196 lines
7.0 KiB
Python
196 lines
7.0 KiB
Python
import numpy as np
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import pandas as pd
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import matplotlib.pyplot as plt
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import os
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from sklearn.linear_model import LinearRegression
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from sklearn.metrics import r2_score
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# Runtime = Add + Extract-min + Relax-attempts + Relax-success
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# = VlogV * k1 + VlogV * k2 + E * k3 + \alpha * logV * k4 (Binary)
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# = V * k1 + VlogV * k2 + E * k3 + \alpha * k4 (Fibonacci)
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# (\alpha = relax_success)
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#
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# V increases -> Add, Extract-min, Relax-attempts, Relax-success all increases.
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# Therfore, critical multicollinearlity occurs.
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#
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# To solve, run regression per each V.
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# Then V becomes constant.
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#
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# Runtime(Binary) = VlogV * k1 + VlogV * k2 + E * k3 + \alpha * logV * k4 (Binary)
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# = intercept + E * k3 + \alpha * k4
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# Runtime(Fibonacci) = V * k1 + VlogV * k2 + E * k3 + \alpha * k4 (Fibonacci)
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# = intercept + E * k3 + \alpha * k4
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#
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# Final equation
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# Runtime of specific V = intercept + E * k3 + \alpha * k4
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#
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# intercept absorbs V*(k1+k2) which is constant within each N.
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# k3: cost per relax_attempt (should be equal across heaps)
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# k4: cost per decrease-key (binary: should scale with log2N; fibonacci: should be constant)
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csv_file = "results/synthetic_data/raw/20260421_031740.csv"
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save_folder = f"results/synthetic_data/derived/{os.path.splitext(os.path.basename(csv_file))[0]}/processing_time_analysis"
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os.makedirs(save_folder, exist_ok=True)
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df = pd.read_csv(csv_file)
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nodes = sorted(df["nodes"].unique())
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algos = ["binary", "fibonacci"]
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records = []
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for algo in algos:
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sub = df[df["algorithm"] == algo]
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for n in nodes:
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g = sub[sub["nodes"] == n]
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X = g[["relax_attempts", "relax_success"]].to_numpy()
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y = g["time"].to_numpy()
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model = LinearRegression().fit(X, y)
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r2 = r2_score(y, model.predict(X))
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records.append({
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"algorithm": algo,
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"N": n,
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"log2N": round(np.log2(n), 4),
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"intercept": model.intercept_,
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"k3 (E)": model.coef_[0],
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"k4 (alpha)":model.coef_[1],
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"r2": r2,
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"n": len(g),
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})
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results = pd.DataFrame(records)
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for algo in algos:
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print(f"=== {algo} ===")
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r = results[results["algorithm"] == algo][["N","log2N","intercept","k3 (E)","k4 (alpha)","r2","n"]]
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print(r.to_string(index=False))
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print()
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grouped = results.set_index(["N", "algorithm"])
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def get_param(param):
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return (
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grouped.loc[(nodes, "binary"), param].values,
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grouped.loc[(nodes, "fibonacci"), param].values
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)
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k3_bin, k3_fib = get_param("k3 (E)")
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k4_bin, k4_fib = get_param("k4 (alpha)")
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int_bin, int_fib = get_param("intercept")
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# binary: k4 ~ log₂N 회귀
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log_n = np.log2(np.array(nodes)).reshape(-1, 1)
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bin_reg = LinearRegression().fit(log_n, k4_bin)
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r2_bin = r2_score(k4_bin, bin_reg.predict(log_n))
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# fibonacci: k4 ~ log₂N 회귀
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fib_reg = LinearRegression().fit(log_n, k4_fib)
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r2_fib = r2_score(k4_fib, fib_reg.predict(log_n))
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n_line = np.linspace(min(nodes), max(nodes), 300)
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log_n_line = np.log2(n_line).reshape(-1, 1)
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print(f"\nbinary log₂N regression: coef={bin_reg.coef_[0]:.4e}, intercept={bin_reg.intercept_:.4e}, R²={r2_bin:.4f}")
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# Plot
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fig, ax = plt.subplots(figsize=(7, 5))
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ax.plot(nodes, k4_bin, marker="o", color="steelblue", label="binary k4")
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ax.plot(nodes, k4_fib, marker="s", color="darkorange", label="fibonacci k4")
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ax.plot(n_line, bin_reg.predict(log_n_line), color="steelblue", linestyle="--", linewidth=1.5,
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label=f"binary fit (∝ log₂N) R²={r2_bin:.3f}")
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ax.plot(n_line, fib_reg.predict(log_n_line), color="steelblue", linestyle="--", linewidth=1.5,
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label=f"fibonacci fit (∝ log₂N) R²={r2_fib:.3f}")
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ax.set_xlabel("N (nodes)")
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ax.set_ylabel("k4 — decrease-key cost per call [s]")
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ax.set_title("k4 (decrease-key unit cost) vs N")
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ax.legend(fontsize=8)
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ax.grid(True, alpha=0.4)
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fig.tight_layout()
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fig.savefig(f"{save_folder}/k4_vs_N.png", dpi=300)
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plt.close(fig)
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print(f"Saved: {save_folder}/k4_vs_N.png")
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# k3
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fig, ax = plt.subplots(figsize=(7, 5))
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ax.plot(nodes, k3_bin, marker="o", color="steelblue", label="binary k4")
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ax.plot(nodes, k3_fib, marker="s", color="darkorange", label="fibonacci k4")
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ax.set_xlabel("N (nodes)")
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# ax.set_ylabel("k3 — decrease-key cost per call [s]")
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# ax.set_title("k3 (decrease-key unit cost) vs N")
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ax.legend(fontsize=8)
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ax.grid(True, alpha=0.4)
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fig.tight_layout()
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fig.savefig(f"{save_folder}/k3_vs_N.png", dpi=300)
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plt.close(fig)
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print(f"Saved: {save_folder}/k3_vs_N.png")
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# Intercept
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fig, ax = plt.subplots(figsize=(7, 5))
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ax.plot(nodes, int_bin, marker="o", color="steelblue", label="binary k4")
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ax.plot(nodes, int_fib, marker="s", color="darkorange", label="fibonacci k4")
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ax.set_xlabel("N (nodes)")
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# ax.set_ylabel("k4 — decrease-key cost per call [s]")
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# ax.set_title("k4 (decrease-key unit cost) vs N")
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ax.legend(fontsize=8)
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ax.grid(True, alpha=0.4)
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fig.tight_layout()
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fig.savefig(f"{save_folder}/int_vs_N.png", dpi=300)
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plt.close(fig)
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print(f"Saved: {save_folder}/int_vs_N.png")
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# ── VIF Check ──────────────────────────────────────────────────────────────────
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# relax_success = ratio × relax_attempts → 두 변수가 선형 상관될 수 있음
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# VIF = 1 / (1 - R²), where R² is from regressing X1 on X2 (2-predictor case)
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# VIF > 10: severe multicollinearity, coefficients become unstable
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vif_records = []
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for algo in algos:
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sub = df[df["algorithm"] == algo]
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for n in nodes:
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g = sub[sub["nodes"] == n]
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X = g[["relax_attempts", "relax_success"]].to_numpy()
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# Regress relax_attempts on relax_success
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reg_vif = LinearRegression().fit(X[:, 1].reshape(-1, 1), X[:, 0])
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r2_vif = r2_score(X[:, 0], reg_vif.predict(X[:, 1].reshape(-1, 1)))
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vif = 1 / (1 - r2_vif) if r2_vif < 1.0 else float("inf")
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# Pearson correlation (simpler diagnostic)
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corr = np.corrcoef(X[:, 0], X[:, 1])[0, 1]
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vif_records.append({
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"algorithm": algo,
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"N": n,
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"corr(E, alpha)": round(corr, 6),
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"R2_vif": round(r2_vif, 6),
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"VIF": round(vif, 2),
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})
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vif_df = pd.DataFrame(vif_records)
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for algo in algos:
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print(f"\n=== VIF — {algo} ===")
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v = vif_df[vif_df["algorithm"] == algo][["N", "corr(E, alpha)", "R2_vif", "VIF"]]
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print(v.to_string(index=False))
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# Plot VIF vs N
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fig, ax = plt.subplots(figsize=(7, 4))
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for algo, color, marker in [("binary", "steelblue", "o"), ("fibonacci", "darkorange", "s")]:
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v = vif_df[vif_df["algorithm"] == algo]
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ax.plot(v["N"], v["VIF"], marker=marker, color=color, label=algo)
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ax.axhline(10, color="red", linestyle="--", linewidth=1.2, label="VIF = 10 (threshold)")
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ax.set_xlabel("N (nodes)")
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ax.set_ylabel("VIF")
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ax.set_title("VIF (relax_attempts vs relax_success) per N")
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ax.legend(fontsize=8)
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ax.grid(True, alpha=0.4)
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fig.tight_layout()
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fig.savefig(f"{save_folder}/vif_vs_N.png", dpi=300)
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plt.close(fig)
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print(f"\nSaved: {save_folder}/vif_vs_N.png") |