It’s got to be frustrating for Jerry Yang.

The 40-year-old co-founder and CEO of Yahoo! Inc. (YHOO) is sitting on top of the world’s most popular web site, yet he can’t compete with Google Inc.’s (GOOG) more effective search-engine advertising machine.

Google rubbed more sand in Yang’s eyes Wednesday when it walked away from a plan announced in June to sell advertisements on Yahoo’s pages after the Justice Department threatened to block the deal on antitrust grounds.

Google already has more than 70% of the search-engine driven advertising market. Yahoo has about 10%, according to BusinessWeek.

For Yang, it was a chance to revive falling sales, even if it meant falling on his sword instead of wielding it against its chief rival.

Now, his shareholders are livid. His future is uncertain. And his best option for survival is a partnership with Microsoft Corp. (MSFT) – the company whose generous takeover offer he rebuffed earlier this year.

The dropped advertising deal between Yahoo and Google revealed a major growth problem for each company.

For Google, it shows that the search engine juggernaut has grown so large that it now has far fewer legal avenues of expansion open to it.

For Yahoo, it shows that Yang is running out answers for Google’s market dominance.

Yahoo’s Troubles

Yahoo has had little to cheer about in the past year.

Its sales growth fell to 3% in the third quarter, down from 14% over the same period last year.