finish all analysis and upload data and results

codes/experiments/real_data/analysis/comparison.py

@@ -0,0 +1,92 @@
+import pandas as pd
+import os
+import matplotlib.pyplot as plt
+from sklearn.metrics import mean_squared_error, mean_absolute_error
+
+raw_path  = "results/real_data/raw/dimacs_s42.csv"
+pred_path = "results/real_data/derived/distribution/dimacs_prediction_result/prediction.csv"
+save_folder = "results/real_data/derived/comparison"
+os.makedirs(save_folder, exist_ok=True)
+
+raw  = pd.read_csv(raw_path)
+pred = pd.read_csv(pred_path)
+
+# real: trial 평균
+agg = (
+    raw.groupby("file")
+    .agg(
+        nodes        = ("nodes",        "first"),
+        density      = ("density",      "first"),
+        real_time    = ("time",         "mean"),
+        real_relax   = ("relax_success","mean"),
+    )
+    .reset_index()
+)
+
+# prediction: file 기준으로 merge
+pred_cols = pred[["file", "predict_time", "relax_success"]].rename(
+    columns={"relax_success": "pred_relax"}
+)
+
+merged = agg.merge(pred_cols, on="file", how="inner")
+
+# 오차 계산
+for real_col, pred_col, prefix in [
+    ("real_time",  "predict_time", "time"),
+    ("real_relax", "pred_relax",   "relax"),
+]:
+    merged[f"{prefix}_abs_err"] = (merged[pred_col] - merged[real_col]).abs()
+    merged[f"{prefix}_rel_err"] = merged[f"{prefix}_abs_err"] / merged[real_col]
+
+cols = [
+    "file", "nodes", "density",
+    "real_time",  "predict_time",  "time_abs_err",  "time_rel_err",
+    "real_relax", "pred_relax",    "relax_abs_err", "relax_rel_err",
+]
+merged[cols].to_csv(os.path.join(save_folder, "comparison.csv"), index=False)
+print(merged[cols].to_string(index=False))
+print(f"\nSaved → {save_folder}/comparison.csv")
+
+for real_col, pred_col, label in [
+    ("real_time",  "predict_time", "time"),
+    ("real_relax", "pred_relax",   "relax_success"),
+]:
+    y     = merged[real_col].to_numpy()
+    y_hat = merged[pred_col].to_numpy()
+    ss_res = ((y - y_hat) ** 2).sum()
+    ss_tot = ((y - y.mean()) ** 2).sum()
+    r2   = 1 - ss_res / ss_tot
+    rmse = mean_squared_error(y, y_hat) ** 0.5
+    mae  = mean_absolute_error(y, y_hat)
+    print(f"\n[{label}]  R²={r2:.4f}  RMSE={rmse:.4g}  MAE={mae:.4g}")
+
+
+# ── Plot ───────────────────────────────────────────────────────────────────────
+fig, axes = plt.subplots(1, 2, figsize=(12, 5))
+
+for ax, real_col, pred_col, label in [
+    (axes[0], "real_time",  "predict_time", "Runtime [s]"),
+    (axes[1], "real_relax", "pred_relax",   "Relax Success"),
+]:
+    x = merged[real_col].to_numpy()
+    y = merged[pred_col].to_numpy()
+    mn, mx = min(x.min(), y.min()), max(x.max(), y.max())
+
+    ax.scatter(x, y, s=60, zorder=3)
+    for _, row in merged.iterrows():
+        ax.annotate(
+            row["file"].replace("USA-road-d.", "").replace(".gr", ""),
+            (row[real_col], row[pred_col]),
+            fontsize=6, textcoords="offset points", xytext=(4, 2)
+        )
+    ax.plot([mn, mx], [mn, mx], color="red", linestyle="--", linewidth=1.2, label="y = x")
+    ax.set_xlabel(f"Real {label}")
+    ax.set_ylabel(f"Predicted {label}")
+    ax.set_title(f"Predicted vs Real — {label}")
+    ax.legend(fontsize=8)
+    ax.grid(True, alpha=0.4)
+
+fig.tight_layout()
+fig.savefig(os.path.join(save_folder, "comparison_plot.png"), dpi=300)
+plt.close(fig)
+print(f"Saved → {save_folder}/comparison_plot.png")

codes/experiments/real_data/analysis/dimacs_prediction.py

@@ -0,0 +1,78 @@
+from experiments.synthetic_data.analysis.processing_time_analysis import mean_l
+from experiments.synthetic_data.analysis.processing_time_analysis import regression_k3
+from experiments.synthetic_data.analysis.processing_time_analysis import regression_m
+from experiments.synthetic_data.analysis.call_number_analysis import (
+    nonlinear_regression,
+)
+import numpy as np
+import pandas as pd
+import os
+
+
+def k3(V):
+    return k3_a * np.exp(-k3_b * V) + k3_c
+
+
+def m(V):
+    return m_a * np.log2(V) + m_b
+
+
+def relax_success(E, S, AVG_DEG):
+    relax_attempts = E
+    relax_success_ratio = (rs_a * np.log(S) + rs_b) * AVG_DEG**rs_c
+    return relax_attempts * relax_success_ratio
+
+
+def runtime_predict(V, D, S):
+    E = V * (V - 1) * D
+    AVG_DEG = (V - 1) * D
+    if AVG_DEG < 1:
+        return False, False
+
+    runtime = V * l + E * k3(V) + relax_success(E, S, AVG_DEG) * m(V)
+    print(relax_success(E, S, AVG_DEG))
+    # runtime_eq = f"[V * {l}] + [E * {k3_a} * exp(-{k3_b} * V) + {k3_c}] + [E * ({rs_a} * log(S) + {rs_b}) * AVG_DEG ** {rs_c} * {m_a} * log_2(V) + {m_b}]"
+
+    return runtime, relax_success(E, S, AVG_DEG)
+
+
+l = mean_l()
+k3_a, k3_b, k3_c = regression_k3()
+m_a, m_b = regression_m()
+rs_a, rs_b, rs_c = nonlinear_regression()
+
+csv_file = "results/real_data/derived/dimacs_graph_distribution/distribution.csv"
+save_folder = f"results/real_data/derived/{os.path.splitext(os.path.basename(csv_file))[0]}/dimacs_prediction_result"
+os.makedirs(save_folder, exist_ok=True)
+
+df = pd.read_csv(csv_file)
+
+records = []
+
+for row in df.itertuples():
+    nodes = row.nodes
+    density = row.density
+    sigma = np.sqrt(np.log((row.std / row.mean) ** 2 + 1))
+
+    pred_time, pred_relax_success = runtime_predict(nodes, density, sigma)
+
+    if pred_time is False:
+        continue
+    records.append(
+        {
+            "file": row.file,
+            "nodes": nodes,
+            "density": density,
+            "sigma": sigma,
+            "predict_time": pred_time,
+            "relax_success": pred_relax_success,
+        }
+    )
+    print(f"finished {row.file}")
+
+result = pd.DataFrame(records)
+out_path = os.path.join(save_folder, "prediction.csv")
+result.to_csv(out_path, index=False)
+print(f"Saved {len(result)} rows → {out_path}")
+
+

codes/experiments/real_data/analysis/graph_distribution.py

@@ -102,18 +102,18 @@ def visualize_weights(file):
 
 folder = "experiments/real_data/data/dimacs_data"
 files = [
-    # "USA-road-d.BAY.gr",
-    # "USA-road-d.CAL.gr",
-    # "USA-road-d.COL.gr",
-    # "USA-road-d.CTR.gr",
-    # "USA-road-d.E.gr",
-    # "USA-road-d.FLA.gr",
-    # "USA-road-d.LKS.gr",
-    # "USA-road-d.NE.gr",
-    # "USA-road-d.NW.gr",
-    # "USA-road-d.NY.gr",
+    "USA-road-d.BAY.gr",
+    "USA-road-d.CAL.gr",
+    "USA-road-d.COL.gr",
+    "USA-road-d.CTR.gr",
+    "USA-road-d.E.gr",
+    "USA-road-d.FLA.gr",
+    "USA-road-d.LKS.gr",
+    "USA-road-d.NE.gr",
+    "USA-road-d.NW.gr",
+    "USA-road-d.NY.gr",
     "USA-road-d.USA.gr",
-    # "USA-road-d.W.gr"
+    "USA-road-d.W.gr"
 ]
 
 res_folder = "results/real_data/derived/dimacs_graph_distribution"

codes/experiments/real_data/run/dimacs_run.py

@@ -1,75 +1,73 @@
 import os
+import gc
 import time
 import pandas as pd
-import numpy as np
+import random
 
 from experiments.real_data.graph_converters.dimacs_graph_converter import dimacs_convert_graph
 from core.dijkstra.heap_dijkstra import heap_dijkstra
 from core.heaps.binary_heap import BinHeap
-from core.heaps.fibonacci_heap import FiboHeap
+
+def done_trials(out_path, file):
+    if not os.path.exists(out_path):
+        return set()
+    df = pd.read_csv(out_path, usecols=["file", "trial"])
+    return set(df[df["file"] == file]["trial"].tolist())
 
 def run_test(
     folder,
     files,
-    trials,
-    base_seed
+    base_seed,
+    out_path,
+    trials=10,
 ):
-    rows = []
     timer = time.perf_counter
-    rng = np.random.default_rng(base_seed)
-    INF = float('inf')
+    write_header = not os.path.exists(out_path)
 
     for file in files:
+        completed = done_trials(out_path, file)
+        remaining = [t for t in range(1, trials + 1) if t not in completed]
+
+        if not remaining:
+            print(f"[SKIP] {file} (all {trials} trials done)")
+            continue
+
+        print(f"[LOAD] {file}  (completed: {sorted(completed)}, remaining: {remaining})")
         nodes, adj = dimacs_convert_graph(f'{folder}/{file}')
         density = len(adj) / (nodes * (nodes - 1))
 
-        for trial in range(1, trials + 1):
-            start, end = rng.choice(nodes, size=2, replace=False) + 1
+        for trial in remaining:
+            print(f"  trial {trial}/{trials}")
+
+            random.seed(base_seed + trial)
+            start = random.randint(1, nodes)
 
             bin_heap = BinHeap(nodes)
             st = timer()
-            dist, stats = heap_dijkstra(nodes, adj, bin_heap, start, end)
+            stats = heap_dijkstra(nodes, adj, bin_heap, start)
             et = timer()
-            rows.append(
-                {
-                    "file": file,
-                    "nodes": nodes,
-                    "density": density,
-                    "trial": trial,
-                    "start": start,
-                    "end": end,
-                    "time": et - st,
-                    "algorithm": "binary",
-                    "reached": dist != INF,
-                    "extract_min_calls": stats.extract_min_calls,
-                    "relax_attempts": stats.relax_attempts,
-                    "relax_success": stats.relax_success,
-                }
-            )
 
-            fibo_heap = FiboHeap(nodes)
-            st = timer()
-            dist, stats = heap_dijkstra(nodes, adj, fibo_heap, start, end)
-            et = timer()
-            rows.append(
-                {
-                    "file": file,
-                    "nodes": nodes,
-                    "density": density,
-                    "trial": trial,
-                    "start": start,
-                    "end": end,
-                    "time": et - st,
-                    "algorithm": "fibonacci",
-                    "reached": dist != INF,
-                    "extract_min_calls": stats.extract_min_calls,
-                    "relax_attempts": stats.relax_attempts,
-                    "relax_success": stats.relax_success,
-                }
-            )
+            row = pd.DataFrame([{
+                "file": file,
+                "nodes": nodes,
+                "density": density,
+                "start": start,
+                "time": et - st,
+                "trial": trial,
+                "extract_min_calls": stats.extract_min_calls,
+                "relax_attempts": stats.relax_attempts,
+                "relax_success": stats.relax_success,
+            }])
+            row.to_csv(out_path, mode="a", header=write_header, index=False)
+            write_header = False
+
+            del bin_heap
+            gc.collect()
+
+        del adj
+        gc.collect()
+        print(f"[DONE] {file}")
 
-    df = pd.DataFrame(rows)
-    return df
 
 # Settings
 folder = "experiments/real_data/data/dimacs_data"
@@ -87,16 +85,15 @@ files = [
 "USA-road-d.USA.gr",
 "USA-road-d.W.gr"
 ]
-trials = 200
 base_seed = 42
 
-df = run_test(
-    folder=folder,
-    files=files,
-    trials=trials,
-    base_seed=base_seed
-)
-
 save_folder = "results/real_data/raw"
 os.makedirs(save_folder, exist_ok=True)
-df.to_csv(f"{save_folder}/dimacs_t{trials}_s{base_seed}.csv", index=False)
+out_path = f"{save_folder}/dimacs_s{base_seed}.csv"
+
+run_test(
+    folder=folder,
+    files=files,
+    base_seed=base_seed,
+    out_path=out_path,
+)

codes/experiments/synthetic_data/analysis/call_number_analysis.py

@@ -7,19 +7,6 @@ from scipy.optimize import curve_fit
 import numpy as np
 
 
-# Initial Setup
-csv_file = "results/synthetic_data/raw/20260421_031740.csv"
-save_folder = f"results/synthetic_data/derived/{os.path.splitext(os.path.basename(csv_file))[0]}/call_number_analysis"
-os.makedirs(save_folder, exist_ok=True)
-
-df = pd.read_csv(csv_file)
-df = df[df["algorithm"] == "binary"].copy()
-df["relax_success_ratio"] = df["relax_success"] / df["relax_attempts"]
-df["E"] = df["nodes"] * (df["nodes"] - 1) * df["density"]
-df["decrease_key"] = df["relax_success"]
-df["avg_degree"] = (df["nodes"] - 1) * df["density"]
-
-
 # 1. E vs relax_attempts
 def E_vs_relax_attempts(df):
     X = df[["E"]].to_numpy()
@@ -292,7 +279,7 @@ def regime_distribution(df):
 
 
 # 6. Nonlinear regression: r = (a·ln(sigma) + b) · avg_deg^c
-def nonlinear_regression(df):
+def nonlinear_regression(compute_local=False):
     # Filter: giant component regime only
     sub = df[(df["avg_degree"] >= 1) & (df["relax_success_ratio"] < 0.99)].copy()
     sub = sub[sub["relax_success_ratio"] > 0].dropna(subset=["relax_success_ratio", "avg_degree", "sigma"])
@@ -301,8 +288,6 @@ def nonlinear_regression(df):
     sigma   = sub["sigma"].to_numpy()
     r       = sub["relax_success_ratio"].to_numpy()
 
-    print(f"Fitting on {len(sub)} data points")
-
     def model(X, a, b, c):
         avg_deg_, sigma_ = X
         return (a * np.log(sigma_) + b) * avg_deg_ ** c
@@ -319,6 +304,9 @@ def nonlinear_regression(df):
     ss_tot = np.sum((r - r.mean()) ** 2)
     r2 = 1 - ss_res / ss_tot
 
+    if compute_local == False:
+        return (a, b, c)
+
     print("\n=== Nonlinear regression: r = (a·ln(σ) + b) · avg_deg^c ===")
     print(f"  a = {a:.6f} ± {perr[0]:.6f}")
     print(f"  b = {b:.6f} ± {perr[1]:.6f}")
@@ -360,9 +348,22 @@ def nonlinear_regression(df):
     print(f"Saved nonlinear regression plots to {nlr_save_folder}")
 
 
+
+# Initial Setup
+csv_file = "results/synthetic_data/raw/20260421_031740.csv"
+save_folder = f"results/synthetic_data/derived/{os.path.splitext(os.path.basename(csv_file))[0]}/call_number_analysis"
+os.makedirs(save_folder, exist_ok=True)
+
+df = pd.read_csv(csv_file)
+df = df[df["algorithm"] == "binary"].copy()
+df["relax_success_ratio"] = df["relax_success"] / df["relax_attempts"]
+df["E"] = df["nodes"] * (df["nodes"] - 1) * df["density"]
+df["decrease_key"] = df["relax_success"]
+df["avg_degree"] = (df["nodes"] - 1) * df["density"]
+
 E_vs_relax_attempts(df) # 1
 sigma_vs_relax_success_ratio(df) # 2
 avg_degree_vs_relax_success_ratio(df) # 3
 log_avg_degree_vs_log_ratio(df) # 4
 regime_distribution(df) # 5
-nonlinear_regression(df) # 6
+nonlinear_regression(compute_local=True) # 6

codes/experiments/synthetic_data/analysis/prediction.py

@@ -0,0 +1,123 @@
+from experiments.synthetic_data.analysis.processing_time_analysis import mean_l
+from experiments.synthetic_data.analysis.processing_time_analysis import regression_k3
+from experiments.synthetic_data.analysis.processing_time_analysis import regression_m
+from experiments.synthetic_data.analysis.call_number_analysis import nonlinear_regression
+import numpy as np
+import pandas as pd
+import os
+import matplotlib.pyplot as plt
+from sklearn.metrics import mean_squared_error, mean_absolute_error
+
+def k3(V):
+    return k3_a * np.exp(-k3_b * V) + k3_c
+
+def m(V):
+    return m_a * np.log2(V) + m_b
+
+def relax_success(E, S, AVG_DEG):
+    relax_attempts = E
+    relax_success_ratio = (rs_a * np.log(S) + rs_b) * AVG_DEG ** rs_c
+    return relax_attempts * relax_success_ratio
+
+
+def runtime_predict(V, D, S):
+    E = V * (V - 1) * D
+    AVG_DEG = (V - 1) * D
+    if AVG_DEG < 1:
+        return False
+    
+    runtime = V * l + E * k3(V) + relax_success(E, S, AVG_DEG) * m(V)
+    print(relax_success(E, S, AVG_DEG))
+    # runtime_eq = f"[V * {l}] + [E * {k3_a} * exp(-{k3_b} * V) + {k3_c}] + [E * ({rs_a} * log(S) + {rs_b}) * AVG_DEG ** {rs_c} * {m_a} * log_2(V) + {m_b}]"
+
+    return runtime
+    
+
+l = mean_l()
+k3_a, k3_b, k3_c = regression_k3()
+m_a, m_b = regression_m()
+rs_a, rs_b, rs_c = nonlinear_regression()
+
+csv_file = "results/synthetic_data/raw/20260421_031740.csv"
+save_folder = f"results/synthetic_data/derived/{os.path.splitext(os.path.basename(csv_file))[0]}/prediction_result"
+os.makedirs(save_folder, exist_ok=True)
+
+df = pd.read_csv(csv_file)
+df = df[df["algorithm"] == "binary"].copy()
+
+records = []
+for row in df.itertuples():
+    predicted = runtime_predict(row.nodes, row.density, row.sigma)
+    if predicted is False:
+        continue
+    records.append({
+        "nodes":        row.nodes,
+        "density":      row.density,
+        "sigma":        row.sigma,
+        "trial":        row.trial,
+        "real_time":    row.time,
+        "predict_time": predicted,
+        "abs_error": abs(row.time - predicted),
+        "rel_error": abs(row.time - predicted) / row.time,
+    })
+
+result = pd.DataFrame(records)
+out_path = os.path.join(save_folder, "prediction.csv")
+result.to_csv(out_path, index=False)
+print(f"Saved {len(result)} rows → {out_path}")
+
+real = result["real_time"].to_numpy()
+pred = result["predict_time"].to_numpy()
+
+ss_res = np.sum((real - pred) ** 2)
+ss_tot = np.sum((real - real.mean()) ** 2)
+r2 = 1 - ss_res / ss_tot
+print(f"R² = {r2:.4f}")
+
+rmse = np.sqrt(mean_squared_error(real, pred))
+mae  = mean_absolute_error(real, pred)
+
+print(f"RMSE: {rmse:.4f} s")  # 평균 제곱 오차의 제곱근
+print(f"MAE:  {mae:.4f} s")   # 평균 절대 오차
+
+mn, mx = min(real.min(), pred.min()), max(real.max(), pred.max())
+
+fig, ax = plt.subplots(figsize=(6, 6))
+ax.scatter(real, pred, s=5, alpha=0.3, color="steelblue")
+ax.plot([mn, mx], [mn, mx], color="red", linewidth=1.5, linestyle="--", label="y = x")
+ax.set_xlabel("real_time [s]")
+ax.set_ylabel("predict_time [s]")
+ax.set_title(f"Predicted vs Real Runtime  R²={r2:.4f}")
+ax.legend(fontsize=9)
+ax.grid(True, alpha=0.4)
+fig.tight_layout()
+fig.savefig(os.path.join(save_folder, "predicted_vs_real.png"), dpi=300)
+plt.close(fig)
+print(f"Saved: {save_folder}/predicted_vs_real.png")
+
+# rel_error distribution
+rel_err = result["rel_error"].to_numpy()
+
+fig, axes = plt.subplots(1, 2, figsize=(12, 5))
+
+# histogram
+axes[0].hist(rel_err, bins=50, color="steelblue", edgecolor="none", alpha=0.8)
+axes[0].axvline(np.median(rel_err), color="red",    linestyle="--", linewidth=1.5, label=f"median={np.median(rel_err):.3f}")
+axes[0].axvline(np.mean(rel_err),   color="orange", linestyle="--", linewidth=1.5, label=f"mean={np.mean(rel_err):.3f}")
+axes[0].set_xlabel("rel_error")
+axes[0].set_ylabel("count")
+axes[0].set_title("Relative Error Distribution")
+axes[0].legend(fontsize=9)
+axes[0].grid(True, alpha=0.4)
+
+# rel_error vs real_time
+axes[1].scatter(real, rel_err, s=5, alpha=0.3, color="steelblue")
+axes[1].set_xlabel("real_time [s]")
+axes[1].set_ylabel("rel_error")
+axes[1].set_title("Relative Error vs Real Time")
+axes[1].grid(True, alpha=0.4)
+
+fig.tight_layout()
+fig.savefig(os.path.join(save_folder, "rel_error_dist.png"), dpi=300)
+plt.close(fig)
+print(f"Saved: {save_folder}/rel_error_dist.png")

codes/experiments/synthetic_data/analysis/processing_time_analysis.py

@@ -4,193 +4,252 @@ import matplotlib.pyplot as plt
 import os
 from sklearn.linear_model import LinearRegression
 from sklearn.metrics import r2_score
+from scipy.optimize import curve_fit
 
+# Heap: Binary
+#
 # Runtime = Add + Extract-min + Relax-attempts + Relax-success
-#         = VlogV * k1 + VlogV * k2 + E * k3 + \alpha * logV * k4 (Binary)
-#         = V * k1 + VlogV * k2 + E * k3 + \alpha * k4 (Fibonacci)
+#         = VlogV * k1 + VlogV * k2 + E * k3 + \alpha * logV * k4
 # (\alpha = relax_success)
 #
 # V increases -> Add, Extract-min, Relax-attempts, Relax-success all increases.
 # Therfore, critical multicollinearlity occurs.
 #
-# To solve, run regression per each V.
+# To solve this problem, run regression per each V.
 # Then V becomes constant.
 #
-# Runtime(Binary) = VlogV * k1 + VlogV * k2 + E * k3 + \alpha * logV * k4 (Binary)
-#                 = intercept + E * k3 + \alpha * k4
-# Runtime(Fibonacci) = V * k1 + VlogV * k2 + E * k3 + \alpha * k4 (Fibonacci)
-#                    = intercept + E * k3 + \alpha * k4
+# Runtime_V = (V) * (logV(k1 + k2)) + (E) * k3 + (\alpha) * (logV * k4)
+#
+# left part: call number, right part: cost per call
+# call number is not concern in operation cost analysis.
+# Important thing is that logV in right sides become constant.
 #
 # Final equation
-# Runtime of specific V = intercept + E * k3 + \alpha * k4
+# Runtime of specific V = V * l + E * k3 + \alpha * m
 # 
-# intercept absorbs V*(k1+k2) which is constant within each N.
-# k3: cost per relax_attempt  (should be equal across heaps)
-# k4: cost per decrease-key   (binary: should scale with log2N; fibonacci: should be constant)
+# Using this equation, we can get l, k3, and m from each regression.
+# l, m are defined like this.
+# l = logV * (k1 + k2)
+# m = logV * k4
+# 
+# 
+# Final result
+# l: cost per each add and extract-min (should scale with log2N)
+# k3: cost per relax_attempt (should be equal across heaps)
+# m: cost per decrease-key (should scale with log2N)
+#
+# (All base of log in this context is 2 due to binary heap.)
 
+
+# contribution diagram
+def contribution():
+    contribution_records = []
+
+    for n in nodes:
+        g = df[df['nodes'] == n]
+        g = g[g['relax_success'] > 0]
+        
+        if len(g) < 3:
+            continue
+        
+        # 해당 N의 l, k3, m 가져오기
+        row = results[results['N'] == n].iloc[0]
+        l_val = row['l']
+        k3_val = row['k3']  # k3_fixed
+        m_val = row['m']
+        
+        # 각 항의 평균값 계산
+        E_mean     = g['relax_attempts'].mean()
+        alpha_mean = g['relax_success'].mean()
+        
+        Vl   = n * l_val           # V·l
+        Ek3  = E_mean * k3_val     # E·k3
+        am   = alpha_mean * m_val  # α·m
+        
+        total = Vl + Ek3 + am
+        
+        contribution_records.append({
+            'N'       : n,
+            'V·l'     : Vl,
+            'E·k3'    : Ek3,
+            'α·m'     : am,
+            'total'   : total,
+            'V·l %'   : Vl   / total * 100,
+            'E·k3 %'  : Ek3  / total * 100,
+            'α·m %'   : am   / total * 100,
+        })
+
+    contrib = pd.DataFrame(contribution_records)
+    print("\n=== Contribution of each operations ===")
+    print(contrib[['N','V·l %','E·k3 %','α·m %']].to_string(index=False))
+
+    # 시각화
+    fig, ax = plt.subplots(figsize=(9, 5))
+
+    x = np.arange(len(contrib))
+    w = 0.25
+
+    ax.bar(x - w, contrib['V·l %'],  width=w, label='V·l  (add+extract)')
+    ax.bar(x,     contrib['E·k3 %'], width=w, label='E·k3 (relax-attempt)')
+    ax.bar(x + w, contrib['α·m %'],  width=w, label='α·m  (decrease-key)')
+
+    ax.set_xticks(x)
+    ax.set_xticklabels(contrib['N'].astype(int))
+    ax.set_xlabel('N (nodes)')
+    ax.set_ylabel('Contribution (%)')
+    ax.set_title('Runtime contribution by operation')
+    ax.legend()
+    ax.grid(True, alpha=0.4)
+    fig.tight_layout()
+    fig.savefig(f"{save_folder}/contribution_vs_N.png", dpi=300)
+    plt.close(fig)
+    print(f"Saved: contribution_vs_N.png")
+
+
+# l
+def mean_l():
+    return results["l"].mean()
+
+def plot_l():
+    fig, ax = plt.subplots(figsize=(7, 5))
+    ax.plot(nodes, l_bin, marker="o", color="steelblue", label="l")
+    ax.set_xlabel("N (nodes)")
+    ax.set_ylabel("l — add + extract-min unit cost [s]")
+    ax.set_title("l (add + extract-min unit cost) vs N")
+    ax.legend(fontsize=8)
+    ax.grid(True, alpha=0.4)
+    fig.tight_layout()
+    fig.savefig(f"{save_folder}/l_vs_N.png", dpi=300)
+    plt.close(fig)
+    print(f"Saved: {save_folder}/l_vs_N.png")
+
+# k3
+def regression_k3():
+    n_arr = np.array(nodes, dtype=float)
+
+    def exp_conv(n, a, b, c):
+        return a * np.exp(-b * n) + c
+
+    k3_arr = np.array(k3_bin, dtype=float)
+    popt_ec, _ = curve_fit(exp_conv, n_arr, k3_arr,
+                            p0=[float(k3_arr.max() - k3_arr.min()), 1/float(n_arr.mean()), float(k3_arr.min())],
+                            maxfev=20000)
+    
+    return popt_ec
+
+def plot_k3():
+    n_arr = np.array(nodes, dtype=float)
+    n_line = np.linspace(min(nodes), max(nodes), 300)
+
+    def exp_conv(n, a, b, c):
+        return a * np.exp(-b * n) + c
+
+    k3_arr = np.array(k3_bin, dtype=float)
+    popt_ec, _ = curve_fit(exp_conv, n_arr, k3_arr,
+                            p0=[float(k3_arr.max() - k3_arr.min()), 1/float(n_arr.mean()), float(k3_arr.min())],
+                            maxfev=20000)
+    pred_ec = exp_conv(n_line, *popt_ec)
+    r2_ec = r2_score(k3_bin, exp_conv(n_arr, *popt_ec))
+
+    print("\n=== k3 exp_conv regression ===")
+    print("a * exp(-b*N) + c")
+    print(popt_ec)
+
+    fig, ax = plt.subplots(figsize=(9, 5))
+    ax.plot(nodes, k3_bin, marker="o", color="black", zorder=5, label="k3 (data)")
+    ax.plot(n_line, pred_ec,  linestyle="--", linewidth=1.5, label=f"exp conv      R²={r2_ec:.4f}")
+    ax.set_xlabel("N (nodes)")
+    ax.set_ylabel("k3 — iteration cost per call [s]")
+    ax.set_title("k3 (iteration unit cost) vs N — model comparison")
+    ax.legend(fontsize=8)
+    ax.grid(True, alpha=0.4)
+    fig.tight_layout()
+    fig.savefig(f"{save_folder}/k3_vs_N.png", dpi=300)
+    plt.close(fig)
+    print(f"Saved: {save_folder}/k3_vs_N.png")
+
+
+# m
+def regression_m():
+    log_n = np.log2(np.array(nodes)).reshape(-1, 1)
+    reg = LinearRegression().fit(log_n, m_bin)
+    return (reg.coef_[0], reg.intercept_)
+
+def plot_m():
+    log_n = np.log2(np.array(nodes)).reshape(-1, 1)
+    reg = LinearRegression().fit(log_n, m_bin)
+    r2_bin = r2_score(m_bin, reg.predict(log_n))
+
+    n_line = np.linspace(min(nodes), max(nodes), 300)
+    log_n_line = np.log2(n_line).reshape(-1, 1)
+
+    print("\n=== m log regression ===")
+    print("m = a * log_2(N) + b")
+    print(reg.coef_[0], reg.intercept_)
+
+    fig, ax = plt.subplots(figsize=(7, 5))
+    ax.plot(nodes, m_bin, marker="o", color="steelblue", label="binary k4")
+    ax.plot(n_line, reg.predict(log_n_line), color="steelblue", linestyle="--", linewidth=1.5,
+            label=f"fit (∝ log₂N)  R²={r2_bin:.3f}")
+    ax.set_xlabel("N (nodes)")
+    ax.set_ylabel("m — decrease-key cost per call [s]")
+    ax.set_title("m (decrease-key unit cost) vs N")
+    ax.legend(fontsize=8)
+    ax.grid(True, alpha=0.4)
+    fig.tight_layout()
+    fig.savefig(f"{save_folder}/m_vs_N.png", dpi=300)
+    plt.close(fig)
+    print(f"Saved: {save_folder}/m_vs_N.png")
+
+
+# Initial process
 csv_file = "results/synthetic_data/raw/20260421_031740.csv"
 save_folder = f"results/synthetic_data/derived/{os.path.splitext(os.path.basename(csv_file))[0]}/processing_time_analysis"
 os.makedirs(save_folder, exist_ok=True)
 
 df = pd.read_csv(csv_file)
 nodes = sorted(df["nodes"].unique())
-algos = ["binary", "fibonacci"]
+df = df[df["algorithm"] == "binary"]
 
 records = []
 
-for algo in algos:
-    sub = df[df["algorithm"] == algo]
-    for n in nodes:
-        g = sub[sub["nodes"] == n]
+for n in nodes:
+    g = df[df["nodes"] == n]
 
-        X = g[["relax_attempts", "relax_success"]].to_numpy()
-        y = g["time"].to_numpy()
+    X = g[["relax_attempts", "relax_success"]].to_numpy()
+    y = g["time"].to_numpy()
 
-        model = LinearRegression().fit(X, y)
-        r2 = r2_score(y, model.predict(X))
+    model = LinearRegression().fit(X, y)
+    r2 = r2_score(y, model.predict(X))
 
-        records.append({
-            "algorithm":      algo,
-            "N":         n,
-            "log2N":     round(np.log2(n), 4),
-            "intercept": model.intercept_,
-            "k3 (E)":    model.coef_[0],
-            "k4 (alpha)":model.coef_[1],
-            "r2":        r2,
-            "n":         len(g),
-        })
+    l = model.intercept_ / n
+    k3 = model.coef_[0]
+    m = model.coef_[1]
+
+    records.append({
+        "N": n,
+        "log2N": round(np.log2(n), 4),
+        "l": l,
+        "k3": k3,
+        "m": m,
+        "r2": r2,
+        "data": len(g),
+    })
 
 results = pd.DataFrame(records)
+grouped = results.set_index(["N"])
+l_bin = grouped.loc[nodes, "l"].values
+k3_bin = grouped.loc[nodes, "k3"].values
+m_bin = grouped.loc[nodes, "m"].values
 
-for algo in algos:
-    print(f"=== {algo} ===")
-    r = results[results["algorithm"] == algo][["N","log2N","intercept","k3 (E)","k4 (alpha)","r2","n"]]
+# Directly run
+if __name__ == "__main__":
+    r = results[["N","log2N","l","k3","m","r2","data"]]
+    print("=== Regression Result ===")
     print(r.to_string(index=False))
-    print()
+    print("\n=== l representative value ===\n", results["l"].describe(), sep="")
 
-grouped = results.set_index(["N", "algorithm"])
-
-def get_param(param):
-    return (
-        grouped.loc[(nodes, "binary"), param].values,
-        grouped.loc[(nodes, "fibonacci"), param].values
-    )
-
-k3_bin, k3_fib = get_param("k3 (E)")
-k4_bin, k4_fib = get_param("k4 (alpha)")
-int_bin, int_fib = get_param("intercept")
-
-# binary: k4 ~ log₂N 회귀
-log_n = np.log2(np.array(nodes)).reshape(-1, 1)
-bin_reg = LinearRegression().fit(log_n, k4_bin)
-r2_bin = r2_score(k4_bin, bin_reg.predict(log_n))
-
-# fibonacci: k4 ~ log₂N 회귀
-fib_reg = LinearRegression().fit(log_n, k4_fib)
-r2_fib = r2_score(k4_fib, fib_reg.predict(log_n))
-
-n_line = np.linspace(min(nodes), max(nodes), 300)
-log_n_line = np.log2(n_line).reshape(-1, 1)
-
-print(f"\nbinary log₂N regression: coef={bin_reg.coef_[0]:.4e}, intercept={bin_reg.intercept_:.4e}, R²={r2_bin:.4f}")
-
-# Plot
-fig, ax = plt.subplots(figsize=(7, 5))
-ax.plot(nodes, k4_bin, marker="o", color="steelblue", label="binary k4")
-ax.plot(nodes, k4_fib, marker="s", color="darkorange", label="fibonacci k4")
-ax.plot(n_line, bin_reg.predict(log_n_line), color="steelblue", linestyle="--", linewidth=1.5,
-        label=f"binary fit (∝ log₂N)  R²={r2_bin:.3f}")
-ax.plot(n_line, fib_reg.predict(log_n_line), color="steelblue", linestyle="--", linewidth=1.5,
-        label=f"fibonacci fit (∝ log₂N)  R²={r2_fib:.3f}")
-ax.set_xlabel("N (nodes)")
-ax.set_ylabel("k4 — decrease-key cost per call [s]")
-ax.set_title("k4 (decrease-key unit cost) vs N")
-ax.legend(fontsize=8)
-ax.grid(True, alpha=0.4)
-fig.tight_layout()
-fig.savefig(f"{save_folder}/k4_vs_N.png", dpi=300)
-plt.close(fig)
-print(f"Saved: {save_folder}/k4_vs_N.png")
-
-
-# k3
-fig, ax = plt.subplots(figsize=(7, 5))
-ax.plot(nodes, k3_bin, marker="o", color="steelblue", label="binary k3")
-ax.plot(nodes, k3_fib, marker="s", color="darkorange", label="fibonacci k3")
-ax.set_xlabel("N (nodes)")
-ax.set_ylabel("k3 — iteration cost per call [s]")
-ax.set_title("k3 (iteration unit cost) vs N")
-ax.legend(fontsize=8)
-ax.grid(True, alpha=0.4)
-fig.tight_layout()
-fig.savefig(f"{save_folder}/k3_vs_N.png", dpi=300)
-plt.close(fig)
-print(f"Saved: {save_folder}/k3_vs_N.png")
-
-
-# Intercept
-fig, ax = plt.subplots(figsize=(7, 5))
-ax.plot(nodes, int_bin, marker="o", color="steelblue", label="binary k4")
-ax.plot(nodes, int_fib, marker="s", color="darkorange", label="fibonacci k4")
-ax.set_xlabel("N (nodes)")
-# ax.set_ylabel("k4 — decrease-key cost per call [s]")
-# ax.set_title("k4 (decrease-key unit cost) vs N")
-ax.legend(fontsize=8)
-ax.grid(True, alpha=0.4)
-fig.tight_layout()
-fig.savefig(f"{save_folder}/int_vs_N.png", dpi=300)
-plt.close(fig)
-print(f"Saved: {save_folder}/int_vs_N.png")
-
-
-# ── VIF Check ──────────────────────────────────────────────────────────────────
-# relax_success = ratio × relax_attempts → 두 변수가 선형 상관될 수 있음
-# VIF = 1 / (1 - R²), where R² is from regressing X1 on X2 (2-predictor case)
-# VIF > 10: severe multicollinearity, coefficients become unstable
-
-vif_records = []
-
-for algo in algos:
-    sub = df[df["algorithm"] == algo]
-    for n in nodes:
-        g = sub[sub["nodes"] == n]
-        X = g[["relax_attempts", "relax_success"]].to_numpy()
-
-        # Regress relax_attempts on relax_success
-        reg_vif = LinearRegression().fit(X[:, 1].reshape(-1, 1), X[:, 0])
-        r2_vif = r2_score(X[:, 0], reg_vif.predict(X[:, 1].reshape(-1, 1)))
-        vif = 1 / (1 - r2_vif) if r2_vif < 1.0 else float("inf")
-
-        # Pearson correlation (simpler diagnostic)
-        corr = np.corrcoef(X[:, 0], X[:, 1])[0, 1]
-
-        vif_records.append({
-            "algorithm": algo,
-            "N": n,
-            "corr(E, alpha)": round(corr, 6),
-            "R2_vif": round(r2_vif, 6),
-            "VIF": round(vif, 2),
-        })
-
-vif_df = pd.DataFrame(vif_records)
-
-for algo in algos:
-    print(f"\n=== VIF — {algo} ===")
-    v = vif_df[vif_df["algorithm"] == algo][["N", "corr(E, alpha)", "R2_vif", "VIF"]]
-    print(v.to_string(index=False))
-
-# Plot VIF vs N
-fig, ax = plt.subplots(figsize=(7, 4))
-for algo, color, marker in [("binary", "steelblue", "o"), ("fibonacci", "darkorange", "s")]:
-    v = vif_df[vif_df["algorithm"] == algo]
-    ax.plot(v["N"], v["VIF"], marker=marker, color=color, label=algo)
-ax.axhline(10, color="red", linestyle="--", linewidth=1.2, label="VIF = 10 (threshold)")
-ax.set_xlabel("N (nodes)")
-ax.set_ylabel("VIF")
-ax.set_title("VIF (relax_attempts vs relax_success) per N")
-ax.legend(fontsize=8)
-ax.grid(True, alpha=0.4)
-fig.tight_layout()
-fig.savefig(f"{save_folder}/vif_vs_N.png", dpi=300)
-plt.close(fig)
-print(f"\nSaved: {save_folder}/vif_vs_N.png")
+    contribution()
+    plot_l()
+    plot_k3()
+    plot_m()