A calculation intensive GUI application

Hi all,
I am developing a GUI application that involves drawing of a graph layout, with nodes and links..
i get through the graph drawing part and I lay out the nodes and edges correctly. My real concerns are adding the user interactions to this graph drawing.
I want to allow the user to drag nodes around the panel, be able to track which node they are visiting or which edge the mouse is currently present on. Also on selecting a particular node I wish that all the others are drawn in gray.
My thoughts are to provide the user with a toolbar, that will have buttons for each of the interaction possible, Hide, Gray, Reorder, etc.. also I need to locate where the mouse pointer is. So for that I provide a panel and as the mouse moves over each line, i populate a label in one of the bottom panels.
I am presently locating that the mouse is on a particular edge / node by simply iterating through the vector and using a contains (Point p ) test. But this is really intensive as my application has 1000s of edges. So everytime the mouse moves, I have to check for most of them to determine which node/edge is the mouse over.
I have to do the same computations when the mouse is clicked as i will be selected a particular node/edge on a mouse click.
Will the command pattern be helpful in my case, I can represent each of the interactions as a command?
How can I make my application efficient and not check through the entire 1000s of elements to determine where the mouse is ? ( i do break out once i find a match but that is still ridiculous)
Will SwingInvoker be of any help ? I do need the return value so dispatching the event to a separate thread might not really help as I have to wait for the computation to complete..
lastly are there classic tutorials / design pattern examples for such applications where there is a lot of interactivity with the drawn components?
Thanks in advance...

Your greatest asset in this situation is probably going to be the LabVIEW examples. Go to the help menu, look for the examples, and just start searching. You may have to look at a few examples to find all of the elements you need.
Once you have gone through those, just post here if you have any more questions.

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