Assigning Rated Items to Locations in non-list Display Layouts

One of the most common ways in which results are displayed by an information retrieval system is in the form of a list, in which the most relevant results appear in the first positions. Today's large screens, however, allow one to create more complex displays of results, especially in cases such as image retrieval, in which each unit returned is fairly compact. For these layouts the simple list model is no longer valid, since the relations between the slots in which the results are placed do not form a sequence, that is, the relation among them is no longer that of a total order. In this paper we model these layouts as partial orders and show that a “stalwart display” property (a layout in which items’ relevance is unambiguously conveyed by their display position) can be obtained only in the case of lists. For the other layouts, we define two classes of representation functions: “safe” functions (which display results without adding spurious structure) and “rich” functions (which do not drop any structure from the result set), as well as an algorithm to optimally display fully ordered result sets in arbitrary display layouts.