Heuristic estimates in shortest path algorithms

Shortest path problems occupy an important position in Operations Research aswell as in Arti¯cial Intelligence. In this paper we study shortest path algorithms thatexploit heuristic estimates. The well-known algorithms are put into one framework.Besides we present an interesting application of binary numbers in the shortest paththeory.operations research;graph theory;network flows;search problems

Solution trees as a basis for game tree search

A game tree algorithm is an algorithm computing the minimax value of the root of a game tree. Many algorithms use the notion of establishing proofs that this value lies above or below some boundary value. We show that this amounts to the construction of a solution tree. We discuss the role of solution trees and critical trees in the following algorithms: Principal Variation Search, alpha-beta, and SSS-2. A general procedure for the construction of a solution tree, based on alpha-beta and Null-Window-Search, is given. Furthermore two new examples of solution tree-based algorithms are presented, that surpass alpha-beta, i.e., never visit more nodes than alpha-beta, and often less

A general framework for shortest path algorithms

In this paper we present a general framework for shortest path algorithms, including amongst others Dijkstra's algorithm and the A* algorithm. By showing that all algorithms are special cases of one algorithm in which some of the nondeterministic choices are made deterministic, termination and correctness can be proved by proving termination and correctness of the root algorithm. Furthermore, several invariants of the algorithms are derived which improve the insight with respect to the operations of the algorithms

Trends in game tree search

This paper deals with algorithms searching trees generated by two-person, zero-sum games with perfect information. The standard algorithm in this field is alpha-beta. We will discuss this algorithm as well as extensions, like transposition tables, iterative deepening and NegaScout. Special attention is devoted to domain knowledge pertaining to game trees, more specifically to solution trees. The above mentioned algorithms implement depth first search. The alternative is best first search. The best known algorithm in this area is Stockman's SSS*. We treat a variant equivalent to SSS* called SSS-2. These algorithms are provably better than alpha-beta, but it needs a lot of tweaking to show this in practice. A variant of SSS-2, cast in alpha-beta terms, will be discussed which does realize this potential. This algorithm is however still worse than NegaScout. On the other hand, applying a similar idea as the one behind NegaScout to this last SSS version yields the best (sequential) game tree searcher known up till now: MTD(f)

Searching informed game trees

Well-known algorithms for the evaluation of the minimax function in game trees are alpha-beta and SSS*. An improved version of SSS* is SSS-2. All these algorithms don't use any heuristic information on the game tree. In this paper the use of heuristic information is introduced into the alpha-beta and the SSS-2 algorithm. Extended versions of these algorithms are presented. The subset of nodes which is visited during execution of each algorithm is characterised completely