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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

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The Greedy Wall Building algorithm

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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


Graph

Closed

Open

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


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

Corps

Corps

Division

Division

Division

Brigade

Brigade

Brigade

Battalion

Battalion

Battalion

Company

Company

Company

Platoon

Platoon

Platoon

Squad

Squad

Squad

Soldier

Soldier

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 00001 move left, then attack from left

……

soldier 00008 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: 0

Offense:0

Mobility: 10

Cover:1

Defense: 1

Offense:1

Mobility: 10

Cover:0


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)


Defense: 2

Offense:3

Mobility: 4

Cover:5

Defense: 2

Offense:5

Mobility: 7

Cover:2

Artillery: 14

Speed: 10

Small Arms: 7

Defense: 0

Offense:0

Mobility: 10

Cover:1

Defense: 1

Offense:1

Mobility: 10

Cover:0

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


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


Computer Player

SQUAD

UNIT

PLATOON

Defend Path

Defend Path (middle)

Defend Location

Ready

Ready

Ready

Enemy spotted

Engaging enemy

Engaging enemy

All Units Attack

Hold Platoon

formation

Back up squad

engage


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