The Greedy Wall Building algorithm Rami Khouri

Ideal definition of Wall Either keeps valuable assets in, or enemies out…mostly keep enemies out Impassable, or slows down opponents in vulnerable positions –Every wall segment has two unique neighbors –Contains an interior protected area –All interior areas are connected through a path

These are not walls Exceptions: Some games will connect blocks on diagonal spaces together, While other games use gates to allow subdivision of inner area. The greedy algorithm is NOT concerned with creating an inner wall.

Greedy Algorithm A plan that takes steps for the best immediate gain…do not plan ahead into the future moves Dijkstra’s Shortest Path is an example of Greedy algorithm that gives optimal results In the case of building a wall, Greedy algorithm does not provide optimal results, but good enough for use.

Basic Premise of Greed… We will try to “push” the walls outward by expanding at the edges Each move is to expand a wall to incorporate one, and only one new space. Moves cannot break the definition of wall as seen earlier – we are always protected

Problem with This Paradigm To push the wall outward, we must have a case for every possible wall configuration. 68 cases if tiles are squares, much more if tiles are hexagonal, more if their octagonal Special cases if the wall is adjacent to a natural barrier. –Thinking of the problem in terms of pushing the wall is complex

Change the paradigm Instead of pushing the walls, expand the inner area Represent the tiles as vertices, and connections between tiles as edges –Now we can have as many edges as we want coming out of a node –We can represent indestructible natural barriers as the absence of an vertex/edge

So how do we apply the algorithm? Keep three lists: –List of all nodes & edges, graph –Closed list: all nodes in the interior space of the wall –Open list: all nodes that are candidates for expansion, in practice this is the perimeter of the enclosed area, i.e. spaces that the wall is occupying Closed Open Graph

List OpenList, ClosedList, Graph WallBuilder (Node Start, Criteria Accept){ While (OpenList != empty && Accept != criteria){ if ( bestChoice.Cost <= affordable){ remove bestChoice() from openList add bestChoice to closedList for each Neighbor of BestChoice(){ if (not in closedList or openList) {add to openList/Build wall on it} }

How to pick the best choice? Pick the move with the highest value and lowest cost. In this case, Value is always 1, so lets worry only about the cost: –Cost of a move is how many wall constructions it would take to seal it from the outside: This is the number of nodes it connects to that are not in the open or closed list Lets call this w(x); for any node x

Demo1 Run Demo1

So now we have Cost(n) = w(n); But now lets extend it to take into account that we want to wall in closer nodes first d(n) = value based on distance, –closer = lower c is a constant higher than max d(n) Cost(n) = c * w(n) + d(n)  what is the effect of this formula in English

Lets extend Cost(n) = 0 if d(n) < minimum distance Cost(n) = infinity > maximum distance Cost(n) = c * w(n) + d(n) Natural barriers have a cost of zero if toughness => walls

Demo2 Run Demo 2

What happens here?

Gates Draw a path to areas of interest (resources or enemy strongholds) On each path place a gate. Gates within a certain distance of each other can be combined

Hierarchy in Strategy Games Division of tasks Maps Message Sending

Demo 3

Without subdivision, movements such as “Human Wave Attacks” are simple: All soldiers: Attack Point (X,Y)” But more complex commands, such as pincer movement, flanking..etc are much harder to implement: Soldier 1 “I am closest to east side, but are there already enough people on that side? Let me ask each soldier and make sure they don’t have too many….etc”

Realistic Solution Army Corps Division Corps Division Brigade Battalion Company Platoon Squad Soldier

Using a realistic solution, we can divide troops into subgroups…troops, squads, platoons…etc. Creating a level of abstraction between the player and individual troops, a concept often used in OOP programming Squad A attack left side Abstracts: soldier move left, then attack from left …… soldier move left, then attack from left

Levels of Hierarchy Unit AI: –Soldier, Tank, Helicopter…etc –Short distance path finding –Report events to Squad –Accept Attack & Move commands Some freedom is given in how to execute move and attack (touched on later)

Element Map: view of unit Unit sees individual elements of the map i.e. soldier will see –A tree –A rock –A destroyed tank –An enemy sniper Soldier know how to select their own targets and engage, and to find strategic locations within a small area when told to attack or support

Squad Interpret commands from higher level (platoon) and send to individual soldiers Set checkpoints for individual soldiers to follow, higher level path finding Maintain reasonable formation, track each unit Receive feedback from units, and move them back up to platoon  move and attack to units. Backup units in need of help

Tile Map: Squad view A Squad can see its own individual troops in detail, but abstracts enemy troop data i.e. enemy attack & Defend Squad abstracts attributes of terrain, i.e. mobility rating, defensive rating, connection to other tiles Defense: 2 Offense:3 Mobility: 4 Cover:5 Defense: 2 Offense:5 Mobility: 7 Cover:2 Defense: 1 Offense:1 Mobility: 10 Cover:0 Defense: 0 Offense:0 Mobility: 10 Cover:1

Platoon Interpret commands from higher level and translate them to squad instructions Platoon movement is handled by setting checkpoints for each squad in a path to destination – let squad handle smaller pathfinding Keep track of squads, interpret messages i.e. squad Strength, encounter enemy, losing fight…etc. Coordinate backup and formation Pass information up to higher levels (Engaging enemy, need backup, need reinforcement…etc)

Tile Map: Platoon view See individual squads of self Abstract enemy values Abstracts attributes of terrain, i.e. mobility rating, defensive rating. Connection to other tiles is most important Basically a continuation of map abstraction from unit to squad, to Platoon Defense: 2 Offense:3 Mobility: 4 Cover:5 Defense: 2 Offense:5 Mobility: 7 Cover:2 Defense: 1 Offense:1 Mobility: 10 Cover:0 Defense: 0 Offense:0 Mobility: 10 Cover:1 Artillery: 14 Speed: 10 Small Arms: 7

Computer Player AI Civilization building –Economics –Technology Building Military Set policy towards neighbors –Offensive/Defensive/Alliance

CPAI map Highest level map. See strength and weakness of enemy See Resources within an area Only pathfinding necessary is “does a path exist”

Interesting Concept! Give commanders of troops personalities! Tactics vary from defensive, aggressive, merciless, highly strategic…etc civilization series, Command & Conquer Generals

Gold:104Offense: 19 Oil:78Defense: 21 Disposition: Friendly Gold:67Offense: 15 Oil:44Defense: 17 Disposition: Hostile Gold:104Offense: 19 Oil:78Defense: 21

SQUAD PLATOON Computer PlayerUNITDefend Path Defend Path (middle) Defend Location Ready Enemy spotted All Units AttackEngaging enemy Back up squad engage Engaging enemy Hold Platoon formation