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The sixth seed got off to the flawless start, winning his opening round-robin match in the Pete Sampras Group as he was able to keep his nerves in check to beat the Austrian 6-3 5-7 7-5.
But Thiem hit back, halting the Bulgarian as he served for the match - only to then immediately donate his serve with two untimely double faults.
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Island Air's last flight will be Flight 449, scheduled to depart Kahului at 10:14 p.m. today and arrive in Honolulu at 10:49 p.m. The airline said in a message on its website that passengers should contact their credit card company for inquiries on refunds.
The pair will meet in Tuesday's second singles match at 20:00 GMT, after Marin Cilic plays Jack Sock at 14:00.
Back came Dimitrov, though, with a break to love and he made no mistake in the final game of the match, converting his third match point as Thiem fired long from the baseline.
Thiem grew in confidence as the match progressed into the second set and thanks to a higher percentage of first serves put the pressure on Dimitrov's shoulders, who was broken in the 12th game of the second set to force the decider.
And Dimitrov finally triumphed after two hours and 22 minutes, serving out victory via a nervy deuce.
The match would be decided in a first-to-10 tie-break but this time it was the Bryans who started fast, storming into a 4-0 lead.