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a965073 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 | {
"claim": "Claim 5: beta* sqrt speedup + ADePM > DePM/DeEPCA (Sec 4)",
"partA_real_data": {
"dataset": "SNAP ego-Facebook (n=d=50 subgraph)",
"ADePM_beats_DePM": true,
"ADePM_beats_DeEPCA": true,
"DeEPCA_over_ADePM_bstar": {
"20": 8.178394353297831,
"40": 1243911.2309841341
},
"DeEPCA_final_L20": 0.003553243467635026,
"DeEPCA_final_L40": 0.003552721959639524,
"ADePM_bstar_final_L20": 0.00043446712326879015,
"ADePM_bstar_final_L40": 2.856089623717561e-09,
"DeEPCA_plateaus_with_L": true,
"ADePM_keeps_improving_with_L": true
},
"partB_sqrt_speedup": {
"exponent": 1.0006978285692545,
"rows": [
{
"gap": 0.1,
"Delta": 0.09999999999999998,
"1_over_Delta": 10.000000000000002,
"1_over_sqrtDelta": 3.16227766016838,
"T_beta_star": 36,
"T_beta_0": 131,
"speedup_ratio": 3.638888888888889
},
{
"gap": 0.03,
"Delta": 0.030000000000000027,
"1_over_Delta": 33.33333333333331,
"1_over_sqrtDelta": 5.773502691896255,
"T_beta_star": 71,
"T_beta_0": 456,
"speedup_ratio": 6.422535211267606
},
{
"gap": 0.01,
"Delta": 0.010000000000000009,
"1_over_Delta": 99.99999999999991,
"1_over_sqrtDelta": 9.999999999999995,
"T_beta_star": 115,
"T_beta_0": 1383,
"speedup_ratio": 12.02608695652174
},
{
"gap": 0.003,
"Delta": 0.0030000000000000027,
"1_over_Delta": 333.33333333333303,
"1_over_sqrtDelta": 18.25741858350553,
"T_beta_star": 211,
"T_beta_0": 4627,
"speedup_ratio": 21.928909952606634
},
{
"gap": 0.001,
"Delta": 0.0010000000000000009,
"1_over_Delta": 999.9999999999991,
"1_over_sqrtDelta": 31.622776601683782,
"T_beta_star": 382,
"T_beta_0": 13894,
"speedup_ratio": 36.3717277486911
},
{
"gap": 0.0003,
"Delta": 0.00029999999999996696,
"1_over_Delta": 3333.3333333337005,
"1_over_sqrtDelta": 57.73502691896576,
"T_beta_star": 709,
"T_beta_0": 46334,
"speedup_ratio": 65.35119887165021
}
],
"theory": 1.0
},
"verdict": "VERIFIED"
} |