Fourth seed Gael Monfils of France takes on Belgian Olivier Rochus in his first match.
Rochus was leading 6-0 4-1 against Irakli Labadze when the Georgian retired with a shoulder injury.
Top seed Lleyton Hewitt also advanced to the quarter-finals by beating Belgium's Olivier Rochus 6-2 6-1.
American James Blake beat Christophe's brother Olivier Rochus 6-4 6-3 in the late match.
Tomas Berdych beat Jiri Novak in straight sets to advance while Belgian Kristof Vliegen upset compatriot Christophe Rochus.
Second seed Djokovic, who had a first-round bye, was surprisingly beaten 6-2 6-7 (7-9) 6-4 by Belgian Olivier Rochus on Friday.
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The reward for Rochus is a third-round clash with Brazilian 27th seed Tomaz Bellucci, who defeated American James Blake 3-6 6-1 6-2.
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Rusedski will face Belgium's Olivier Rochus in the second round on Wednesday.
Next up for Federer is Julian Reister after he beat Olivier Rochus.
He went out of the doubles when he and Australian partner Stephen Huss lost 2-6 6-4 6-4 to Guillermo Garcia-Lopez and Olivier Rochus.
At Wimbledon, he crashed out in the second round to 5ft 5ins Belgian Olivier Rochus and at the US Open to a resurgent Gustavo Kuerten.
Czech seventh seed Tomas Berdych went through after beating Belgium's Olivier Rochus in straight sets, and will next play big-serving South African No. 30 Kevin Anderson.
World number one Federer thrashed Vik 6-3 6-2, while Russia's Youzhny reached his first semi-final of the year when he overwhelmed Belgium's Olivier Rochus 6-3 6-1.
Spain's David Ferrer , his country's highest-seeded male in the absence of 11-time grand slam champion Rafael Nadal, breezed past Olivier Rochus of Belgium in straight sets.
In the other men's grass-court tournament being played, second seed Novak Djokovic is through to the final in Halle after a 7-6 6-4 victory over Belgian Olivier Rochus.
Spain's Alex Corretja takes on compatriot David Sanchez while second-seeded German Rainer Schuettler meets Belgian Christophe Rochus and Czech Radek Stepanek, the eighth seed, faces Swiss Michel Kratochvil.
World number two Rafael Nadal , who Murray is seeded to meet in the semi-finals, was given a walkover into the next round when his opponent Olivier Rochus pulled out with a foot injury.
No. 1 Federer brushed aside unseeded Belgian Christophe Rochus 6-1 6-2 in the first round of the Qatar Open in Doha, while second seed Nadal was similarly untroubled in defeating Italy's Simone Bolelli 6-3 6-3.
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In a week of records, Novak Djokovic's first-round match against Olivier Rochus was the latest-ever finish at Wimbledon, while Taylor Dent's 148mph serve against Djokovic in round two was the fastest recorded at the All England club.
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