Lem_in

Intro

Lem_in is an algorithm project about graph traversal and flow optimization.

You start with a given number of ants, located in a starting room of an anthill.
An anthill is made of 'rooms' (or nodes in a graph) and each room is linked to other rooms by 'tunnels' (or edges).
There are two special rooms among them, the starting and the ending rooms.
The goal is to make all ants going from the starting room to the ending room within the minimum number of rounds.
The difficulty is that a room (except for starting and ending rooms) can only contain 1 ant at a time.
An ant can move once a round to a linked room (using a 'tunnel').
Therefore, to optimize the solution, we usually have to find multiple distinct paths to reduce the number of rounds.

Visual

You can type ./visual.sh [existing_map] or ./visual.sh --flow-thousand (using the generator).
./generator --help

Input

10          // Number of ants in starting room at the beginning
A 200 200   // [Room name] [X coordinate] [Y coordinates]
B 550 150
C 550 450
##start     // Next room will be the starting room -> room 'D'
D 250 450
##end       // Next room will be the ending room -> room 'E'
E 850 450
F 850 150
A-B         // Room 'A' and 'B' are linked by a tunnel
A-C
A-D
B-D
B-F
B-E
C-D
C-E
C-F
E-F

Output

./lem_in --solution < [map_above]
L[ant]-[room]

L1-B L2-C       //Round 1 : Ant number 1 goes to room B. Ant number 2 goes to room C.
L1-E L2-E L3-B L4-C
L3-E L4-E L5-B L6-C
L5-E L6-E L7-B L8-C
L7-E L8-E L9-B L10-C
L9-E L10-E

Algorithm

We adapted Edmonds-Karp max-flow algorithm to fit our problem. We use a BFS (Breadth First Search) to find paths in the graph. What we do is:

• We find the shortest path:
  -> We calculate how many rounds the ants would take to go from starting to ending room using this path.
  
• Then we look for an additional path. If we find one, we test the new solution (ants use one more path):
  -> While the solution is better, we continue searching for one more path.
  -> When the new solution is not better, we just keep the previous one and stop here.

Example

./lem_in --paths < maps/tricky2

Initialized 1 path:
This solution would take 23 rounds    // 23 rounds using 1 path
#  1: A-B-C-End
Initialized 2 paths:
This solution would take 15 rounds    // 15 rounds using 2 paths (15 < 23, so we keep searching)
#  2: A-B-C-End
#  3: K-4-M-N-O-P-End
Initialized 3 paths:
This solution would take 12 rounds    // 12 rounds using 3 paths (12 < 15, so we keep searching)
#  5: D-E-B-C-End
#  4: A-G-H-I-J-End
#  6: K-4-M-N-O-P-End
Initialized 4 paths:
This solution would take 12 rounds    // 12 using 4 paths so we keep the previous solution (3 paths)

L1-D L2-A L3-K
L1-E L2-G L3-4 L4-D L5-A L6-K
L1-B L2-H L3-M L4-E L5-G L6-4 L7-D L8-A L9-K
L1-C L2-I L3-N L4-B L5-H L6-M L7-E L8-G L9-4 L10-D L11-A L12-K
L1-End L2-J L3-O L4-C L5-I L6-N L7-B L8-H L9-M L10-E L11-G L12-4 L13-D L14-A L15-K
L2-End L3-P L4-End L5-J L6-O L7-C L8-I L9-N L10-B L11-H L12-M L13-E L14-G L15-4 L16-D L17-A
L3-End L5-End L6-P L7-End L8-J L9-O L10-C L11-I L12-N L13-B L14-H L15-M L16-E L17-G L18-D L19-A
L6-End L8-End L9-P L10-End L11-J L12-O L13-C L14-I L15-N L16-B L17-H L18-E L19-G L20-D
L9-End L11-End L12-P L13-End L14-J L15-O L16-C L17-I L18-B L19-H L20-E
L12-End L14-End L15-P L16-End L17-J L18-C L19-I L20-B
L15-End L17-End L18-End L19-J L20-C
L19-End L20-End