clusterlin: use 'cost' terminology instead of 'iters' (refactor)

diff --git a/src/bench/cluster_linearize.cpp b/src/bench/cluster_linearize.cpp
index d345a7ca..0799cc2c 100644
--- a/src/bench/cluster_linearize.cpp
+++ b/src/bench/cluster_linearize.cpp
@@ -55,7 +55,7 @@ void BenchLinearizeOptimallyTotal(benchmark::Bench& bench, const std::string& na
         // Benchmark the total time to optimal.
         uint64_t rng_seed = 0;
         bench.name(bench_name).run([&] {
-            auto [_lin, optimal, _cost] = Linearize(depgraph, /*max_iterations=*/10000000, rng_seed++, IndexTxOrder{});
+            auto [_lin, optimal, _cost] = Linearize(depgraph, /*max_cost=*/10000000, rng_seed++, IndexTxOrder{});
             assert(optimal);
         });
     }
@@ -72,7 +72,7 @@ void BenchLinearizeOptimallyPerCost(benchmark::Bench& bench, const std::string&
         // Determine the cost of 100 rng_seeds.
         uint64_t total_cost = 0;
         for (uint64_t iter = 0; iter < 100; ++iter) {
-            auto [_lin, optimal, cost] = Linearize(depgraph, /*max_iterations=*/10000000, /*rng_seed=*/iter, IndexTxOrder{});
+            auto [_lin, optimal, cost] = Linearize(depgraph, /*max_cost=*/10000000, /*rng_seed=*/iter, IndexTxOrder{});
             total_cost += cost;
         }
 
@@ -80,7 +80,7 @@ void BenchLinearizeOptimallyPerCost(benchmark::Bench& bench, const std::string&
         bench.name(bench_name).unit("cost").batch(total_cost).run([&] {
             uint64_t recompute_cost = 0;
             for (uint64_t iter = 0; iter < 100; ++iter) {
-                auto [_lin, optimal, cost] = Linearize(depgraph, /*max_iterations=*/10000000, /*rng_seed=*/iter, IndexTxOrder{});
+                auto [_lin, optimal, cost] = Linearize(depgraph, /*max_cost=*/10000000, /*rng_seed=*/iter, IndexTxOrder{});
                 assert(optimal);
                 recompute_cost += cost;
             }
diff --git a/src/bench/txgraph.cpp b/src/bench/txgraph.cpp
index 00074db6..c56a284a 100644
--- a/src/bench/txgraph.cpp
+++ b/src/bench/txgraph.cpp
@@ -51,9 +51,9 @@ void BenchTxGraphTrim(benchmark::Bench& bench)
     static constexpr int NUM_DEPS_PER_BOTTOM_TX = 100;
     /** Set a very large cluster size limit so that only the count limit is triggered. */
     static constexpr int32_t MAX_CLUSTER_SIZE = 100'000 * 100;
-    /** Set a very high number for acceptable iterations, so that we certainly benchmark optimal
+    /** Set a very high number for acceptable cost, so that we certainly benchmark optimal
      *  linearization. */
-    static constexpr uint64_t NUM_ACCEPTABLE_ITERS = 100'000'000;
+    static constexpr uint64_t HIGH_ACCEPTABLE_COST = 100'000'000;
 
     /** Refs to all top transactions. */
     std::vector<TxGraph::Ref> top_refs;
@@ -65,7 +65,7 @@ void BenchTxGraphTrim(benchmark::Bench& bench)
     std::vector<size_t> top_components;
 
     InsecureRandomContext rng(11);
-    auto graph = MakeTxGraph(MAX_CLUSTER_COUNT, MAX_CLUSTER_SIZE, NUM_ACCEPTABLE_ITERS, PointerComparator);
+    auto graph = MakeTxGraph(MAX_CLUSTER_COUNT, MAX_CLUSTER_SIZE, HIGH_ACCEPTABLE_COST, PointerComparator);
 
     // Construct the top chains.
     for (int chain = 0; chain < NUM_TOP_CHAINS; ++chain) {
diff --git a/src/cluster_linearize.h b/src/cluster_linearize.h
index 8f2076ca..57df4512 100644
--- a/src/cluster_linearize.h
+++ b/src/cluster_linearize.h
@@ -1742,7 +1742,7 @@ public:
 /** Find or improve a linearization for a cluster.
  *
  * @param[in] depgraph            Dependency graph of the cluster to be linearized.
- * @param[in] max_iterations      Upper bound on the amount of work that will be done.
+ * @param[in] max_cost            Upper bound on the amount of work that will be done.
  * @param[in] rng_seed            A random number seed to control search order. This prevents peers
  *                                from predicting exactly which clusters would be hard for us to
  *                                linearize.
@@ -1762,7 +1762,7 @@ public:
 template<typename SetType>
 std::tuple<std::vector<DepGraphIndex>, bool, uint64_t> Linearize(
     const DepGraph<SetType>& depgraph,
-    uint64_t max_iterations,
+    uint64_t max_cost,
     uint64_t rng_seed,
     const StrongComparator<DepGraphIndex> auto& fallback_order,
     std::span<const DepGraphIndex> old_linearization = {},
@@ -1778,23 +1778,23 @@ std::tuple<std::vector<DepGraphIndex>, bool, uint64_t> Linearize(
     }
     // Make improvement steps to it until we hit the max_iterations limit, or an optimal result
     // is found.
-    if (forest.GetCost() < max_iterations) {
+    if (forest.GetCost() < max_cost) {
         forest.StartOptimizing();
         do {
             if (!forest.OptimizeStep()) break;
-        } while (forest.GetCost() < max_iterations);
+        } while (forest.GetCost() < max_cost);
     }
     // Make chunk minimization steps until we hit the max_iterations limit, or all chunks are
     // minimal.
     bool optimal = false;
-    if (forest.GetCost() < max_iterations) {
+    if (forest.GetCost() < max_cost) {
         forest.StartMinimizing();
         do {
             if (!forest.MinimizeStep()) {
                 optimal = true;
                 break;
             }
-        } while (forest.GetCost() < max_iterations);
+        } while (forest.GetCost() < max_cost);
     }
     return {forest.GetLinearization(fallback_order), optimal, forest.GetCost()};
 }
diff --git a/src/test/cluster_linearize_tests.cpp b/src/test/cluster_linearize_tests.cpp
index e14b5ebc..4f851c1d 100644
--- a/src/test/cluster_linearize_tests.cpp
+++ b/src/test/cluster_linearize_tests.cpp
@@ -88,9 +88,15 @@ void TestOptimalLinearization(std::span<const uint8_t> enc, std::initializer_lis
                 is_topological = false;
                 break;
             }
-            std::tie(lin, opt, cost) = Linearize(depgraph, 1000000000000, rng.rand64(), IndexTxOrder{}, lin, is_topological);
+            std::tie(lin, opt, cost) = Linearize(
+                /*depgraph=*/depgraph,
+                /*max_cost=*/1000000000000,
+                /*rng_seed=*/rng.rand64(),
+                /*fallback_order=*/IndexTxOrder{},
+                /*old_linearization=*/lin,
+                /*is_topological=*/is_topological);
             BOOST_CHECK(opt);
-            BOOST_CHECK(cost <= MaxOptimalLinearizationIters(depgraph.TxCount()));
+            BOOST_CHECK(cost <= MaxOptimalLinearizationCost(depgraph.TxCount()));
             SanityCheck(depgraph, lin);
             BOOST_CHECK(std::ranges::equal(lin, optimal_linearization));
         }
diff --git a/src/test/fuzz/cluster_linearize.cpp b/src/test/fuzz/cluster_linearize.cpp
index 5dc7eb21..adee8f2e 100644
--- a/src/test/fuzz/cluster_linearize.cpp
+++ b/src/test/fuzz/cluster_linearize.cpp
@@ -984,7 +984,7 @@ FUZZ_TARGET(clusterlin_sfl)
 
     // Verify that optimality is reached within an expected amount of work. This protects against
     // hypothetical bugs that hugely increase the amount of work needed to reach optimality.
-    assert(sfl.GetCost() <= MaxOptimalLinearizationIters(depgraph.TxCount()));
+    assert(sfl.GetCost() <= MaxOptimalLinearizationCost(depgraph.TxCount()));
 
     // The result must be as good as SimpleLinearize.
     auto [simple_linearization, simple_optimal] = SimpleLinearize(depgraph, MAX_SIMPLE_ITERATIONS / 10);
@@ -1011,15 +1011,15 @@ FUZZ_TARGET(clusterlin_linearize)
 {
     // Verify the behavior of Linearize().
 
-    // Retrieve an RNG seed, an iteration count, a depgraph, and whether to make it connected from
-    // the fuzz input.
+    // Retrieve an RNG seed, a maximum amount of work, a depgraph, and whether to make it connected
+    // from the fuzz input.
     SpanReader reader(buffer);
     DepGraph<TestBitSet> depgraph;
     uint64_t rng_seed{0};
-    uint64_t iter_count{0};
+    uint64_t max_cost{0};
     uint8_t flags{7};
     try {
-        reader >> VARINT(iter_count) >> Using<DepGraphFormatter>(depgraph) >> rng_seed >> flags;
+        reader >> VARINT(max_cost) >> Using<DepGraphFormatter>(depgraph) >> rng_seed >> flags;
     } catch (const std::ios_base::failure&) {}
     bool make_connected = flags & 1;
     // The following 3 booleans have 4 combinations:
@@ -1043,8 +1043,14 @@ FUZZ_TARGET(clusterlin_linearize)
     }
 
     // Invoke Linearize().
-    iter_count &= 0x7ffff;
-    auto [linearization, optimal, cost] = Linearize(depgraph, iter_count, rng_seed, IndexTxOrder{}, old_linearization, /*is_topological=*/claim_topological_input);
+    max_cost &= 0x7ffff;
+    auto [linearization, optimal, cost] = Linearize(
+        /*depgraph=*/depgraph,
+        /*max_cost=*/max_cost,
+        /*rng_seed=*/rng_seed,
+        /*fallback_order=*/IndexTxOrder{},
+        /*old_linearization=*/old_linearization,
+        /*is_topological=*/claim_topological_input);
     SanityCheck(depgraph, linearization);
     auto chunking = ChunkLinearization(depgraph, linearization);
 
@@ -1056,8 +1062,8 @@ FUZZ_TARGET(clusterlin_linearize)
         assert(cmp >= 0);
     }
 
-    // If the iteration count is sufficiently high, an optimal linearization must be found.
-    if (iter_count > MaxOptimalLinearizationIters(depgraph.TxCount())) {
+    // If the maximum amount of work is sufficiently high, an optimal linearization must be found.
+    if (max_cost > MaxOptimalLinearizationCost(depgraph.TxCount())) {
         assert(optimal);
     }
 
@@ -1145,7 +1151,7 @@ FUZZ_TARGET(clusterlin_linearize)
 
         // Redo from scratch with a different rng_seed. The resulting linearization should be
         // deterministic, if both are optimal.
-        auto [linearization2, optimal2, cost2] = Linearize(depgraph, MaxOptimalLinearizationIters(depgraph.TxCount()) + 1, rng_seed ^ 0x1337, IndexTxOrder{});
+        auto [linearization2, optimal2, cost2] = Linearize(depgraph, MaxOptimalLinearizationCost(depgraph.TxCount()) + 1, rng_seed ^ 0x1337, IndexTxOrder{});
         assert(optimal2);
         assert(linearization2 == linearization);
     }
diff --git a/src/test/fuzz/txgraph.cpp b/src/test/fuzz/txgraph.cpp
index 59c65bde..0fc4e047 100644
--- a/src/test/fuzz/txgraph.cpp
+++ b/src/test/fuzz/txgraph.cpp
@@ -325,8 +325,8 @@ FUZZ_TARGET(txgraph)
     auto max_cluster_count = provider.ConsumeIntegralInRange<DepGraphIndex>(1, MAX_CLUSTER_COUNT_LIMIT);
     /** The maximum total size of transactions in a (non-oversized) cluster. */
     auto max_cluster_size = provider.ConsumeIntegralInRange<uint64_t>(1, 0x3fffff * MAX_CLUSTER_COUNT_LIMIT);
-    /** The number of iterations to consider a cluster acceptably linearized. */
-    auto acceptable_iters = provider.ConsumeIntegralInRange<uint64_t>(0, 10000);
+    /** The amount of work to consider a cluster acceptably linearized. */
+    auto acceptable_cost = provider.ConsumeIntegralInRange<uint64_t>(0, 10000);
 
     /** The set of uint64_t "txid"s that have been assigned before. */
     std::set<uint64_t> assigned_txids;
@@ -342,7 +342,7 @@ FUZZ_TARGET(txgraph)
     auto real = MakeTxGraph(
         /*max_cluster_count=*/max_cluster_count,
         /*max_cluster_size=*/max_cluster_size,
-        /*acceptable_iters=*/acceptable_iters,
+        /*acceptable_cost=*/acceptable_cost,
         /*fallback_order=*/fallback_order);
 
     std::vector<SimTxGraph> sims;
@@ -758,9 +758,9 @@ FUZZ_TARGET(txgraph)
                 break;
             } else if (command-- == 0) {
                 // DoWork.
-                uint64_t iters = provider.ConsumeIntegralInRange<uint64_t>(0, alt ? 10000 : 255);
-                bool ret = real->DoWork(iters);
-                uint64_t iters_for_optimal{0};
+                uint64_t max_cost = provider.ConsumeIntegralInRange<uint64_t>(0, alt ? 10000 : 255);
+                bool ret = real->DoWork(max_cost);
+                uint64_t cost_for_optimal{0};
                 for (unsigned level = 0; level < sims.size(); ++level) {
                     // DoWork() will not optimize oversized levels, or the main level if a builder
                     // is present. Note that this impacts the DoWork() return value, as true means
@@ -773,24 +773,24 @@ FUZZ_TARGET(txgraph)
                     if (ret) {
                         sims[level].real_is_optimal = true;
                     }
-                    // Compute how many iterations would be needed to make everything optimal.
+                    // Compute how much work would be needed to make everything optimal.
                     for (auto component : sims[level].GetComponents()) {
-                        auto iters_opt_this_cluster = MaxOptimalLinearizationIters(component.Count());
-                        if (iters_opt_this_cluster > acceptable_iters) {
-                            // If the number of iterations required to linearize this cluster
-                            // optimally exceeds acceptable_iters, DoWork() may process it in two
+                        auto cost_opt_this_cluster = MaxOptimalLinearizationCost(component.Count());
+                        if (cost_opt_this_cluster > acceptable_cost) {
+                            // If the amount of work required to linearize this cluster
+                            // optimally exceeds acceptable_cost, DoWork() may process it in two
                             // stages: once to acceptable, and once to optimal.
-                            iters_for_optimal += iters_opt_this_cluster + acceptable_iters;
+                            cost_for_optimal += cost_opt_this_cluster + acceptable_cost;
                         } else {
-                            iters_for_optimal += iters_opt_this_cluster;
+                            cost_for_optimal += cost_opt_this_cluster;
                         }
                     }
                 }
                 if (!ret) {
-                    // DoWork can only have more work left if the requested number of iterations
+                    // DoWork can only have more work left if the requested amount of work
                     // was insufficient to linearize everything optimally within the levels it is
                     // allowed to touch.
-                    assert(iters <= iters_for_optimal);
+                    assert(max_cost <= cost_for_optimal);
                 }
                 break;
             } else if (sims.size() == 2 && !sims[0].IsOversized() && !sims[1].IsOversized() && command-- == 0) {
@@ -1165,7 +1165,7 @@ FUZZ_TARGET(txgraph)
             auto real_redo = MakeTxGraph(
                 /*max_cluster_count=*/max_cluster_count,
                 /*max_cluster_size=*/max_cluster_size,
-                /*acceptable_iters=*/acceptable_iters,
+                /*acceptable_cost=*/acceptable_cost,
                 /*fallback_order=*/fallback_order);
             /** Vector (indexed by SimTxGraph::Pos) of TxObjects in real_redo). */
             std::vector<std::optional<SimTxObject>> txobjects_redo;
diff --git a/src/test/txgraph_tests.cpp b/src/test/txgraph_tests.cpp
index f069e5bd..444e2185 100644
--- a/src/test/txgraph_tests.cpp
+++ b/src/test/txgraph_tests.cpp
@@ -15,9 +15,9 @@ BOOST_AUTO_TEST_SUITE(txgraph_tests)
 
 namespace {
 
-/** The number used as acceptable_iters argument in these tests. High enough that everything
+/** The number used as acceptable_cost argument in these tests. High enough that everything
  *  should be optimal, always. */
-constexpr uint64_t NUM_ACCEPTABLE_ITERS = 100'000'000;
+constexpr uint64_t HIGH_ACCEPTABLE_COST = 100'000'000;
 
 std::strong_ordering PointerComparator(const TxGraph::Ref& a, const TxGraph::Ref& b) noexcept
 {
@@ -48,7 +48,7 @@ BOOST_AUTO_TEST_CASE(txgraph_trim_zigzag)
     static constexpr int32_t MAX_CLUSTER_SIZE = 100'000 * 100;
 
     // Create a new graph for the test.
-    auto graph = MakeTxGraph(MAX_CLUSTER_COUNT, MAX_CLUSTER_SIZE, NUM_ACCEPTABLE_ITERS, PointerComparator);
+    auto graph = MakeTxGraph(MAX_CLUSTER_COUNT, MAX_CLUSTER_SIZE, HIGH_ACCEPTABLE_COST, PointerComparator);
 
     // Add all transactions and store their Refs.
     std::vector<TxGraph::Ref> refs;
@@ -111,7 +111,7 @@ BOOST_AUTO_TEST_CASE(txgraph_trim_flower)
     /** Set a very large cluster size limit so that only the count limit is triggered. */
     static constexpr int32_t MAX_CLUSTER_SIZE = 100'000 * 100;
 
-    auto graph = MakeTxGraph(MAX_CLUSTER_COUNT, MAX_CLUSTER_SIZE, NUM_ACCEPTABLE_ITERS, PointerComparator);
+    auto graph = MakeTxGraph(MAX_CLUSTER_COUNT, MAX_CLUSTER_SIZE, HIGH_ACCEPTABLE_COST, PointerComparator);
 
     // Add all transactions and store their Refs.
     std::vector<TxGraph::Ref> refs;
@@ -197,7 +197,7 @@ BOOST_AUTO_TEST_CASE(txgraph_trim_huge)
     std::vector<size_t> top_components;
 
     FastRandomContext rng;
-    auto graph = MakeTxGraph(MAX_CLUSTER_COUNT, MAX_CLUSTER_SIZE, NUM_ACCEPTABLE_ITERS, PointerComparator);
+    auto graph = MakeTxGraph(MAX_CLUSTER_COUNT, MAX_CLUSTER_SIZE, HIGH_ACCEPTABLE_COST, PointerComparator);
 
     // Construct the top chains.
     for (int chain = 0; chain < NUM_TOP_CHAINS; ++chain) {
@@ -270,7 +270,7 @@ BOOST_AUTO_TEST_CASE(txgraph_trim_big_singletons)
     static constexpr int NUM_TOTAL_TX = 100;
 
     // Create a new graph for the test.
-    auto graph = MakeTxGraph(MAX_CLUSTER_COUNT, MAX_CLUSTER_SIZE, NUM_ACCEPTABLE_ITERS, PointerComparator);
+    auto graph = MakeTxGraph(MAX_CLUSTER_COUNT, MAX_CLUSTER_SIZE, HIGH_ACCEPTABLE_COST, PointerComparator);
 
     // Add all transactions and store their Refs.
     std::vector<TxGraph::Ref> refs;
@@ -304,7 +304,7 @@ BOOST_AUTO_TEST_CASE(txgraph_trim_big_singletons)
 BOOST_AUTO_TEST_CASE(txgraph_chunk_chain)
 {
     // Create a new graph for the test.
-    auto graph = MakeTxGraph(50, 1000, NUM_ACCEPTABLE_ITERS, PointerComparator);
+    auto graph = MakeTxGraph(50, 1000, HIGH_ACCEPTABLE_COST, PointerComparator);
 
     auto block_builder_checker = [&graph](std::vector<std::vector<TxGraph::Ref*>> expected_chunks) {
         std::vector<std::vector<TxGraph::Ref*>> chunks;
@@ -383,7 +383,7 @@ BOOST_AUTO_TEST_CASE(txgraph_staging)
     /* Create a new graph for the test.
      * The parameters are max_cluster_count, max_cluster_size, acceptable_iters
      */
-    auto graph = MakeTxGraph(10, 1000, NUM_ACCEPTABLE_ITERS, PointerComparator);
+    auto graph = MakeTxGraph(10, 1000, HIGH_ACCEPTABLE_COST, PointerComparator);
 
     std::vector<TxGraph::Ref> refs;
     refs.reserve(2);
diff --git a/src/test/util/cluster_linearize.h b/src/test/util/cluster_linearize.h
index 3814c3fc..f50a51bd 100644
--- a/src/test/util/cluster_linearize.h
+++ b/src/test/util/cluster_linearize.h
@@ -394,13 +394,13 @@ void SanityCheck(const DepGraph<SetType>& depgraph, std::span<const DepGraphInde
     }
 }
 
-inline uint64_t MaxOptimalLinearizationIters(DepGraphIndex cluster_count)
+inline uint64_t MaxOptimalLinearizationCost(DepGraphIndex cluster_count)
 {
     // These are the largest numbers seen returned as cost by Linearize(), in a large randomized
     // trial. There exist almost certainly far worse cases, but they are unlikely to be
     // encountered in randomized tests. The purpose of these numbers is guaranteeing that for
     // *some* reasonable cost bound, optimal linearizations are always found.
-    static constexpr uint64_t ITERS[65] = {
+    static constexpr uint64_t COSTS[65] = {
         0,
         0, 4, 10, 34, 76, 156, 229, 380,
         441, 517, 678, 933, 1037, 1366, 1464, 1711,
@@ -411,9 +411,9 @@ inline uint64_t MaxOptimalLinearizationIters(DepGraphIndex cluster_count)
         34046, 26227, 34662, 38019, 40814, 31113, 41448, 33968,
         35024, 59207, 42872, 41277, 42365, 51833, 63410, 67035
     };
-    assert(cluster_count < std::size(ITERS));
+    assert(cluster_count < std::size(COSTS));
     // Multiply the table number by two, to account for the fact that they are not absolutes.
-    return ITERS[cluster_count] * 2;
+    return COSTS[cluster_count] * 2;
 }
 
 } // namespace
diff --git a/src/txgraph.cpp b/src/txgraph.cpp
index a9d502b4..ca12bca6 100644
--- a/src/txgraph.cpp
+++ b/src/txgraph.cpp
@@ -217,7 +217,7 @@ public:
     virtual void ApplyDependencies(TxGraphImpl& graph, int level, std::span<std::pair<GraphIndex, GraphIndex>> to_apply) noexcept = 0;
     /** Improve the linearization of this Cluster. Returns how much work was performed and whether
      *  the Cluster's QualityLevel improved as a result. */
-    virtual std::pair<uint64_t, bool> Relinearize(TxGraphImpl& graph, int level, uint64_t max_iters) noexcept = 0;
+    virtual std::pair<uint64_t, bool> Relinearize(TxGraphImpl& graph, int level, uint64_t max_cost) noexcept = 0;
     /** For every chunk in the cluster, append its FeeFrac to ret. */
     virtual void AppendChunkFeerates(std::vector<FeeFrac>& ret) const noexcept = 0;
     /** Add a TrimTxData entry (filling m_chunk_feerate, m_index, m_tx_size) for every
@@ -296,7 +296,7 @@ public:
     [[nodiscard]] bool Split(TxGraphImpl& graph, int level) noexcept final;
     void Merge(TxGraphImpl& graph, int level, Cluster& cluster) noexcept final;
     void ApplyDependencies(TxGraphImpl& graph, int level, std::span<std::pair<GraphIndex, GraphIndex>> to_apply) noexcept final;
-    std::pair<uint64_t, bool> Relinearize(TxGraphImpl& graph, int level, uint64_t max_iters) noexcept final;
+    std::pair<uint64_t, bool> Relinearize(TxGraphImpl& graph, int level, uint64_t max_cost) noexcept final;
     void AppendChunkFeerates(std::vector<FeeFrac>& ret) const noexcept final;
     uint64_t AppendTrimData(std::vector<TrimTxData>& ret, std::vector<std::pair<GraphIndex, GraphIndex>>& deps) const noexcept final;
     void GetAncestorRefs(const TxGraphImpl& graph, std::span<std::pair<Cluster*, DepGraphIndex>>& args, std::vector<TxGraph::Ref*>& output) noexcept final;
@@ -353,7 +353,7 @@ public:
     [[nodiscard]] bool Split(TxGraphImpl& graph, int level) noexcept final;
     void Merge(TxGraphImpl& graph, int level, Cluster& cluster) noexcept final;
     void ApplyDependencies(TxGraphImpl& graph, int level, std::span<std::pair<GraphIndex, GraphIndex>> to_apply) noexcept final;
-    std::pair<uint64_t, bool> Relinearize(TxGraphImpl& graph, int level, uint64_t max_iters) noexcept final;
+    std::pair<uint64_t, bool> Relinearize(TxGraphImpl& graph, int level, uint64_t max_cost) noexcept final;
     void AppendChunkFeerates(std::vector<FeeFrac>& ret) const noexcept final;
     uint64_t AppendTrimData(std::vector<TrimTxData>& ret, std::vector<std::pair<GraphIndex, GraphIndex>>& deps) const noexcept final;
     void GetAncestorRefs(const TxGraphImpl& graph, std::span<std::pair<Cluster*, DepGraphIndex>>& args, std::vector<TxGraph::Ref*>& output) noexcept final;
@@ -400,9 +400,8 @@ private:
     const DepGraphIndex m_max_cluster_count;
     /** This TxGraphImpl's maximum cluster size limit. */
     const uint64_t m_max_cluster_size;
-    /** The number of linearization improvement steps needed per cluster to be considered
-     *  acceptable. */
-    const uint64_t m_acceptable_iters;
+    /** The amount of linearization work needed per cluster to be considered acceptable. */
+    const uint64_t m_acceptable_cost;
     /** Fallback ordering for transactions. */
     const std::function<std::strong_ordering(const TxGraph::Ref&, const TxGraph::Ref&)> m_fallback_order;
 
@@ -636,12 +635,12 @@ public:
     explicit TxGraphImpl(
         DepGraphIndex max_cluster_count,
         uint64_t max_cluster_size,
-        uint64_t acceptable_iters,
+        uint64_t acceptable_cost,
         const std::function<std::strong_ordering(const TxGraph::Ref&, const TxGraph::Ref&)>& fallback_order
     ) noexcept :
         m_max_cluster_count(max_cluster_count),
         m_max_cluster_size(max_cluster_size),
-        m_acceptable_iters(acceptable_iters),
+        m_acceptable_cost(acceptable_cost),
         m_fallback_order(fallback_order),
         m_main_chunkindex(ChunkOrder(this))
     {
@@ -803,7 +802,7 @@ public:
     void AddDependency(const Ref& parent, const Ref& child) noexcept final;
     void SetTransactionFee(const Ref&, int64_t fee) noexcept final;
 
-    bool DoWork(uint64_t iters) noexcept final;
+    bool DoWork(uint64_t max_cost) noexcept final;
 
     void StartStaging() noexcept final;
     void CommitStaging() noexcept final;
@@ -2155,7 +2154,7 @@ void TxGraphImpl::ApplyDependencies(int level) noexcept
     clusterset.m_group_data = GroupData{};
 }
 
-std::pair<uint64_t, bool> GenericClusterImpl::Relinearize(TxGraphImpl& graph, int level, uint64_t max_iters) noexcept
+std::pair<uint64_t, bool> GenericClusterImpl::Relinearize(TxGraphImpl& graph, int level, uint64_t max_cost) noexcept
 {
     // We can only relinearize Clusters that do not need splitting.
     Assume(!NeedsSplitting());
@@ -2168,7 +2167,13 @@ std::pair<uint64_t, bool> GenericClusterImpl::Relinearize(TxGraphImpl& graph, in
         const auto ref_b = graph.m_entries[m_mapping[b]].m_ref;
         return graph.m_fallback_order(*ref_a, *ref_b);
     };
-    auto [linearization, optimal, cost] = Linearize(m_depgraph, max_iters, rng_seed, fallback_order, m_linearization, /*is_topological=*/IsTopological());
+    auto [linearization, optimal, cost] = Linearize(
+        /*depgraph=*/m_depgraph,
+        /*max_cost=*/max_cost,
+        /*rng_seed=*/rng_seed,
+        /*fallback_order=*/fallback_order,
+        /*old_linearization=*/m_linearization,
+        /*is_topological=*/IsTopological());
     // Postlinearize to improve the linearization (if optimal, only the sub-chunk order).
     // This also guarantees that all chunks are connected (even when non-optimal).
     PostLinearize(m_depgraph, linearization);
@@ -2179,7 +2184,7 @@ std::pair<uint64_t, bool> GenericClusterImpl::Relinearize(TxGraphImpl& graph, in
     if (optimal) {
         graph.SetClusterQuality(level, m_quality, m_setindex, QualityLevel::OPTIMAL);
         improved = true;
-    } else if (max_iters >= graph.m_acceptable_iters && !IsAcceptable()) {
+    } else if (max_cost >= graph.m_acceptable_cost && !IsAcceptable()) {
         graph.SetClusterQuality(level, m_quality, m_setindex, QualityLevel::ACCEPTABLE);
         improved = true;
     } else if (!IsTopological()) {
@@ -2191,7 +2196,7 @@ std::pair<uint64_t, bool> GenericClusterImpl::Relinearize(TxGraphImpl& graph, in
     return {cost, improved};
 }
 
-std::pair<uint64_t, bool> SingletonClusterImpl::Relinearize(TxGraphImpl& graph, int level, uint64_t max_iters) noexcept
+std::pair<uint64_t, bool> SingletonClusterImpl::Relinearize(TxGraphImpl& graph, int level, uint64_t max_cost) noexcept
 {
     // All singletons are optimal, oversized, or need splitting. Each of these precludes
     // Relinearize from being called.
@@ -2203,7 +2208,7 @@ void TxGraphImpl::MakeAcceptable(Cluster& cluster, int level) noexcept
 {
     // Relinearize the Cluster if needed.
     if (!cluster.NeedsSplitting() && !cluster.IsAcceptable() && !cluster.IsOversized()) {
-        cluster.Relinearize(*this, level, m_acceptable_iters);
+        cluster.Relinearize(*this, level, m_acceptable_cost);
     }
 }
 
@@ -3105,9 +3110,9 @@ void TxGraphImpl::SanityCheck() const
     assert(actual_chunkindex == expected_chunkindex);
 }
 
-bool TxGraphImpl::DoWork(uint64_t iters) noexcept
+bool TxGraphImpl::DoWork(uint64_t max_cost) noexcept
 {
-    uint64_t iters_done{0};
+    uint64_t cost_done{0};
     // First linearize everything in NEEDS_RELINEARIZE to an acceptable level. If more budget
     // remains after that, try to make everything optimal.
     for (QualityLevel quality : {QualityLevel::NEEDS_FIX, QualityLevel::NEEDS_RELINEARIZE, QualityLevel::ACCEPTABLE}) {
@@ -3121,23 +3126,23 @@ bool TxGraphImpl::DoWork(uint64_t iters) noexcept
             if (clusterset.m_oversized == true) continue;
             auto& queue = clusterset.m_clusters[int(quality)];
             while (!queue.empty()) {
-                if (iters_done >= iters) return false;
+                if (cost_done >= max_cost) return false;
                 // Randomize the order in which we process, so that if the first cluster somehow
-                // needs more work than what iters allows, we don't keep spending it on the same
+                // needs more work than what max_cost allows, we don't keep spending it on the same
                 // one.
                 auto pos = m_rng.randrange<size_t>(queue.size());
-                auto iters_now = iters - iters_done;
+                auto cost_now = max_cost - cost_done;
                 if (quality == QualityLevel::NEEDS_FIX || quality == QualityLevel::NEEDS_RELINEARIZE) {
                     // If we're working with clusters that need relinearization still, only perform
-                    // up to m_acceptable_iters iterations. If they become ACCEPTABLE, and we still
+                    // up to m_acceptable_cost work. If they become ACCEPTABLE, and we still
                     // have budget after all other clusters are ACCEPTABLE too, we'll spend the
                     // remaining budget on trying to make them OPTIMAL.
-                    iters_now = std::min(iters_now, m_acceptable_iters);
+                    cost_now = std::min(cost_now, m_acceptable_cost);
                 }
-                auto [cost, improved] = queue[pos].get()->Relinearize(*this, level, iters_now);
-                iters_done += cost;
+                auto [cost, improved] = queue[pos].get()->Relinearize(*this, level, cost_now);
+                cost_done += cost;
                 // If no improvement was made to the Cluster, it means we've essentially run out of
-                // budget. Even though it may be the case that iters_done < iters still, the
+                // budget. Even though it may be the case that cost_done < max_cost still, the
                 // linearizer decided there wasn't enough budget left to attempt anything with.
                 // To avoid an infinite loop that keeps trying clusters with minuscule budgets,
                 // stop here too.
@@ -3565,8 +3570,12 @@ TxGraph::Ref::Ref(Ref&& other) noexcept
 std::unique_ptr<TxGraph> MakeTxGraph(
     unsigned max_cluster_count,
     uint64_t max_cluster_size,
-    uint64_t acceptable_iters,
+    uint64_t acceptable_cost,
     const std::function<std::strong_ordering(const TxGraph::Ref&, const TxGraph::Ref&)>& fallback_order) noexcept
 {
-    return std::make_unique<TxGraphImpl>(max_cluster_count, max_cluster_size, acceptable_iters, fallback_order);
+    return std::make_unique<TxGraphImpl>(
+        /*max_cluster_count=*/max_cluster_count,
+        /*max_cluster_size=*/max_cluster_size,
+        /*acceptable_cost=*/acceptable_cost,
+        /*fallback_order=*/fallback_order);
 }
diff --git a/src/txgraph.h b/src/txgraph.h
index 8c7a9174..f76915c8 100644
--- a/src/txgraph.h
+++ b/src/txgraph.h
@@ -102,10 +102,10 @@ public:
     virtual void SetTransactionFee(const Ref& arg, int64_t fee) noexcept = 0;
 
     /** TxGraph is internally lazy, and will not compute many things until they are needed.
-     *  Calling DoWork will perform some work now (controlled by iters) so that future operations
+     *  Calling DoWork will perform some work now (controlled by max_cost) so that future operations
      *  are fast, if there is any. Returns whether all currently-available work is done. This can
      *  be invoked while oversized, but oversized graphs will be skipped by this call. */
-    virtual bool DoWork(uint64_t iters) noexcept = 0;
+    virtual bool DoWork(uint64_t max_cost) noexcept = 0;
 
     /** Create a staging graph (which cannot exist already). This acts as if a full copy of
      *  the transaction graph is made, upon which further modifications are made. This copy can
@@ -257,7 +257,7 @@ public:
  *  and on the sum of transaction sizes within a cluster.
  *
  * - max_cluster_count cannot exceed MAX_CLUSTER_COUNT_LIMIT.
- * - acceptable_iters controls how many linearization optimization steps will be performed per
+ * - acceptable_cost controls how much linearization optimization work will be performed per
  *   cluster before they are considered to be of acceptable quality.
  * - fallback_order determines how to break tie-breaks between transactions:
  *   fallback_order(a, b) < 0 means a is "better" than b, and will (in case of ties) be placed
@@ -266,7 +266,7 @@ public:
 std::unique_ptr<TxGraph> MakeTxGraph(
     unsigned max_cluster_count,
     uint64_t max_cluster_size,
-    uint64_t acceptable_iters,
+    uint64_t acceptable_cost,
     const std::function<std::strong_ordering(const TxGraph::Ref&, const TxGraph::Ref&)>& fallback_order
 ) noexcept;
 
diff --git a/src/txmempool.cpp b/src/txmempool.cpp
index 27b4c886..bfff1816 100644
--- a/src/txmempool.cpp
+++ b/src/txmempool.cpp
@@ -179,7 +179,7 @@ CTxMemPool::CTxMemPool(Options opts, bilingual_str& error)
     m_txgraph = MakeTxGraph(
         /*max_cluster_count=*/m_opts.limits.cluster_count,
         /*max_cluster_size=*/m_opts.limits.cluster_size_vbytes * WITNESS_SCALE_FACTOR,
-        /*acceptable_iters=*/ACCEPTABLE_ITERS,
+        /*acceptable_cost=*/ACCEPTABLE_COST,
         /*fallback_order=*/[&](const TxGraph::Ref& a, const TxGraph::Ref& b) noexcept {
             const Txid& txid_a = static_cast<const CTxMemPoolEntry&>(a).GetTx().GetHash();
             const Txid& txid_b = static_cast<const CTxMemPoolEntry&>(b).GetTx().GetHash();
@@ -221,7 +221,7 @@ void CTxMemPool::Apply(ChangeSet* changeset)
 
         addNewTransaction(it);
     }
-    if (!m_txgraph->DoWork(POST_CHANGE_WORK)) {
+    if (!m_txgraph->DoWork(/*max_cost=*/POST_CHANGE_COST)) {
         LogDebug(BCLog::MEMPOOL, "Mempool in non-optimal ordering after addition(s).");
     }
 }
@@ -380,7 +380,7 @@ void CTxMemPool::removeForReorg(CChain& chain, std::function<bool(txiter)> check
     for (indexed_transaction_set::const_iterator it = mapTx.begin(); it != mapTx.end(); it++) {
         assert(TestLockPointValidity(chain, it->GetLockPoints()));
     }
-    if (!m_txgraph->DoWork(POST_CHANGE_WORK)) {
+    if (!m_txgraph->DoWork(/*max_cost=*/POST_CHANGE_COST)) {
         LogDebug(BCLog::MEMPOOL, "Mempool in non-optimal ordering after reorg.");
     }
 }
@@ -425,7 +425,7 @@ void CTxMemPool::removeForBlock(const std::vector<CTransactionRef>& vtx, unsigne
     }
     lastRollingFeeUpdate = GetTime();
     blockSinceLastRollingFeeBump = true;
-    if (!m_txgraph->DoWork(POST_CHANGE_WORK)) {
+    if (!m_txgraph->DoWork(/*max_cost=*/POST_CHANGE_COST)) {
         LogDebug(BCLog::MEMPOOL, "Mempool in non-optimal ordering after block.");
     }
 }
diff --git a/src/txmempool.h b/src/txmempool.h
index 9feeee3e..5a870f4c 100644
--- a/src/txmempool.h
+++ b/src/txmempool.h
@@ -49,14 +49,13 @@ struct bilingual_str;
 /** Fake height value used in Coin to signify they are only in the memory pool (since 0.8) */
 static const uint32_t MEMPOOL_HEIGHT = 0x7FFFFFFF;
 
-/** How many linearization iterations required for TxGraph clusters to have
- * "acceptable" quality, if they cannot be optimally linearized with fewer
- * iterations. */
-static constexpr uint64_t ACCEPTABLE_ITERS = 1'700;
+/** How much linearization cost required for TxGraph clusters to have
+ * "acceptable" quality, if they cannot be optimally linearized with less cost. */
+static constexpr uint64_t ACCEPTABLE_COST = 1'700;
 
 /** How much work we ask TxGraph to do after a mempool change occurs (either
  * due to a changeset being applied, a new block being found, or a reorg). */
-static constexpr uint64_t POST_CHANGE_WORK = 5 * ACCEPTABLE_ITERS;
+static constexpr uint64_t POST_CHANGE_COST = 5 * ACCEPTABLE_COST;
 
 /**
  * Test whether the LockPoints height and time are still valid on the current chain