Search Party Efficiency

I've been trying to research the most efficient way to perform a search. Not a computer search algorithm! I mean a real-world search, like the kind you'd design if you wanted to find a lost hiker in the wilderness and 50 volunteers showed up to help. This is a standard situation for any game trying to model an imperfect information situation, like two armies trying to engage one another on a battlefield with limited visibility. For my own design project -- a classic wilderness hexcrawl -- this kind of mechanic is close to the heart of the game.

These days, a normal game is most likely to implement searching as a skill that has a fixed numerical score, like a Perception check. If you are "good at searching", the you notice details more often. If you have more people available, you get to make more individual checks. This makes a reasonable amount of success in a tightly constrained environment like the stereotypical RPG dungeon.

But if you're wandering around outdoors with a troop of dozens of adventurers trying to find the secret entrance to that lair, you probably won't wander past it all the same time to make simultaneous skill checks. Instead you'll set up a base camp nearby, and have everyone fan out in small groups to explore little areas of terrain. Perception skill matters less than distribution strategy. It's not noticing the entrance that's hard, it's making sure that you assign your little search parties to the right locations as efficiently as possible, so that they don't cover one another's territory and waste time, or miss an important region entirely.

I can think of two sources of dimishing returns here:

1. As the number of parties increases, they need to cover more terrain, and some of them will need to move farther from the base camp before they even begin. If you have them fan out into quadrants, then every search party after the eighth will need to walk at least the distance of one quadrant before they even start searching. You can subdivide your fan pattern into more wedges than quadrants, but then once you saturate, you'll need to send people even farther to get beyond the radius of those longer-and-skinnier wedges. And for something beyond octants, you now have too many groups overlapping close to the camp.
2. Some features you might want to discover (say, a mountain, or a mysterious tower ruin) might be visible from far enough away that you wouldn't need fine subdivisions of the geographical area. Instead, you'd much rather have everyone devote more of their time to spreading out over a larger area. So the optimal subdivision shape isn't much like a wedge, but more like a square... which makes it less efficient to perform the initial spreading-out stage of the search.

I'm not entirely sure of how the model the latter effect, in particular. At the moment, my wilderness hexcrawl game rules are using a unified mechanic for all diminishing returns where the size of the party is used to determine a number of dice to use by taking its square-root and rounding down. That's not a terrible assumption, I think, but I wish it were on sturdier grounds. Alas, all attempts to find an actual mathematical model for search parties keep turning up
only computer search algorithms!