Navigation%20Set%20Hierarchy

1
Navigation Set Hierarchy

• Tom Gianos
• Chapter 2.2

2
Mike Dickheiser

• Works (worked?) for Red Storm Entertainment
• Part of Ubisoft
• Developer of Tom Clancy Games like Ghost Recon
  and Rainbow Six
• His work focuses on efficient AI systems for
  games and AI control of highly realistic vehicles

3
Problem With Dynamic Pathfinding

• Dynamic pathfinding acts as CPU hog
• Blocks the development of more exciting AI
  features by wasting CPU cycles
• Solution
• Precompute navigation information

4
Issues with Precomputation

• Levels/maps of games today are massive
• Could contain thousands of nodes
• Precomputed navigation information could take up
  massive amounts of memory
• Solution
• Navigation Set Hierarchy

5
What is Navigation Set Hierarchy?

• A multitier extension of the basic preprocessed
  navigation solution with comparable speed and
  considerably less memory overhead

6
What is the basic precomputed solution?

• Basic component is a lookup table (called a
  transition or solution table) where each entry
  represents the next step between a source node
  and a goal node
• In other words, for every pair of nodes Source
  and Goal, the entry SG represents the node
  that should be visited next

7
A Simple Example
Table Size n2
8
Simple Code

• Void buildBestPath(int source, int goal,
  listltintgt path)
• path.push_back(source)
• while(source ! goal)
• source _transitionTablesourcegoal
• path.push_back(source)

9
Navigation Sets

• Transform the single monolithic navigation map
  into a hierarchy of several smaller sub-maps
  called navigation sets
• Navigation Set
• A self contained collection of nodes that
  requires no links to external nodes in order to
  complete a path from one internal node to another
• A complete precomputed transition table can be
  constructed for each navigation set

10
Interface Nodes and the Interface Navigation Set

• Once the monolithic map is broken up into
  navigation sets a problem that arises is cross
  set navigation
• To solve this, identify all nodes in the
  navigation sets that connect to nodes in other
  navigation sets (Interface Nodes)
• These navigation nodes together create their own
  second level navigation set called an Interface
  Set Transition table and hence the Navigation Set
  Hierarchy

11
Navigation Set Hierarchy Example
Monolithic Map 441 transition table entries
(212), 21 Nodes, 1 Navigation Set
Hierarchical Map 183 transition table entries
(72 72 72 62) Memory overhead reduced 60
12
Constructing the Hierarchy

• Key goals for deconstructing single large
  transition table into navigation sets
• Determining the number of smaller tables to
  create
• Intelligently choosing where to partition to
  minimize number of interface nodes

13
Selecting the Number of Navigation Sets

• Depends on the resources of the project
• In breaking up a monolithic map into n
  equal-sized partitions, reduce data size to 1/n
  of the original size plus the interface set
• Once size of partition is chosen designers can
  control the number of interface nodes and thus
  the size of the interface set
• If the interface nodes are chosen wisely
  navigation sets can become larger and the
  relative cost of the interface sets will become
  smaller

14
Partitioning a 1000-node Map
Partitions Transition Table Entries Interface Nodes Interface Table Entries Total Table Entries
1 10002 1,000,000 0 0 1,000,000
2 25002 500,000 10 100 500,100
5 52002 200,000 25 625 200,625
10 101002 100,000 50 2500 102,500
50 50202 20,000 250 62,500 82,500
15
Selecting the Partition Boundaries

• Keeping the number of interface nodes as low as
  possible is the number one goal for two reasons
• Fewer interface nodes results in a smaller
  interface table size, saving memory
• Fewer interface nodes there are per set the
  faster the pathfinding process will be
• Identify natural choke points in navigation data,
  a small collection of nodes that single-handedly
  connect to larger collection of nodes
• If natural choke points do not present themselves
  then modify the map

16
Choke Point Demo
17
The Complete Pathfinding Solution

• If source and goal nodes are in the same
  navigation set, the process is the same as before
• Inter-set pathfinding requires more work
• 4 step process

18
The 4 Steps

• 1) Determine the best paths leading from the
  source node to the boundary of the source set
  (interface nodes)
• 2) Determine the best path from the source set
  boundary to the goal set boundary
• 3) Determine the best paths from the goal set
  boundary (interface nodes) to the goal node
• 4) create a list of complete paths assembled from
  the first three steps and chose path with the
  least cost

19
Example going from A3 to C7
20
Transition Tables
21
Example Step 1
Source Goal Sub-path Cost
A3 A6 A3, A6 10
A3 A7 A3, A6, A7 20

• Using transition table for set A, find the best
  paths leading from A3 to the boundary set of A
  (A6 and A7).

22
Example Step 2
Source Goal Sub-Path Cost
A6 C3 A6, A7, C3 20
A6 C5 A6, B2, C5 22
A7 C3 A7, C3 10
A7 C5 A7, C3, C5 20

• Using the interface node transition table, find
  the best paths leading from the boundary set of A
  (A6 and A7) to the boundary set of C (C3 and C5)
• In other words, the best path from each interface
  node in one set to each interface node in the
  other set

23
Example Step 3
Source Goal Sub-path Cost
C3 C7 C3, C5, C7 20
C5 C7 C5, C7 10

• Best path from boundary set of C to goal node C7
• Opposite of Step 1

24
Example Step 4
Path Cost
A3, A6, A7, C3, C5, C7 50
A3, A6, B2, C5, C7 42

• Determine all distinct paths that can be
  generated from source to goal by combining
  results of steps 1-3 and choose path with the
  least cost

25
Possible Performance Issues?

• Does 4 step process return us to expensive
  runtime computation we were trying to escape to
  begin with?
• The amount of searching is dependent only on the
  amount of interface nodes in source and goal sets
  only and not the actual number of nodes in the
  navigation sets themselves
• The cost of the inter-set path search does not
  scale up with navigation set size, number or
  complexity

26
Conclusion

• Attempting to give best of both worlds
• Extremely fast pathfinding
• Relatively low memory cost
• Easy to implement since navigation sets and
  tables sit on top of existing underlying data
  structures of nodes and edges
• Allows for more creative use of gained CPU cycles
  not spent on A or other dynamic methods