LibGdx / Box2D - How To Group Tiles Into One Larger Polygon

I am making a tile based top-down 2D RPG and am using Box2D for the physics. Since my game is tile-based, there are many tiles on each map that cannot be moved through. This results in many small individual Box2D bodies. This is obviously very inefficient and makes the game lag. Therefore I figured that combining the individual tiles' bodies into larger complex groups would be better.

The way I thought of doing it is to, first, group together tiles into groups of tiles that all share 2 vertices with at least one other tile in the group. Then, for each group I do the following. First I get all of the uncommon vertices (these should be the ones on the outside of the polygon). Then I connect all of those vertices and then remove all of the overlapping lines. This should result in only lines on the outside of the polygon. Then I sort the lines so that the first line in the sorted array shares its end point with the second line's start point, etc. Then I remove the doubled vertices and using those remaining vertices (I called them the "true vertices") I create the polygon. I know that Box2D only supports convex polygons, but with Box2DSeparator I should be able to do this, but I first want this method to actually work.

/**
* Attempts to combine the given blocks into larger bodies to improve performance.
* @param bs The created wall blocks.
* @param w The world. Used for body creation.
*/
private void makeLargeBodies(Block[][] bs, World w) {
Array<Tile> tiles = new Array<Tile>();
for(int i = 0; i < bs.length; i++) {

[Code] .....

However, this is where the first problem arises. This method is extremely slow for large maps (like 200x200 tiles). I have worked at this for very long and right now my head can't figure out how to make the loop more efficient...

Now for the next part. After that I attempt to create the bodies for the TileGroups:

//create all the groups' bodies
size = groups.size;
System.out.println(size + " groups");
for(int i = 0; i < size; i++) {
TileGroup g = groups.get(i);
System.out.println("Starting group " + i + ".");
long timeCheck = TimeUtils.millis();
g.createBody(w);
System.out.println("Group 0 took " + (TimeUtils.millis() - timeCheck) + " millis");
}

*Note that the printing is for debugging purposes*...

This method is probably not a problem; it is what is inside createBody(World) that is the issue...

public void createBody(World w) {
Array<Vector2> allVertices = new Array<Vector2>();
Array<Vector2> uncommonVertices = new Array<Vector2>();
System.out.print("Starting search for uncommon vertices. ");
long timeCheck = TimeUtils.millis();

[Code] .....

Most of the code is self-explanatory (with comments). My current issue is where I connect the uncommon vertices (see the printed statements). This method does not actually finish (I have let it run for several minutes and it does not complete). This is likely due to a large number of vertices (often around 3000 in a 60x60 map), but I cannot figure out how to make the loop more efficient... Because of this early failure I don't know if the rest of the method works, both physically and in theory.

All relevant classes (Tile, TileGroup, Line) are below:

private class Tile {
private Vector2[] vertices;
private TileGroup group;
public Tile(int x, int y) {
vertices = new Vector2[4];

[Code] ....