Comments on: Online Lunch http://cstheory.blogoverflow.com/2011/10/online-lunch/ The Theoretical Computer Science Stack Exchange Blog Fri, 18 Mar 2016 21:21:18 +0000 hourly 1 https://wordpress.org/?v=4.5.6 By: daveagp http://cstheory.blogoverflow.com/2011/10/online-lunch/#comment-220 Wed, 16 Nov 2011 08:13:34 +0000 http://cstheory.blogoverflow.com/?p=850#comment-220 That’s absolutely correct… upon re-inspection there is an additive constant’s worth of gap in the expected number of matches achieved. One might try to fix this by noting there is a better lower bound of 1 on x1, but it does not help enough.

I am not sure if a better analysis removes this gap or if it is inherent to the algorithm. This coupling argument seems pretty rigid to me. There is a longer analysis by Goel and Mehta (http://dl.acm.org/citation.cfm?id=1347189) of which Birnbaum-Mathieu is a distillate, but I could not parse a yes or no answer from there immediately.

]]> By: Anon http://cstheory.blogoverflow.com/2011/10/online-lunch/#comment-210 Mon, 14 Nov 2011 02:05:25 +0000 http://cstheory.blogoverflow.com/?p=850#comment-210 1-(n/(n+1))^n <= 1-1/e and not 1-(n/(n+1))^n>= 1-1/e. It approaches 1-1/e from below and not above. Hence the proof of 1-1/e approximation is only for large enough n.

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