What does "boot" mean here?

I am confused by the exact meaning of the word "boot" in the following two sentences. Anyone to help me? Thanks!

a) In early 1998 the Saudis booted out Hume A. Horan.

b) ...eating habits under control by booting the French chef and his staff.

In this sense, "boot" means to "kick out, expel".

yes: to use a BOOT on ones FOOT to KICK someone out of the DOOR, and thereby get rid of them.

Well it doesn't imply a physical "kicking" action necessarily, but the meaning certainly is from that image.

There's actually a lot more to this question, or rather, to the answer to this question, than first appears. "Boot", used as a verb, has many, many vernacular ('slang') uses in the dialects of English spoken in England and the U.S.A. (a colleague and I just came up with a dozen different uses in under two minutes... and we speak the exact same American dialect natively). Both of the posters above are right, while each is different. In example a), the specific use of 'booted' is actually only understandable when joined with 'out' and contextual clues. In example b) the specific usage of 'booting' requires clues given by the context of the sentence only.

In a), 'booted out' will typically involve one of two meanings. The first could be understood, as Cow and Tiffany put it, to have 'kicked out' (not in the literal sense, but the figurative sense). This usage is common when speaking of removal from an actual, physical edifice or place.

ex. I was booted out of the bar, arena, kitchen, etc.

However, this sentence speaks of 'the Saudis' in reference to a political or business group or body. In English, even the vernacular has degrees of formality, so it would be most proper to use Tiffany's second definition of 'expel', as 'expelled' would be the proper term here replaced by 'booted out'. To clarify:

ex. I was expelled from the bar, arena, kitchen, etc.

... would actually not make clear sense, and could confuse native speakers, or at least sound overly formal, while:

ex. I was expelled from the council, United Nations, stockholder meeting, etc.

... would be more clear.

In b), again two common usages could be seen, but here the two are much more different from each other. The first would be as above, to suggest the French chef and his staff being unceremoniously ejected from a kitchen or a place where food is served. However, there is the suggestion that the French chef and his staff's relationship with the subject (cut off from the fragment provided) was ending, thus it is almost certain that in this example 'booting' is used as a euphamism for 'firing' or 'terminating the employment of.'

I apologize if this answer was a bit wordy, but for the 'exact meaning' to be clear, a good bit of explaining was needed. Just for fun, I'll offer some other instances of 'boot' (verb or gerund) being used in vernacular.

The punter booted the ball.
"Boot to the head." (This is a line from a popular American sketch comedy.)
I booted up my computer this evening.
He put the groceries into the boot. (British usage.)
John's looking for work again. It seems his employer 'gave him the boot.'
John's looking for love again. It seems Jennifer 'gave him the boot.'
He's taking too long, go plant a boot in him.
Buy the stereo, and I'll throw in the speakers to boot.

Great question. I hope I helped.

Thank you guys so much! A particular word of thanks to Dave --- your reply is truly helpful!