diff --git a/lowtime/__init__.py b/lowtime/__init__.py
index 71b63b8..ee2edd1 100644
--- a/lowtime/__init__.py
+++ b/lowtime/__init__.py
@@ -14,4 +14,4 @@
 
 """A library for solving the time-cost tradeoff problem."""
 
-__version__ = "0.1.0"
+__version__ = "0.2.0"
diff --git a/lowtime/cost_model.py b/lowtime/cost_model.py
index 376f0f5..44a2b7d 100644
--- a/lowtime/cost_model.py
+++ b/lowtime/cost_model.py
@@ -197,6 +197,10 @@ def l2_error(coefficients: tuple[float, float, float]) -> float:
             if error == np.inf:
                 continue
 
+            # The exponential model must be convex.
+            if opt_a < 0.0:
+                continue
+
             # We have coefficients that somewhat fit the data.
             logger.info(
                 "Initial guess %s fit with coefficients %s and error %f.",
@@ -224,6 +228,6 @@ def l2_error(coefficients: tuple[float, float, float]) -> float:
         return best_coefficients
 
     @lru_cache
-    def __call__(self, quant_time: int) -> float:
+    def __call__(self, quant_time: int) -> float:  # pyright: ignore
         """Predict execution cost given quantized time."""
         return self.fn(quant_time, *self.coefficients)
diff --git a/lowtime/graph_utils.py b/lowtime/graph_utils.py
index 3a09ac8..72859ad 100644
--- a/lowtime/graph_utils.py
+++ b/lowtime/graph_utils.py
@@ -279,6 +279,9 @@ def aoa_to_critical_dag(aoa_dag: nx.DiGraph, attr_name: str = "op") -> nx.DiGrap
         - The graph has only one source node, annotated as "source_node" on the graph.
         - The graph has only one sink node, annotated as "sink_node" on the graph.
     """
+    if not nx.is_directed_acyclic_graph(aoa_dag):
+        raise ValueError("The given graph is not a DAG.")
+
     # Clear all earliest/latest start/end times.
     for _, _, edge_attr in aoa_dag.edges(data=True):
         operation: Operation = edge_attr[attr_name]
diff --git a/lowtime/operation.py b/lowtime/operation.py
index 7051afb..91cccc9 100644
--- a/lowtime/operation.py
+++ b/lowtime/operation.py
@@ -94,9 +94,12 @@ class CandidateExecutionOptions(Generic[KnobT]):
 
     Args:
         options: All candidate execution options of the operation.
+        noise_factor: A factor to multiply `real_time` and `cost` by to allow some slack.
+
     """
 
     options: list[ExecutionOption[KnobT]]
+    noise_factor: float = 1.0
     _knob_cache: dict[int, KnobT] = field(init=False, repr=False, factory=dict)
 
     def __attrs_post_init__(self) -> None:
@@ -105,8 +108,10 @@ def __attrs_post_init__(self) -> None:
         orig_options = sorted(self.options, key=lambda x: x.real_time, reverse=True)
         filtered_options: list[ExecutionOption[KnobT]] = []
         for option in orig_options:
+            real_time = option.real_time * self.noise_factor
+            cost = option.cost * self.noise_factor
             if any(
-                other.real_time < option.real_time and other.cost < option.cost
+                other.real_time < real_time and other.cost < cost
                 for other in orig_options
             ):
                 continue
@@ -215,7 +220,7 @@ def __attrs_post_init__(self) -> None:
         self.min_duration = min(quant_times)
 
         # By default, execute with the slowest speed. `assigned_knob` will
-        # automatically be set by `duration_setter`.
+        # automatically be set by `_knob_setter`.
         self.duration = self.max_duration
 
     def __str__(self) -> str:
@@ -257,6 +262,6 @@ def __str__(self) -> str:
         """Return a readable string representation."""
         return "DummyOperation()"
 
-    def get_cost(self, _: int | None = None) -> float:
+    def get_cost(self, _: int | None = None) -> float:  # pyright: ignore
         """No cost for dummy operations."""
         raise AttributeError("DummyOperation has no cost.")
diff --git a/pyproject.toml b/pyproject.toml
index b0b8afe..a8296f6 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -48,6 +48,9 @@ include = ["lowtime*"]
 exclude = ["examples", "scripts", "stubs", "tests"]
 
 [tool.ruff]
+line-length = 120
+
+[tool.ruff.lint]
 select = [
   "E",   # pycodestyle error
   "F",   # pyflakes
@@ -69,12 +72,11 @@ ignore = [
   "SIM115",   # Context manager for opening files
   "E501",     # Line too long
 ]
-line-length = 120
 
-[tool.ruff.pydocstyle]
+[tool.ruff.lint.pydocstyle]
 convention = "google"
 
-[tool.ruff.per-file-ignores]
+[tool.ruff.lint.per-file-ignores]
 "**/__init__.py" = ["F401", "F403"]
 
 [tool.pyright]
diff --git a/scripts/lint.sh b/scripts/lint.sh
index 8ebdebc..1aa50c6 100755
--- a/scripts/lint.sh
+++ b/scripts/lint.sh
@@ -8,5 +8,5 @@ else
   black --check lowtime
 fi
 
-ruff lowtime
+ruff check lowtime
 pyright lowtime