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The logic behind separating the parents in such away is that each side can introduce the guests to the other parent.
For example: Uncle John (Grooms side) can be introduced to the Brides mother by the Grooms father, then by the Grooms mother to the Brides Father and so on.

You can also have as short a line as you wish.

Seating Arrangements
Have a chat with the venue to see how they normally lay out for a wedding because they will know what works best for that particular room and the style of table. The usual lay out is a Top table then a selection of Guest tables, a cake table and a Gift table for those guests who brought their gifts along.

The Top Table is usually a long rectangular table, which gives the best view of the wedding party. The guest tables if possible, should be round, and this will help your guest to feel more comfortable. The guests tables are arranged so that direct family members are seated close to the top table, with other family and friends further away. If you do not have round tables for the guests the formal seating arrangement are set so that a husband sits across from his wife and it is customary to alternate male and female guests. Always try to leave children with there parents and seat groups of people that know each other together. This will make them feel at ease.

The Top Table
This should be straight forward, however, relationships are never straight forward. What happens if one of the parents is divorced, remarried. What if both parents are not talking to each other....the list goes on.
Here are a few examples of the seating arrangements you can have.

Traditional seating plan

As for the guests, place cards should be used to make sure everyone is where they should be. The place cards should be in keeping with the invitation sent out.

Some may not wish to be as  formal as this and decide to have a stand up buffet, with the wedding party  moving around, greeting the guests as the reception goes on. This is ideal if space is limited or if you decide to have a marquee. Remember to have some chairs and tables for some of the less fit guests.