Fig. 1. (a) Line display for Example 1. (b) Letter display for Example 2. (c) Letter display for Example 1. Treatments connected by a common line (a) or having a common letter (b, c) are not significantly different.

Fig. 2. Equivalence of CLD-C and CLIQUE COVER: consider the CLD-C instance with n=5 and H={{1,5},{2,3},{2,5},{3,5}}. This instance can be translated into the graph G=(V,E) with V={1,2,3,4,5} and E={{1,2},{1,3},{1,4},{2,4},{3,4},{4,5}}, shown in (a): treatments correspond to vertices in the graph, and two vertices i and j are connected iff {i,j} is not in H. In (b) we give a letter display for H and in (c) the corresponding clique cover: columns in the letter display correspond to cliques in the graph where the “1”-entries of the column determine the set of vertices in the corresponding clique.

Fig. 3. Comparison of the output quality of the three algorithms. Averaged over 10 random instances.

Fig. 4. Comparison of the runtime of the three algorithms. Averaged over 10 random instances.

Overview on the theoretical characteristics of the three algorithms solving COMPACT LETTER DISPLAY, with respect to their runtime and their guarantees of producing a solution with a minimum number of columns or a minimum number of 1s

Comparison of the performance of the Search-Tree algorithm, the Clique-Growing heuristic, and the Insert–Absorb heuristic on five datasets from real-world statistical analyses. For each dataset and each heuristic we report the number of columns of the computed letter display (cols), the number of 1s (1s), and the runtime in seconds (time)

Overview on the empirical analysis of the three algorithms solving COMPACT LETTER DISPLAY, with respect to their runtime and their performance in producing a solution with a small number of columns or a small number of 1s. We indicate the ranking (first, second, third) of the algorithms with respect to each criterion