Garbine Muguruza dominated Paula Badosa in a 6-3, 6-3 victory and will play Anett Kontaveit for the title at the WTA Finals. Eighth-seeded Kontaveit beat Maria Sakkari 6-1, 3-6, 6-3 in the other semi-final.
Wimbledon starts June 27, and Federer has not played on tour since a straight-set loss at this year's Wimbledon in the quarterfinals in July. Within weeks he underwent his third knee surgery in 18 months.
The World No. 1 Serb is attempting to match Roger Federer's record of six titles at the elite season-ending event for the top eight players.
Sakkari will face Anett Kontaveit in the semifinals while Badosa will face her Spanish compatriot Garbine Muguruza.
US Open champion Medvedev post a 6-7 (5), 6-3, 6-4 win over first-time qualifier Hubert Hurkacz in the opening match of the ATP Finals; 2018 champion Alexander Zverev won when local favourite Matteo Berrettini retired early in the second set.
Muguruza and Kontaveit, who was earlier assured of advancing, will march into the knockout stages from Group Tiotehuacan as the former's straight-set win pushed Karolina Pliskova out of the title race.
Djokovic, who has already secured a record-breaking seventh year-end as No. 1, has his sights set on levelling Swiss ace Roger Federer's record six ATP Finals titles.
Sharmada Balu continued with her fairytale run in the Fenesta Open National tennis championship.
Second seed Vaidehi Chaudhari was put through the wringer by Akanksha Nitture in the quarter-finals of the Fenesta Open tennis championship.
Sharmada Balu tore the form book to shreds as she used her tons of experience and cunning to outlast third seed Sravya Shivani Chilakalapudi 5-7, 6-1, 2-0 (retired) to enter the quarter-finals.
Medvedev's loss left the combined ATP and WTA tournament without its top two men's and women's seeds.
Naomi, 23, dropped from 7 to 12th position, ending her streak of 140 consecutive weeks in the Top 10, a streak that started on September 17, 2018.
The ATP announced Monday it is looking into “allegations concerning Alexander Zverev at the ATP Masters 1000 event in Shanghai in 2019.”
The second-seeded Indo-Chinese duo defeated the third-seeded pair of American Christian and New Zealander Routliffe 6-3 6-2 in the summit clash in one hour and four minutes.
Federer said on the sidelines of Laver Cup that the recovery and rehabilitation are "going to take me a few more months and then we'll see how things are at some point next year".
The second-seeded Indo-Chinese duo defeated the Japanese pair 6-2 7-5 in the semifinals in one hour 21 minutes
The Scot looked set to pay the price for failing to convert a series of break point chances before he found his range to dispatch the world number 26 4-6, 6-3, 6-2.
Both Prajnesh Gunneswaran and Ramkumar had lost their singles matches on Friday and to stay alive in the tie, the Indians needed to win the doubles.
Up against Otto Virtanen, ranked as low as 419 in the ATP ranking chart, the 165th ranked Prajnesh lost 3-6 6-7(1) in just one hour 25 minutes.
Gunneswaran, who is coming back from a wrist injury and had undergone rehabilitation in his hometown Chennai, struggled for rhythm as his serve was broken in the sixth game.
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