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How can I write an efficient version of the following statement?

Cases[list, {_, feature_} /; feature < constant]; // AbsoluteTiming

List is of the form, list = {{feature11,feature12},...,{featuren1,featuren2}}. It has a length in the order of 10^5. On my laptop, a Macbook pro from last year it takes around 0.25s. However, I need to evaluate this expression a lot of times. Any suggestion. Thank you.

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data = RandomReal[1, {500000, 2}];
constant = 0.3;
(ans1 = Cases[data, {_, feature_} /; feature < constant]); // AbsoluteTiming

{0.880057, Null}

(ans2 = Select[data, Last@# < constant &]); // AbsoluteTiming

{1.219078, Null}

(ans3 = Pick[data, Round[Last@# + (0.5 - constant)] & /@ data, 0]); // AbsoluteTiming

{0.110006, Null}

(ans4 = Pick[data, Round[data[[All, 2]] + (0.5 - constant)], 0]); // AbsoluteTiming

{0.045003, Null}

ans1 == ans2 == ans3 == ans4

True

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  • $\begingroup$ For those data which have a larger range than {0,1}, using Round[(constant - data[[All, 2]])/10^n - .5] instead of Round[data[[All, 2]] + (0.5 - constant)] may be helpful. n can be any number to assure that Abs[(constant - data[[All, 2]])/10^n] < 0.5. $\endgroup$ – wuyingddg Sep 3 '14 at 15:26
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    $\begingroup$ Pick[data, Sign[data[[All, 2]] - constant], -1] $\endgroup$ – Coolwater Sep 3 '14 at 18:08

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