The simplest solution that I know of is to retrieve the current version number from the Internet, compare it with the existing installed version, and if there is an update available, a pop-up dialog box with a link to the Android Market page for a specific application.
So basically you decide when you want to check (application launch, regular intervals, etc.)
And then you request a remote file containing the latest version number.
You compare this to the installed version number, and if latest > installed shows the user a link to the Android Market.
afaik, you cannot silently update the application for security reasons
Here is some code where someone implemented the above solution: http://www.androidsnippets.com/check-for-updates-once-a-day
Launching the Android market on the device: http://developer.android.com/guide/publishing/publishing.html#marketintent
Steven james
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