Treemaps for Search-Tree Visualization

Large Alpha-Beta search trees generated by game-playing programs are hard to represent graphically. This paper describes how treemaps can be applied to the visualization of these trees. The principle of treemaps is presented, and difficulties of its application to the particular structure of search trees are reviewed. An original “ordered squarified” layout is proposed. It has been implemented in a freely available program, that can be easily re-used by computer-chess programmers. Introduction Many game-playing programs are based on the alpha-beta algorithm [5] and can explore huge search trees in a few seconds. Being able to visualize these large trees could be of a great help to tune search algorithms. Unfortunately, they may have millions of nodes (up to 200 million nodes per second for Deep Blue [3]), and traditional node-and-link diagrams do not allow to represent them conveniently. Treemaps, developed by Shneiderman and Johnson [6, 4], are particularly well adapted to this problem. They are extremely efficient to represent extensive attributes (size, cost, value) of elements organized in a hierarchy. Their first application was the visualization of disk usage in a large directory structure. This paper shows how the visualization of search trees can also take advantage of treemaps properties. The first section of this paper presents the general basic principle of treemap visualization. The second part deals with aspects of this problem that are specific to alphabeta trees. In particular, obtaining a good aspect ratio for rectangles while keeping move-ordering information is a key issue. An “ordered squarified” layout is proposed to solve this problem. 1 Principle Figure 1 illustrates the principle of treemaps. The whole tree is represented as a rectangle. Each sub-tree is represented as a sub-rectangle of its parent rectangle. At the first level of the hierarchy, the whole rectangle is split vertically. Then, sub-rectangles are split horizontally. Sub-sub-rectangles are split vertically, and so on. Each splitting is done so that the area covered by a rectangle is proportional to the number of nodes it contains.