       bool forceComplete = true) {
+  // Get the big decision tree with all the levels, and then go down the
+  // branches based on the value of the parent variables.
+  DiscreteLookupTable::ADT adt(conditional);
+  size_t value;
+  for (Key j : conditional.parents()) {
+    try {
+      value = given.at(j);
+      adt = adt.choose(j, value);  // ADT keeps getting smaller.
+    } catch (std::out_of_range&) {
+      if (forceComplete) {
+        given.print("parentsValues: ");
+        throw std::runtime_error(
+            "DiscreteLookupTable::Choose: parent value missing");
+      }
+    }
+  }
+  return adt;
+}
+
+/* ************************************************************************** */
+void DiscreteLookupTable::argmaxInPlace(DiscreteValues* values) const {
+  ADT pFS = Choose(*this, *values);  // P(F|S=parentsValues)
+
+  // Initialize
+  DiscreteValues mpe;
+  double maxP = 0;
+
+  // Get all Possible Configurations
+  const auto allPosbValues = frontalAssignments();
+
+  // Find the maximum
+  for (const auto& frontalVals : allPosbValues) {
+    double pValueS = pFS(frontalVals);  // P(F=value|S=parentsValues)
+    // Update maximum solution if better
+    if (pValueS > maxP) {
+      maxP = pValueS;
+      mpe = frontalVals;
+    }
+  }
+
+  // set values (inPlace) to maximum
+  for (Key j : frontals()) {
+    (*values)[j] = mpe[j];
+  }
+}
+
+/* ************************************************************************** */
+size_t DiscreteLookupTable::argmax(const DiscreteValues& parentsValues) const {
+  ADT pFS = Choose(*this, parentsValues);  // P(F|S=parentsValues)
+
+  // Then, find the max over all remaining
+  // TODO(Duy): only works for one key now, seems horribly slow this way
+  size_t mpe = 0;
+  DiscreteValues frontals;
+  double maxP = 0;
+  assert(nrFrontals() == 1);
+  Key j = (firstFrontalKey());
+  for (size_t value = 0; value < cardinality(j); value++) {
+    frontals[j] = value;
+    double pValueS = pFS(frontals);  // P(F=value|S=parentsValues)
+    // Update MPE solution if better
+    if (pValueS > maxP) {
+      maxP = pValueS;
+      mpe = value;
+    }
+  }
+  return mpe;
+}
+
+/* ************************************************************************** */
+DiscreteValues DiscreteLookupDAG::argmax() const {
+  DiscreteValues result;
+  return argmax(result);
+}
+
+DiscreteValues DiscreteLookupDAG::argmax(DiscreteValues result) const {
+  // Argmax each node in turn in topological sort order (parents first).
+  for (auto lookupTable : boost::adaptors::reverse(*this))
+    lookupTable->argmaxInPlace(&result);
+  return result;
+}
+/* ************************************************************************** */
+
+}  // namespace gtsam
diff --git a/gtsam/discrete/DiscreteLookupDAG.h b/gtsam/discrete/DiscreteLookupDAG.h
new file mode 100644
index 000000000..a69b0b1ee
--- /dev/null
+++ b/gtsam/discrete/DiscreteLookupDAG.h
@@ -0,0 +1,138 @@
+/* ----------------------------------------------------------------------------
+
+ * GTSAM Copyright 2010, Georgia Tech Research Corporation,
+ * Atlanta, Georgia 30332-0415
+ * All Rights Reserved
+ * Authors: Frank Dellaert, et al. (see THANKS for the full author list)
+
+ * See LICENSE for the license information
+
+ * -------------------------------------------------------------------------- */
+
+/**
+ * @file DiscreteLookupDAG.h
+ * @date JAnuary, 2022
+ * @author Frank dellaert
+ */
+
+#pragma once
+
+#include <gtsam/discrete/DiscreteDistribution.h>
+#include <gtsam/inference/BayesNet.h>
+#include <gtsam/inference/FactorGraph.h>
+
+#include <boost/shared_ptr.hpp>
+
+#include <vector>
+
+namespace gtsam {
+
+/**
+ * @brief DiscreteLookupTable table for max-product
+ */
+class DiscreteLookupTable
+    : public DecisionTreeFactor,
+      public Conditional<DecisionTreeFactor, DiscreteLookupTable> {
+ public:
+  using This = DiscreteLookupTable;
+  using shared_ptr = boost::shared_ptr<This>;
+  using BaseConditional = Conditional<DecisionTreeFactor, This>;
+
+  /**
+   * @brief Construct a new Discrete Lookup Table object
+   *
+   * @param nFrontals number of frontal variables
+   * @param keys a orted list of gtsam::Keys
+   * @param potentials the algebraic decision tree with lookup values
+   */
+  DiscreteLookupTable(size_t nFrontals, const DiscreteKeys& keys,
+                      const ADT& potentials)
+      : DecisionTreeFactor(keys, potentials), BaseConditional(nFrontals) {}
+
+  /// GTSAM-style print
+  void print(
+      const std::string& s = "Discrete Lookup Table: ",
+      const KeyFormatter& formatter = DefaultKeyFormatter) const override;
+
+  /**
+   * @brief return assignment for single frontal variable that maximizes value.
+   * @param parentsValues Known assignments for the parents.
+   * @return maximizing assignment for the frontal variable.
+   */
+  size_t argmax(const DiscreteValues& parentsValues) const;
+
+  /**
+   * @brief Calculate assignment for frontal variables that maximizes value.
+   * @param (in/out) parentsValues Known assignments for the parents.
+   */
+  void argmaxInPlace(DiscreteValues* parentsValues) const;
+
+  /// Return all assignments for frontal variables.
+  std::vector<DiscreteValues> frontalAssignments() const;
+};
+
+/** A DAG made from lookup tables, as defined above. */
+class GTSAM_EXPORT DiscreteLookupDAG : public BayesNet<DiscreteLookupTable> {
+ public:
+  using Base = BayesNet<DiscreteLookupTable>;
+  using This = DiscreteLookupDAG;
+  using shared_ptr = boost::shared_ptr<This>;
+
+  /// @name Standard Constructors
+  /// @{
+
+  /// Construct empty DAG.
+  DiscreteLookupDAG() {}
+
+  /// Destructor
+  virtual ~DiscreteLookupDAG() {}
+
+  /// @}
+
+  /// @name Testable
+  /// @{
+
+  /** Check equality */
+  bool equals(const This& bn, double tol = 1e-9) const;
+
+  /// @}
+
+  /// @name Standard Interface
+  /// @{
+
+  /**
+   * @brief argmax by back-substitution.
+   *
+   * Assumes the DAG is reverse topologically sorted, i.e. last
+   * conditional will be optimized first. If the DAG resulted from
+   * eliminating a factor graph, this is true for the elimination ordering.
+   *
+   * @return optimal assignment for all variables.
+   */
+  DiscreteValues argmax() const;
+
+  /**
+   * @brief argmax by back-substitution, given certain variables.
+   *
+   * Assumes the DAG is reverse topologically sorted *and* that the
+   * DAG does not contain any conditionals for the given variables.
+   *
+   * @return given assignment extended w. optimal assignment for all variables.
+   */
+  DiscreteValues argmax(DiscreteValues given) const;
+  /// @}
+
+ private:
+  /** Serialization function */
+  friend class boost::serialization::access;
+  template <class ARCHIVE>
+  void serialize(ARCHIVE& ar, const unsigned int /*version*/) {
+    ar& BOOST_SERIALIZATION_BASE_OBJECT_NVP(Base);
+  }
+};
+
+// traits
+template <>
+struct traits<DiscreteLookupDAG> : public Testable<DiscreteLookupDAG> {};
+
+}  // namespace gtsam