A Local-Pattern Related Look-Up Table

TL;DR

This paper introduces a Relevance-Zone pattern table (RZT) that enhances game solving in Go by efficiently storing and retrieving exact game values using pattern matching with radix trees, reducing search nodes.

Contribution

The paper presents a novel RZT structure with a heuristic for efficient lookups, improving upon traditional transposition tables in Go game solving.

Findings

RZT reduces search nodes in Go problem solving.

Lookup overhead is minimized to 10% with the heuristic.

Time complexity remains logarithmic with increasing table size.

Abstract

This paper describes a Relevance-Zone pattern table (RZT) that can be used to replace a traditional transposition table. An RZT stores exact game values for patterns that are discovered during a Relevance-Zone-Based Search (RZS), which is the current state-of-the-art in solving L&D problems in Go. Positions that share the same pattern can reuse the same exact game value in the RZT. The pattern matching scheme for RZTs is implemented using a radix tree, taking into consideration patterns with different shapes. To improve the efficiency of table lookups, we designed a heuristic that prevents redundant lookups. The heuristic can safely skip previously queried patterns for a given position, reducing the overhead to 10% of the original cost. We also analyze the time complexity of the RZT both theoretically and empirically. Experiments show the overhead of traversing the radix tree in practice during lookup remain flat logarithmically in relation to the number of entries stored in the table. Experiments also show that the use of an RZT instead of a traditional transposition table significantly reduces the number of searched nodes on two data sets of 7x7 and 19x19 L&D Go problems.