Back

ⓘ Search game




Search game
                                     

ⓘ Search game

A search game is a two-person zero-sum game which takes place in a set called the search space. The searcher can choose any continuous trajectory subject to a maximal velocity constraint. It is always assumed that neither the searcher nor the hider has any knowledge about the movement of the other player until their distance apart is less than or equal to the discovery radius and at this very moment capture occurs. As mathematical models, search games can be applied to areas such as hide-and-seek games that children play or representations of some tactical military situations. The area of search games was introduced in the last chapter of Rufus Isaacs classic book "Differential Games" and has been developed further by Shmuel Gal and Steve Alpern. The princess and monster game deals with a moving target.

                                     

1. Strategy

A natural strategy to search for a stationary target in a graph is to find a minimal closed curve L that covers all the arcs of the graph. L is called a Chinese postman tour. Then, traverse L with probability 1/2 for each direction. This strategy seems to work well if the graph is Eulerian. In general, this random Chinese postman tour is indeed an optimal search strategy if and only if the graph consists of a set of Eulerian graphs connected in a tree-like structure. A misleadingly simple example of a graph not in this family consists of two nodes connected by three arcs. The random Chinese postman tour equivalent to traversing the three arcs in a random order is not optimal, and the optimal way to search these three arcs is complicated.

                                     

2. Unbounded domains

In general, the reasonable framework for searching an unbounded domain, as in the case of an online algorithm, is to use a normalized cost function called the competitive ratio in Computer Science literature. The minimax trajectory for problems of these types is always a geometric sequence or exponential function for continuous problems. This result yields an easy method to find the minimax trajectory by minimizing over a single parameter the generator of this sequence instead of searching over the whole trajectory space. This tool has been used for the linear search problem, i.e., finding a target on the infinite line, which has attracted much attention over several decades and has been analyzed as a search game. It has also been used to find a minimax trajectory for searching a set of concurrent rays. Optimal searching in the plane is performed by using exponential spirals. Searching a set of concurrent rays was later re-discovered in Computer Science literature as the cow-path problem.

                                     
  • in a game is to search the game tree using any of numerous tree search algorithms, combined with minimax - like rules to prune the tree. The game tree for
  • In computer science, a search algorithm is any algorithm which solves the search problem, namely, to retrieve information stored within some data structure
  • web search engine or Internet search engine is a software system that is designed to carry out web search Internet search which means to search the
  • different kinds of searches including image search video search academic search news search and industry - specific vertical search engines. Optimizing
  • 41 Squadron RAF Search Destroy: Tactical Combat Vietnam 1965 - 1966, a 1975 board wargame Seek and Destroy 1996 video game a game developed by Safari
  • In computer science, binary search also known as half - interval search logarithmic search or binary chop, is a search algorithm that finds the position
  • The Great Waldo Search is a video game released in 1992. It is based on the third Waldo book, which was originally released under the same name in North
  • E.V.O.: Search for Eden is a side - scrolling action video game developed by Almanic Corporation and published by Enix for the Super Nintendo Entertainment
  • web search engine owned and operated by Microsoft. The service has its origins in Microsoft s previous search engines: MSN Search Windows Live Search and
  • In computer science, brute - force search or exhaustive search also known as generate and test, is a very general problem - solving technique and algorithmic
  • Monte Carlo tree search MCTS is a heuristic search algorithm for some kinds of decision processes, most notably those employed in game play. MCTS was
  • George of the Jungle and the Search for the Secret George of the Jungle in PAL regions is a platform video game based on the animated television program