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Competitive ratio ·dualobjโ‰คdual optโ‰คprimal opt=OPT ·primal objโ‰ค(1+2)dual obj ·Combine together,,competitive ratioโ‰คใ€‚ไบŒCompetitive ratio โ€ข ๐‘‘๐‘ข๐‘Ž๐‘™ ๐‘œ๐‘๐‘— โ‰ค ๐‘‘๐‘ข๐‘Ž๐‘™ ๐‘œ๐‘๐‘ก โ‰ค ๐‘๐‘Ÿ๐‘–๐‘š๐‘Ž๐‘™ ๐‘œ๐‘๐‘ก = ๐‘‚๐‘ƒ๐‘‡ โ€ข ๐‘๐‘Ÿ๐‘–๐‘š๐‘Ž๐‘™ ๐‘œ๐‘๐‘— โ‰ค (1 + 1 ๐‘ )๐‘‘๐‘ข๐‘Ž๐‘™ ๐‘œ๐‘๐‘— โ€ข Combine together, competitive ratio โ‰ค ๐‘’ ๐‘’โˆ’1
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