What is the most efficient seach pattern to use to cover the most volume in space by one vessel?

Answer 1

the two most common (2D) search patterns are a grid or a spiral. Grid covers a large area efficiently because you never cross the same path. A spiral is used when you have a fixed starting point, but don't know what direction the item you are searching for has moved. 3D versions of these would be a cube and for lack of a better term, a ball of yarn. A cube would probably cover a fixed search area most efficiently. The "yarn" would probably cover an ever increasing area most efficiently.

Answer 2

The pattern won't matter, as long as you never cover the same area of space twice.

Think of it like this:
Imagine a grid (be it 2 or 3 dimentional). Let's say you can "scan" one cube at a time, and your ships life span is 14 cubes of travel.

No matter which way you move, as long as you don't visit the same cube more than once, you will have scanned 14 cubes of equal volume, regardless of how you move.

Answer 3

There are many that are equally efficient. Spiral is one. Fractal border is another.

Answer 4

This should be in any high-school level Starfleet textbook.