The Weissman score is an efficiency metric for lossless compression applications, which was developed for fictional use. It compares both required time and compression ratio of measured applications, with those of a de facto standard according to the data type. It was developed by Tsachy Weissman, a professor at Stanford University, and Vinith Mishra, a graduate student, at the request of producers for HBO's television series Silicon Valley, about a fictional tech start-up.
The formula is the following; where r is the compression ratio, T is the time required to compress, the overlined ones are the same metrics for a standard compressor, and alpha is a scaling constant.
Weissman score was used in Dropbox Tech Blog to explain real-world work on lossless compression.
|Application||Compression ratio||Compression time [min]||Weissman score|
Although the value is relative to the standards against which it is compared, the unit used to measure the times changes the score (see examples 1 and 2), and the multiplier also can't have a numeric value of 1 or less, because the logarithm of 1 is 0 (examples 3 and 4), and the logarithm of any value less than 1 is negative (examples 5 and 6); that would result in scores of value 0 (even with changes), undefined, or negative (even if better than positive).
|#||standard compressor||scored compressor||Weissman score||Observations|
|compression ratio||compression time||log(compression time)||compression ratio||compression time||log(compression time)|
|1||2.1||2 min||0.30103||3.4||3 min||0.477121||1*(3.4/2.1)*(0.30103/0.477121)=1.021506||Change in unit or scale, changes the result.|
|2||2.1||120 s||2.079181||3.4||180 s||2.255273||1*(3.4/2.1)*(2.079181/2.255273)=1.492632|
|3||2.2||1 min||0||3.3||1.5 min||0.176091||1*(3.3/2.2)*(0/0.176091)=0||If time is 1, its log is 0; then the score can be 0 or infinity.|
|4||2.2||0.667 min||-0.176091||3.3||1 min||0||1*(3.3/2.2)*(-0.176091/0)=infinity|
|5||1.6||0.5 h||-0.30103||2.9||1.1 h||0.041393||1*(2.9/1.6)*(-0.30103/0.041393)=-13.18138||If time is less than 1, its log is negative; then the score can be negative.|
|6||1.6||1.1 h||0.041393||1.6||0.9 h||-0.045757||1*(1.6/1.6)*(0.041393/-0.045757)=-0.904627|
- Perry, Tekla (July 28, 2014). "A Fictional Compression Metric Moves Into the Real World". Retrieved January 25, 2016.
- Perry, Tekla (July 25, 2014). "A Made-For-TV Compression Algorithm". Retrieved January 25, 2016.
- Sandberg, Elise (April 12, 2014). "HBO's 'Silicon Valley' Tech Advisor on Realism, Possible Elon Musk Cameo". The Hollywood Reporter. Retrieved June 10, 2014.
- Jurgensen, John; Rusli, Evelyn M. (April 3, 2014). "There's a New Geek in Town: HBO's 'Silicon Valley'". The Wall Street Journal. Retrieved June 10, 2014.
- "Lossless compression with Brotli in Rust for a bit of Pied Piper on the backend". Dropbox Tech Blog. Retrieved 2017-06-24.
- Hutter, Marcus (July 2016). "Contestants". Retrieved January 25, 2016.