Elsevier

Information Sciences

Volume 154, Issues 3–4, September 2003, Pages 141-155
Information Sciences

Application of the killer-tree heuristic and the lambda-search method to lines of action

https://doi.org/10.1016/S0020-0255(03)00047-1Get rights and content

Abstract

This paper investigates the application of the the killer-tree heuristic (KTH) and the λ1-search method to the endgame of lines of action. Both techniques are developed to be used in the endgame of shogi. They are incorporated into two depth-first searches: iterative deepening αβ and PDS. λ1-Search, in which the move generation is limited to λ1-moves, shows a poor ability to find winning solutions. When using λ1-sorting, in which λ1-moves are put at the front of the move list, the number of nodes searched is reduced considerably, but the solving ability is diminished because of the inefficiency of the move generation. Using the KTH, the number of nodes searched and the solving time are reduced by 5% in iterative deepening αβ and by 20% in PDS. Consequently, the solving ability has been enhanced.

Introduction

In the studies on shogi endgames, major progress has been made on the mating-search technique using λ1-search [17]. In addition, related to the mating search, a smart technique for reusing the results of previous mating searches was proposed by Tanase [16], which is generalized as the killer-tree heuristic (KTH) [14]. These two search techniques have not yet well been studied in other domains than shogi. This paper explores the possibility of applying these techniques in the domain of lines of action (LOA).

LOA is a two-person connection-based game with perfect information. Since the aim of a player is to connect all his stones, important characteristics of the game are: concentration, centralization, solid formations, connections and (partial) blocking. They are very different from those in chess or shogi. A further noteworthy difference is the complexity: the state-space complexity and game-tree complexity of LOA are much lower than those for shogi or chess [18]. Therefore, in order to develop a strong LOA program, we probably need other methods than for chess or shogi. In the domain of computer shogi, several endgame-search techniques (e.g., PN*-search [15]) and its enhancements have been developed with significant results. In this paper we investigate the research question whether the effectiveness of these search techniques also holds for the endgame search for a connection-based game like LOA.

In Section 2 we will discuss the above-mentioned endgame techniques: lambda-search and the KTH. Then, in Section 3, we will briefly describe the game of LOA and give reasons why this domain is chosen as subject for our research. Section 4 then will describe the set-up of the experiments and will give experimental results and a discussion thereof. Finally, Section 5 will present our main conclusions.

Section snippets

Endgame-search techniques

In this section we describe the two endgame-search techniques investigated in this paper: lambda-search and the KTH.

Endgame search in lines of action

LOA is a connection-based two-player game with perfect information using an 8 × 8 board. It has been invented by Claude Soucie around 1960 [11]. The basic features for developing a program for LOA are detailed in [18], [20].

Experimental results and discussions

In this section we describe the set-up of the experiments and present and discuss all results.

Conclusions

In the present contribution, we have examined two search techniques in the domain of LOA.

The first technique is λ1-search. The use of pure λ1-search appears to be quite ineffective to find a winning sequence, because many solutions contain non-λ1-moves. The λ1-sorting method, in which λ1-moves are sorted in the front of a search, reduces the number of nodes searched roughly by half. However, the solving ability is declined because of the inefficiency of the λ1-move generation. This could be

Acknowledgements

We thank Mark Winands for kindly offering us his LOA test set. We further greatly acknowledge the constructive comments of three anonymous referees on an earlier version of this paper.

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