computing Computing is any goal-oriented activity requiring, benefiting from, or creating computer, computing machinery. It includes the study and experimentation of algorithmic processes, and the development of both computer hardware, hardware and softw ...

, tree data structures, and

game theory Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed ...

, the branching factor is the number of

children A child () is a human being between the stages of childbirth, birth and puberty, or between the Development of the human body, developmental period of infancy and puberty. The term may also refer to an unborn human being. In English-speaking ...

at each

node In general, a node is a localized swelling (a "knot") or a point of intersection (a vertex). Node may refer to: In mathematics * Vertex (graph theory), a vertex in a mathematical graph *Vertex (geometry), a point where two or more curves, lines ...

, the outdegree. If this value is not uniform, an ''average branching factor'' can be calculated. For example, in

chess Chess is a board game for two players. It is an abstract strategy game that involves Perfect information, no hidden information and no elements of game of chance, chance. It is played on a square chessboard, board consisting of 64 squares arran ...

, if a "node" is considered to be a legal position, the average branching factor has been said to be about 35, and a statistical analysis of over 2.5 million games revealed an average of 31. This means that, on average, a player has about 31 to 35 legal moves at their disposal at each turn. By comparison, the average branching factor for the game Go is 250. Higher branching factors make algorithms that follow every branch at every node, such as exhaustive brute force searches, computationally more expensive due to the exponentially increasing number of nodes, leading to

combinatorial explosion In mathematics, a combinatorial explosion is the rapid growth of the complexity of a problem due to the way its combinatorics depends on input, constraints and bounds. Combinatorial explosion is sometimes used to justify the intractability of cert ...

. For example, if the branching factor is 10, then there will be 10 nodes one level down from the current position, 10² (or 100) nodes two levels down, 10³ (or 1,000) nodes three levels down, and so on. The higher the branching factor, the faster this "explosion" occurs. The branching factor can be cut down by a pruning algorithm. The average branching factor can be quickly calculated as the number of non-root nodes (the size of the tree, minus one; or the number of edges) divided by the number of non-leaf nodes (the number of nodes with children).

References

{{reflist, refs= {{cite web, title=The Mystery of Go, the Ancient Game That Computers Still Can't Win , url= https://www.wired.com/2014/05/the-world-of-computer-go/ , first=Alan, last= Levinovitz , date= 12 May 2014 , publisher= Wired , quote=The rate at which possible positions increase is directly related to a game’s “branching factor,” or the average number of moves available on any given turn. Chess’s branching factor is 35. Go’s is 250. Games with high branching factors make classic search algorithms like minimax extremely costly. , accessdate= 2014-06-02 Trees (data structures) Analysis of algorithms Combinatorial game theory Computer chess

See also

References