Mixing
properties of $min(x_1…x_n)$
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I want to take measurements of algorithm performance. I have two algorithms A and B that run one after the other (composition)
I want to measure how well the composition of algorithms is better than the algorithms individually.
I propose to get run times of A and B individually as rA and rB and their run times when composed together as prA and prB (pr for partial run time)
and take the min(prA/rA, prB/rB) as a performance metric.
What properties does min(x,y) have? I know max(x,y) gives the $L^infty$ norm on $mathbbR^2$ but what about min? What other performance metrics are good for comparing a composition of algorithms?
metric-spaces algorithms norm maxima-minima
edited Jul 19 at 22:58
Bernard
110k635103
asked Jul 19 at 22:55
user352102
34028
add a comment |Â
up vote
1
down vote
favorite
I want to take measurements of algorithm performance. I have two algorithms A and B that run one after the other (composition)
I want to measure how well the composition of algorithms is better than the algorithms individually.
I propose to get run times of A and B individually as rA and rB and their run times when composed together as prA and prB (pr for partial run time)
and take the min(prA/rA, prB/rB) as a performance metric.
What properties does min(x,y) have? I know max(x,y) gives the $L^infty$ norm on $mathbbR^2$ but what about min? What other performance metrics are good for comparing a composition of algorithms?
metric-spaces algorithms norm maxima-minima
edited Jul 19 at 22:58
Bernard
110k635103
asked Jul 19 at 22:55
user352102
34028
I wanted to note that taking min may be a bad idea since we may have min(1,.5)= min(.5,.5) but clearly .5 run time ratio for both algorithms A and B is better than one, say A, with .5 ratio and the other, say B, with no improvement. Either way, what are properties of min(x,y)? I was also thinking of a performance metric like ax+by where a and b are constant weights and x and y are variables. what are properties of ax+by? certainly we get equivalence classes of slanted lines.
– user352102
Jul 19 at 23:44
Also, how about (prA+prB)/(rA+rB)?
– user352102
Jul 19 at 23:51
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I want to take measurements of algorithm performance. I have two algorithms A and B that run one after the other (composition)
I want to measure how well the composition of algorithms is better than the algorithms individually.
I propose to get run times of A and B individually as rA and rB and their run times when composed together as prA and prB (pr for partial run time)
and take the min(prA/rA, prB/rB) as a performance metric.
What properties does min(x,y) have? I know max(x,y) gives the $L^infty$ norm on $mathbbR^2$ but what about min? What other performance metrics are good for comparing a composition of algorithms?
metric-spaces algorithms norm maxima-minima
edited Jul 19 at 22:58
Bernard
110k635103
asked Jul 19 at 22:55
user352102
34028
I want to take measurements of algorithm performance. I have two algorithms A and B that run one after the other (composition)
I want to measure how well the composition of algorithms is better than the algorithms individually.
I propose to get run times of A and B individually as rA and rB and their run times when composed together as prA and prB (pr for partial run time)
and take the min(prA/rA, prB/rB) as a performance metric.
What properties does min(x,y) have? I know max(x,y) gives the $L^infty$ norm on $mathbbR^2$ but what about min? What other performance metrics are good for comparing a composition of algorithms?
metric-spaces algorithms norm maxima-minima
edited Jul 19 at 22:58
Bernard
110k635103
asked Jul 19 at 22:55
user352102
34028
edited Jul 19 at 22:58
Bernard
110k635103
edited Jul 19 at 22:58
Bernard
110k635103
edited Jul 19 at 22:58
Bernard
110k635103
110k635103
asked Jul 19 at 22:55
user352102
34028
asked Jul 19 at 22:55
user352102
34028
asked Jul 19 at 22:55
user352102
34028
34028
I wanted to note that taking min may be a bad idea since we may have min(1,.5)= min(.5,.5) but clearly .5 run time ratio for both algorithms A and B is better than one, say A, with .5 ratio and the other, say B, with no improvement. Either way, what are properties of min(x,y)? I was also thinking of a performance metric like ax+by where a and b are constant weights and x and y are variables. what are properties of ax+by? certainly we get equivalence classes of slanted lines.
– user352102
Jul 19 at 23:44
Also, how about (prA+prB)/(rA+rB)?
– user352102
Jul 19 at 23:51
add a comment |Â
I wanted to note that taking min may be a bad idea since we may have min(1,.5)= min(.5,.5) but clearly .5 run time ratio for both algorithms A and B is better than one, say A, with .5 ratio and the other, say B, with no improvement. Either way, what are properties of min(x,y)? I was also thinking of a performance metric like ax+by where a and b are constant weights and x and y are variables. what are properties of ax+by? certainly we get equivalence classes of slanted lines.
– user352102
Jul 19 at 23:44
Also, how about (prA+prB)/(rA+rB)?
– user352102
Jul 19 at 23:51
I wanted to note that taking min may be a bad idea since we may have min(1,.5)= min(.5,.5) but clearly .5 run time ratio for both algorithms A and B is better than one, say A, with .5 ratio and the other, say B, with no improvement. Either way, what are properties of min(x,y)? I was also thinking of a performance metric like ax+by where a and b are constant weights and x and y are variables. what are properties of ax+by? certainly we get equivalence classes of slanted lines.
– user352102
Jul 19 at 23:44
I wanted to note that taking min may be a bad idea since we may have min(1,.5)= min(.5,.5) but clearly .5 run time ratio for both algorithms A and B is better than one, say A, with .5 ratio and the other, say B, with no improvement. Either way, what are properties of min(x,y)? I was also thinking of a performance metric like ax+by where a and b are constant weights and x and y are variables. what are properties of ax+by? certainly we get equivalence classes of slanted lines.
– user352102
Jul 19 at 23:44
Also, how about (prA+prB)/(rA+rB)?
– user352102
Jul 19 at 23:51
Also, how about (prA+prB)/(rA+rB)?
– user352102
Jul 19 at 23:51
add a comment |Â
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I wanted to note that taking min may be a bad idea since we may have min(1,.5)= min(.5,.5) but clearly .5 run time ratio for both algorithms A and B is better than one, say A, with .5 ratio and the other, say B, with no improvement. Either way, what are properties of min(x,y)? I was also thinking of a performance metric like ax+by where a and b are constant weights and x and y are variables. what are properties of ax+by? certainly we get equivalence classes of slanted lines.
– user352102
Jul 19 at 23:44
Also, how about (prA+prB)/(rA+rB)?
– user352102
Jul 19 at 23:51