Djokovic will play Germany's Florian Mayer as he bids to reach his ninth final on tour this year.
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In the second round, home hope Florian Mayer upset third seed Jarkko Nieminen, beating the Finn 6-4 3-6 6-4.
And this year, he upset 22nd seeded Florian Mayer and top 100 player Flavio Cipolla to reach the third round.
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Other seeds to progress were Nikolay Davydenko (four), who beat Florian Mayer 6-3 6-4 and David Ferrer (eight), who overcame Denis Istomin 6-4 6-1.
Dimitrov is also on a roll, having followed up his opening victory over world No. 10 Janko Tipsarevic by beating Germany's Florian Mayer 6-2 6-4.
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Sock had the seeming tough luck of drawing 22nd seed Florian Mayer, a wily 28-year old veteran who had made it to the Wimbledon quarterfinals.
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The world number four cruised to a 6-3 6-4 win over Frenchman Jeremy Chardy and will next face Jo-Wilfried Tsonga, who beat Florian Mayer 7-5 6-3.
Colombian Alejandro Falla handed victory to Bulgarian 26th seed Grigor Dimotrov while Germany's Florian Mayer , seeded 28, quit during his clash with Denis Istomin of Uzbekistan.
Simon, who reached the semifinals in Brisbane last year, will play Marcos Baghdatis in the next round after the Cypriot defeated sixth-seeded German Florian Mayer 6-4 6-2.
Unlike Federer, the world No. 3, Britain's Andy Murray , was made to work hard for his place in round three after overcoming Germany's Florian Mayer 7-6 7-6.
Fifth seed Tommy Robredo also progressed with a 7-6 (7-4) 6-4 win over Dutch wildcard Robin Haase, and the Spanish world No. 15 will next play Florian Mayer.
Eighth seed Mikhail Youzhny was ousted by Germany's Florian Mayer 6-4 6-7 (5-7) 6-1 while Serbia's Marin Cilic, seeded 14th, went down 6-2 6-2 to Andreas Seppi of Italy.
Murray starts his defense of his Shanghai Masters title against Florian Mayer on Wednesday after the German beat Australia's Bernard Tomic 6-4 6-0 in the first round, while Djokovic faces Grigor Dimitrov of Bulgaria.
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