Alexander Reinefeld

Enhanced iterative-deepening search

Iterative-deepening searches mimic a breadth-first node expansion with a series of depth-first searches that operate with successively extended search horizons. They have been proposed as a simple way to reduce the space complexity of best-first searches like A* from exponential to linear in the search depth. But there is more to iterative-deepening than just a reduction of storage space. As the authors show, the search efficiency can be greatly improved by exploiting previously gained node information. The information management techniques considered here owe much to their counterparts from the domain of two-player games, namely the use of fast-execution memory functions to guide the search. The authors methods not only save node expansions, but are also faster and easier to implement than previous proposals. >

Effective solution of qualitative interval constraint problems

Abstract We present a fast algorithm for solving qualitative interval constraint problems, which returns solutions of random problems in less than half a second on average, with the hardest problem taking only half a minute on a RISC workstation. This is a surprising result considering the problem is NP-complete. The fast solution time is attributed to the extraordinary pruning power of the path-consistency computation, and to the fact that all our randomly generated interval networks of size ⩾ 14 were found to be inconsistent, which is rapidly detected by a path-consistency computation. While inconsistency is relatively easy to prove, our algorithm also solves large consistent networks with 100 edges. We conclude that our algorithm suffices for solving qualitative interval constraint problems in practice. Other conclusions are that path-consistency reduces the solution search to an almost linear selection of atomic labels and that path-consistency is by itself an excellent consistency heuristic for random networks with fewer than 6 or more than 15 nodes.

Low overhead alternatives to SSS

Abstract Of the many minimax algorithms, sss∗ is noteworthy because it usually searches the smallest game trees. Its success can be attributed to the accumulation and use of information acquired while traversing the tree. The main disadvantages of sss∗ are its high storage needs and management costs. This paper describes a class of methods, based on the popular alpha-beta algorithm, that acquire and use information to guide a tree search. They retain a given search direction and yet are as good as sss∗ , even while searching random trees. Further, although some of these new algorithms also require substantial storage, they are more flexible and can be programmed to use only the space available, at the cost of some degradation in performance.

Fast algebraic methods for interval constraint problems

We describe an effective generic method for solving constraint problems, based on Tarski’s relation algebra, using path-consistency as a pruning technique. We investigate the performance of this method on interval constraint problems. Time performance is affected strongly by the path-consistency calculations, which involve the calculation of compositions of relations. We investigate various methods of tuning composition calculations, and also path-consistency computations. Space performance is affected by the branching factor during search. Reducing this branching factor depends on the existence of ‘nice’ subclasses of the constraint domain. Finally, we survey the statistics of consistency properties of interval constraint problems. Problems of up to 500 variables may be solved in expected cubic time. Evidence is presented that the ‘phase transition’ occurs in the range 6 ≤ n.c ≤15, where n is the number of variables, and c is the ratio of non-trivial constraints to possible constraints.

Time-efficient state space search

Abstract We present two time-efficient state space algorithms for searching minimax trees. Because they are based on SSS∗ and Dual∗, both dominate Alpha-Beta on a node count basis. Moreover, one of them is always faster in searching random trees, even when the leaf node evaluation time is negligible. The fast execution time is attributed to the recursive nature of our algorithms and to their efficient data structure (a simple array) for storing the best-first node information. In practical applications with more expensive leaf evaluations we conjecture that the recursive state space search algorithms perform even better and might eventually supersede the popular directional search methods.

A Symbolic Approach to Interval Constraint Problems

We report on a symbolic approach to solving constraint problems, which uses relation algebra. The method gives good results for problems with constraints that are relations on intervals. Problems of up to 500 variables may be solved in expected cubic time. Strong evidence is presented that significant backtracking on random problems occurs only in the range 6 ≤ n.c ≤ 15, for c ≥ 0.5, where n is the number of variables, and c is the ratio of non-trivial constraints to possible constraints in the problem. Space performance of the method is affected by the branching factor during search, and time performance by path-consistency calculations, including the calculation of compositions of relations.

Heuristic Search in One and Two Player Games

With the continuing price performance improvement of small computers there is growing interest in looking again at some of the heuristic techniques developed for problem solving and planning programs to see if they can be enhanced or replaced by more algorithmic methods The application of raw computing power while and anathema to some often provides better answers than is possible by reasoning or analogy Thus brute force techniques form a good basis against which to compare more sophisticated methods designed to mirror the human deductive process One source of extra computing power comes through the use of parallel processing on a multicomputer an so this aspect is also covered here Here we review the development of heuristic algorithms for application in single agent and adversary games We provide a detailed study of iterative deepening A and its many variants and show how e ective various enhancements including the use of refutation lines and a transposition table can be For adversary games a full review of improved versions of the alpha beta algorithm e g Principal Variation Search is provided and various comparisons made to SSS Aspiration Search and Scout The importance of memory functions is also brought out The second half of the paper deals exclusively with parallel methods not only for single agent search but also with a variety of parallelizations for adversary games In the latter case there is an emphasis on the problems that pruning poses in unbalancing the work load and so the paper covers some of the dynamic tree splitting methods that have evolved This survey will be of interest to those concerned with fundamental issues in com puting but should be especially appealing to experimentalists who want to explore the limitations of theoretical models and to extend their utility Hopefully this will lead to the development of new theories for dealing with the search of average trees

State Space Algorithms for Searching Game Trees

Modifying SSS*’s node expansion strategy yields different state space algorithms for searching game trees. The dual node expansion employed by DUAL*, for example, performs most often superior to SSS*. Introducing directional search characteristics to SSS* and DUAL* gives insight in the utility of global node information. As a result, the totally directional αβ search is shown to be just a restricted case of SSS* and D UAL*.